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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// nbtheory.cpp - originally written and placed in the public domain by Wei Dai</span></div><div class="line"><a name="l00002"></a><span class="lineno"> 2</span> </div><div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="preprocessor">#include "<a class="code" href="pch_8h.html">pch.h</a>"</span></div><div class="line"><a name="l00004"></a><span class="lineno"> 4</span> </div><div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="preprocessor">#ifndef CRYPTOPP_IMPORTS</span></div><div class="line"><a name="l00006"></a><span class="lineno"> 6</span> </div><div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="preprocessor">#include "<a class="code" href="nbtheory_8h.html">nbtheory.h</a>"</span></div><div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="preprocessor">#include "<a class="code" href="integer_8h.html">integer.h</a>"</span></div><div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="preprocessor">#include "<a class="code" href="modarith_8h.html">modarith.h</a>"</span></div><div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="preprocessor">#include "<a class="code" href="algparam_8h.html">algparam.h</a>"</span></div><div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="preprocessor">#include "<a class="code" href="smartptr_8h.html">smartptr.h</a>"</span></div><div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor">#include "<a class="code" href="misc_8h.html">misc.h</a>"</span></div><div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="preprocessor">#include "<a class="code" href="stdcpp_8h.html">stdcpp.h</a>"</span></div><div class="line"><a name="l00014"></a><span class="lineno"> 14</span> </div><div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="preprocessor">#ifdef _OPENMP</span></div><div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="preprocessor"># include <omp.h></span></div><div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span> </div><div class="line"><a name="l00019"></a><span class="lineno"> 19</span> NAMESPACE_BEGIN(<a class="code" href="namespace_crypto_p_p.html">CryptoPP</a>)</div><div class="line"><a name="l00020"></a><span class="lineno"> 20</span> </div><div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="keyword">const</span> word s_lastSmallPrime = 32719;</div><div class="line"><a name="l00022"></a><span class="lineno"> 22</span> </div><div class="line"><a name="l00023"></a><span class="lineno"><a class="line" href="struct_new_prime_table.html"> 23</a></span> <span class="keyword">struct </span><a class="code" href="struct_new_prime_table.html">NewPrimeTable</a></div><div class="line"><a name="l00024"></a><span class="lineno"> 24</span> {</div><div class="line"><a name="l00025"></a><span class="lineno"> 25</span>  std::vector<word16> * operator()()<span class="keyword"> const</span></div><div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="keyword"> </span>{</div><div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  <span class="keyword">const</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> maxPrimeTableSize = 3511;</div><div class="line"><a name="l00028"></a><span class="lineno"> 28</span> </div><div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  <a class="code" href="classmember__ptr.html">member_ptr<std::vector<word16></a> > pPrimeTable(<span class="keyword">new</span> std::vector<word16>);</div><div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  std::vector<word16> &primeTable = *pPrimeTable;</div><div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  primeTable.reserve(maxPrimeTableSize);</div><div class="line"><a name="l00032"></a><span class="lineno"> 32</span> </div><div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  primeTable.push_back(2);</div><div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> testEntriesEnd = 1;</div><div class="line"><a name="l00035"></a><span class="lineno"> 35</span> </div><div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> p=3; p<=s_lastSmallPrime; p+=2)</div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  {</div><div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> j;</div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  <span class="keywordflow">for</span> (j=1; j<testEntriesEnd; j++)</div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  <span class="keywordflow">if</span> (p%primeTable[j] == 0)</div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  <span class="keywordflow">break</span>;</div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  <span class="keywordflow">if</span> (j == testEntriesEnd)</div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  {</div><div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  primeTable.push_back(word16(p));</div><div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  testEntriesEnd = <a class="code" href="misc_8h.html#ac8391e7d9d613a6c401787d2cdab1f51">UnsignedMin</a>(54U, primeTable.size());</div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  }</div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  }</div><div class="line"><a name="l00048"></a><span class="lineno"> 48</span> </div><div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  <span class="keywordflow">return</span> pPrimeTable.release();</div><div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  }</div><div class="line"><a name="l00051"></a><span class="lineno"> 51</span> };</div><div class="line"><a name="l00052"></a><span class="lineno"> 52</span> </div><div class="line"><a name="l00053"></a><span class="lineno"><a class="line" href="nbtheory_8h.html#aa41f53fa846ea7546d7269b5d5c6a29f"> 53</a></span> <span class="keyword">const</span> word16 * <a class="code" href="nbtheory_8h.html#aa41f53fa846ea7546d7269b5d5c6a29f">GetPrimeTable</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> &size)</div><div class="line"><a name="l00054"></a><span class="lineno"> 54</span> {</div><div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  <span class="keyword">const</span> std::vector<word16> &primeTable = <a class="code" href="class_singleton.html">Singleton<std::vector<word16></a>, <a class="code" href="struct_new_prime_table.html">NewPrimeTable</a>>().Ref();</div><div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  size = (<span class="keywordtype">unsigned</span> int)primeTable.size();</div><div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <span class="keywordflow">return</span> &primeTable[0];</div><div class="line"><a name="l00058"></a><span class="lineno"> 58</span> }</div><div class="line"><a name="l00059"></a><span class="lineno"> 59</span> </div><div class="line"><a name="l00060"></a><span class="lineno"><a class="line" href="nbtheory_8h.html#a7bfb6022241ff5fb96250e366c68d49e"> 60</a></span> <span class="keywordtype">bool</span> <a class="code" href="nbtheory_8h.html#a7bfb6022241ff5fb96250e366c68d49e">IsSmallPrime</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &p)</div><div class="line"><a name="l00061"></a><span class="lineno"> 61</span> {</div><div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> primeTableSize;</div><div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="keyword">const</span> word16 * primeTable = <a class="code" href="nbtheory_8h.html#aa41f53fa846ea7546d7269b5d5c6a29f">GetPrimeTable</a>(primeTableSize);</div><div class="line"><a name="l00064"></a><span class="lineno"> 64</span> </div><div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="keywordflow">if</span> (p.<a class="code" href="class_integer.html#a13ddbfd8e9729932c2a99b0dff530978">IsPositive</a>() && p <= primeTable[primeTableSize-1])</div><div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="keywordflow">return</span> std::binary_search(primeTable, primeTable+primeTableSize, (word16)p.<a class="code" href="class_integer.html#a2e90d8f4c5a13e203b94f9abc24d733f">ConvertToLong</a>());</div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span> }</div><div class="line"><a name="l00070"></a><span class="lineno"> 70</span> </div><div class="line"><a name="l00071"></a><span class="lineno"><a class="line" href="nbtheory_8h.html#aef5a456e724cba394ff8ad788eae777d"> 71</a></span> <span class="keywordtype">bool</span> <a class="code" href="nbtheory_8h.html#aef5a456e724cba394ff8ad788eae777d">TrialDivision</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &p, <span class="keywordtype">unsigned</span> bound)</div><div class="line"><a name="l00072"></a><span class="lineno"> 72</span> {</div><div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> primeTableSize;</div><div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="keyword">const</span> word16 * primeTable = <a class="code" href="nbtheory_8h.html#aa41f53fa846ea7546d7269b5d5c6a29f">GetPrimeTable</a>(primeTableSize);</div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span> </div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <a class="code" href="trap_8h.html#adf3b392588bc94cbeae9f415a78c7b95">CRYPTOPP_ASSERT</a>(primeTable[primeTableSize-1] >= bound);</div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span> </div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i;</div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="keywordflow">for</span> (i = 0; primeTable[i]<bound; i++)</div><div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  <span class="keywordflow">if</span> ((p % primeTable[i]) == 0)</div><div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div><div class="line"><a name="l00082"></a><span class="lineno"> 82</span> </div><div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="keywordflow">if</span> (bound == primeTable[i])</div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <span class="keywordflow">return</span> (p % bound == 0);</div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span> }</div><div class="line"><a name="l00088"></a><span class="lineno"> 88</span> </div><div class="line"><a name="l00089"></a><span class="lineno"><a class="line" href="nbtheory_8h.html#a7d7be62fa8075e10432f49cc08273707"> 89</a></span> <span class="keywordtype">bool</span> <a class="code" href="nbtheory_8h.html#a7d7be62fa8075e10432f49cc08273707">SmallDivisorsTest</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &p)</div><div class="line"><a name="l00090"></a><span class="lineno"> 90</span> {</div><div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> primeTableSize;</div><div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  <span class="keyword">const</span> word16 * primeTable = <a class="code" href="nbtheory_8h.html#aa41f53fa846ea7546d7269b5d5c6a29f">GetPrimeTable</a>(primeTableSize);</div><div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="keywordflow">return</span> !<a class="code" href="nbtheory_8h.html#aef5a456e724cba394ff8ad788eae777d">TrialDivision</a>(p, primeTable[primeTableSize-1]);</div><div class="line"><a name="l00094"></a><span class="lineno"> 94</span> }</div><div class="line"><a name="l00095"></a><span class="lineno"> 95</span> </div><div class="line"><a name="l00096"></a><span class="lineno"><a class="line" href="nbtheory_8h.html#abcaf62227292dc648e6f2f11f2a6e158"> 96</a></span> <span class="keywordtype">bool</span> <a class="code" href="nbtheory_8h.html#abcaf62227292dc648e6f2f11f2a6e158">IsFermatProbablePrime</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &n, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &b)</div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span> {</div><div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="keywordflow">if</span> (n <= 3)</div><div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <span class="keywordflow">return</span> n==2 || n==3;</div><div class="line"><a name="l00100"></a><span class="lineno"> 100</span> </div><div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <a class="code" href="trap_8h.html#adf3b392588bc94cbeae9f415a78c7b95">CRYPTOPP_ASSERT</a>(n>3 && b>1 && b<n-1);</div><div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  <span class="keywordflow">return</span> a_exp_b_mod_c(b, n-1, n)==1;</div><div class="line"><a name="l00103"></a><span class="lineno"> 103</span> }</div><div class="line"><a name="l00104"></a><span class="lineno"> 104</span> </div><div class="line"><a name="l00105"></a><span class="lineno"><a class="line" href="nbtheory_8h.html#a97c6199f98f7c5174373422d1e1c39af"> 105</a></span> <span class="keywordtype">bool</span> <a class="code" href="nbtheory_8h.html#a97c6199f98f7c5174373422d1e1c39af">IsStrongProbablePrime</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &n, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &b)</div><div class="line"><a name="l00106"></a><span class="lineno"> 106</span> {</div><div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  <span class="keywordflow">if</span> (n <= 3)</div><div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <span class="keywordflow">return</span> n==2 || n==3;</div><div class="line"><a name="l00109"></a><span class="lineno"> 109</span> </div><div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <a class="code" href="trap_8h.html#adf3b392588bc94cbeae9f415a78c7b95">CRYPTOPP_ASSERT</a>(n>3 && b>1 && b<n-1);</div><div class="line"><a name="l00111"></a><span class="lineno"> 111</span> </div><div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="keywordflow">if</span> ((n.<a class="code" href="class_integer.html#afedf9af097a3417d8bd3742ec53f9593">IsEven</a>() && n!=2) || <a class="code" href="nbtheory_8h.html#ac1d98aa1d0ed1df97bf0dc194da5169a">GCD</a>(b, n) != 1)</div><div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00114"></a><span class="lineno"> 114</span> </div><div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <a class="code" href="class_integer.html">Integer</a> nminus1 = (n-1);</div><div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> a;</div><div class="line"><a name="l00117"></a><span class="lineno"> 117</span> </div><div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  <span class="comment">// calculate a = largest power of 2 that divides (n-1)</span></div><div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <span class="keywordflow">for</span> (a=0; ; a++)</div><div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="keywordflow">if</span> (nminus1.<a class="code" href="class_integer.html#a0e377d23bde55fc7dc6ea2208c587d19">GetBit</a>(a))</div><div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  <span class="keywordflow">break</span>;</div><div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  <a class="code" href="class_integer.html">Integer</a> m = nminus1>>a;</div><div class="line"><a name="l00123"></a><span class="lineno"> 123</span> </div><div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <a class="code" href="class_integer.html">Integer</a> z = a_exp_b_mod_c(b, m, n);</div><div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  <span class="keywordflow">if</span> (z==1 || z==nminus1)</div><div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div><div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> j=1; j<a; j++)</div><div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  {</div><div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  z = z.Squared()%n;</div><div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <span class="keywordflow">if</span> (z==nminus1)</div><div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div><div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <span class="keywordflow">if</span> (z==1)</div><div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  }</div><div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00136"></a><span class="lineno"> 136</span> }</div><div class="line"><a name="l00137"></a><span class="lineno"> 137</span> </div><div class="line"><a name="l00138"></a><span class="lineno"><a class="line" href="nbtheory_8h.html#a637fa2abf1a48bc38f3c0d7c7edd679a"> 138</a></span> <span class="keywordtype">bool</span> <a class="code" href="nbtheory_8h.html#a637fa2abf1a48bc38f3c0d7c7edd679a">RabinMillerTest</a>(<a class="code" href="class_random_number_generator.html">RandomNumberGenerator</a> &rng, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &n, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> rounds)</div><div class="line"><a name="l00139"></a><span class="lineno"> 139</span> {</div><div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  <span class="keywordflow">if</span> (n <= 3)</div><div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  <span class="keywordflow">return</span> n==2 || n==3;</div><div class="line"><a name="l00142"></a><span class="lineno"> 142</span> </div><div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  <a class="code" href="trap_8h.html#adf3b392588bc94cbeae9f415a78c7b95">CRYPTOPP_ASSERT</a>(n>3);</div><div class="line"><a name="l00144"></a><span class="lineno"> 144</span> </div><div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  <a class="code" href="class_integer.html">Integer</a> b;</div><div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i<rounds; i++)</div><div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  {</div><div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  b.Randomize(rng, 2, n-2);</div><div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  <span class="keywordflow">if</span> (!<a class="code" href="nbtheory_8h.html#a97c6199f98f7c5174373422d1e1c39af">IsStrongProbablePrime</a>(n, b))</div><div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  }</div><div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div><div class="line"><a name="l00153"></a><span class="lineno"> 153</span> }</div><div class="line"><a name="l00154"></a><span class="lineno"> 154</span> </div><div class="line"><a name="l00155"></a><span class="lineno"><a class="line" href="nbtheory_8h.html#aada479f79cb8988f4df16df1e321fc7b"> 155</a></span> <span class="keywordtype">bool</span> <a class="code" href="nbtheory_8h.html#aada479f79cb8988f4df16df1e321fc7b">IsLucasProbablePrime</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &n)</div><div class="line"><a name="l00156"></a><span class="lineno"> 156</span> {</div><div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  <span class="keywordflow">if</span> (n <= 1)</div><div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00159"></a><span class="lineno"> 159</span> </div><div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  <span class="keywordflow">if</span> (n.<a class="code" href="class_integer.html#afedf9af097a3417d8bd3742ec53f9593">IsEven</a>())</div><div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  <span class="keywordflow">return</span> n==2;</div><div class="line"><a name="l00162"></a><span class="lineno"> 162</span> </div><div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  <a class="code" href="trap_8h.html#adf3b392588bc94cbeae9f415a78c7b95">CRYPTOPP_ASSERT</a>(n>2);</div><div class="line"><a name="l00164"></a><span class="lineno"> 164</span> </div><div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  <a class="code" href="class_integer.html">Integer</a> b=3;</div><div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0;</div><div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  <span class="keywordtype">int</span> j;</div><div class="line"><a name="l00168"></a><span class="lineno"> 168</span> </div><div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  <span class="keywordflow">while</span> ((j=<a class="code" href="nbtheory_8h.html#abffe3c03543252f53fcf59fdb2df765c">Jacobi</a>(b.Squared()-4, n)) == 1)</div><div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  {</div><div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  <span class="keywordflow">if</span> (++i==64 && n.<a class="code" href="class_integer.html#a3acfdfd7aa905d2600073449c31eb3c4">IsSquare</a>()) <span class="comment">// avoid infinite loop if n is a square</span></div><div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  ++b; ++b;</div><div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  }</div><div class="line"><a name="l00175"></a><span class="lineno"> 175</span> </div><div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  <span class="keywordflow">if</span> (j==0)</div><div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  <span class="keywordflow">return</span> <a class="code" href="nbtheory_8h.html#a6f8b2f16d9cb4cdc4bfa5a785928044a">Lucas</a>(n+1, b, n)==2;</div><div class="line"><a name="l00180"></a><span class="lineno"> 180</span> }</div><div class="line"><a name="l00181"></a><span class="lineno"> 181</span> </div><div class="line"><a name="l00182"></a><span class="lineno"><a class="line" href="nbtheory_8h.html#a9167952dad6998d1b854dee8355b53a0"> 182</a></span> <span class="keywordtype">bool</span> <a class="code" href="nbtheory_8h.html#a9167952dad6998d1b854dee8355b53a0">IsStrongLucasProbablePrime</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &n)</div><div class="line"><a name="l00183"></a><span class="lineno"> 183</span> {</div><div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  <span class="keywordflow">if</span> (n <= 1)</div><div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00186"></a><span class="lineno"> 186</span> </div><div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  <span class="keywordflow">if</span> (n.<a class="code" href="class_integer.html#afedf9af097a3417d8bd3742ec53f9593">IsEven</a>())</div><div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  <span class="keywordflow">return</span> n==2;</div><div class="line"><a name="l00189"></a><span class="lineno"> 189</span> </div><div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  <a class="code" href="trap_8h.html#adf3b392588bc94cbeae9f415a78c7b95">CRYPTOPP_ASSERT</a>(n>2);</div><div class="line"><a name="l00191"></a><span class="lineno"> 191</span> </div><div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  <a class="code" href="class_integer.html">Integer</a> b=3;</div><div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0;</div><div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  <span class="keywordtype">int</span> j;</div><div class="line"><a name="l00195"></a><span class="lineno"> 195</span> </div><div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  <span class="keywordflow">while</span> ((j=<a class="code" href="nbtheory_8h.html#abffe3c03543252f53fcf59fdb2df765c">Jacobi</a>(b.Squared()-4, n)) == 1)</div><div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  {</div><div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  <span class="keywordflow">if</span> (++i==64 && n.<a class="code" href="class_integer.html#a3acfdfd7aa905d2600073449c31eb3c4">IsSquare</a>()) <span class="comment">// avoid infinite loop if n is a square</span></div><div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  ++b; ++b;</div><div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  }</div><div class="line"><a name="l00202"></a><span class="lineno"> 202</span> </div><div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  <span class="keywordflow">if</span> (j==0)</div><div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00205"></a><span class="lineno"> 205</span> </div><div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  <a class="code" href="class_integer.html">Integer</a> n1 = n+1;</div><div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> a;</div><div class="line"><a name="l00208"></a><span class="lineno"> 208</span> </div><div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  <span class="comment">// calculate a = largest power of 2 that divides n1</span></div><div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  <span class="keywordflow">for</span> (a=0; ; a++)</div><div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  <span class="keywordflow">if</span> (n1.<a class="code" href="class_integer.html#a0e377d23bde55fc7dc6ea2208c587d19">GetBit</a>(a))</div><div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  <span class="keywordflow">break</span>;</div><div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  <a class="code" href="class_integer.html">Integer</a> m = n1>>a;</div><div class="line"><a name="l00214"></a><span class="lineno"> 214</span> </div><div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  <a class="code" href="class_integer.html">Integer</a> z = <a class="code" href="nbtheory_8h.html#a6f8b2f16d9cb4cdc4bfa5a785928044a">Lucas</a>(m, b, n);</div><div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  <span class="keywordflow">if</span> (z==2 || z==n-2)</div><div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div><div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  <span class="keywordflow">for</span> (i=1; i<a; i++)</div><div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  {</div><div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  z = (z.Squared()-2)%n;</div><div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  <span class="keywordflow">if</span> (z==n-2)</div><div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div><div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  <span class="keywordflow">if</span> (z==2)</div><div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  }</div><div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00227"></a><span class="lineno"> 227</span> }</div><div class="line"><a name="l00228"></a><span class="lineno"> 228</span> </div><div class="line"><a name="l00229"></a><span class="lineno"><a class="line" href="struct_new_last_small_prime_squared.html"> 229</a></span> <span class="keyword">struct </span><a class="code" href="struct_new_last_small_prime_squared.html">NewLastSmallPrimeSquared</a></div><div class="line"><a name="l00230"></a><span class="lineno"> 230</span> {</div><div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  <a class="code" href="class_integer.html">Integer</a> * operator()()<span class="keyword"> const</span></div><div class="line"><a name="l00232"></a><span class="lineno"> 232</span> <span class="keyword"> </span>{</div><div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  <span class="keywordflow">return</span> <span class="keyword">new</span> <a class="code" href="class_integer.html">Integer</a>(<a class="code" href="class_integer.html">Integer</a>(s_lastSmallPrime).Squared());</div><div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  }</div><div class="line"><a name="l00235"></a><span class="lineno"> 235</span> };</div><div class="line"><a name="l00236"></a><span class="lineno"> 236</span> </div><div class="line"><a name="l00237"></a><span class="lineno"><a class="line" href="nbtheory_8h.html#ae8442dd787d99d3604436a91799552bf"> 237</a></span> <span class="keywordtype">bool</span> <a class="code" href="nbtheory_8h.html#ae8442dd787d99d3604436a91799552bf">IsPrime</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &p)</div><div class="line"><a name="l00238"></a><span class="lineno"> 238</span> {</div><div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  <span class="keywordflow">if</span> (p <= s_lastSmallPrime)</div><div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  <span class="keywordflow">return</span> <a class="code" href="nbtheory_8h.html#a7bfb6022241ff5fb96250e366c68d49e">IsSmallPrime</a>(p);</div><div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (p <= <a class="code" href="class_singleton.html">Singleton<Integer, NewLastSmallPrimeSquared></a>().Ref())</div><div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  <span class="keywordflow">return</span> <a class="code" href="nbtheory_8h.html#a7d7be62fa8075e10432f49cc08273707">SmallDivisorsTest</a>(p);</div><div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  <span class="keywordflow">return</span> <a class="code" href="nbtheory_8h.html#a7d7be62fa8075e10432f49cc08273707">SmallDivisorsTest</a>(p) && <a class="code" href="nbtheory_8h.html#a97c6199f98f7c5174373422d1e1c39af">IsStrongProbablePrime</a>(p, 3) && <a class="code" href="nbtheory_8h.html#a9167952dad6998d1b854dee8355b53a0">IsStrongLucasProbablePrime</a>(p);</div><div class="line"><a name="l00245"></a><span class="lineno"> 245</span> }</div><div class="line"><a name="l00246"></a><span class="lineno"> 246</span> </div><div class="line"><a name="l00247"></a><span class="lineno"><a class="line" href="nbtheory_8h.html#a633d17045e229eccc3614426df054463"> 247</a></span> <span class="keywordtype">bool</span> <a class="code" href="nbtheory_8h.html#a633d17045e229eccc3614426df054463">VerifyPrime</a>(<a class="code" href="class_random_number_generator.html">RandomNumberGenerator</a> &rng, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &p, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> level)</div><div class="line"><a name="l00248"></a><span class="lineno"> 248</span> {</div><div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  <span class="keywordtype">bool</span> pass = <a class="code" href="nbtheory_8h.html#ae8442dd787d99d3604436a91799552bf">IsPrime</a>(p) && <a class="code" href="nbtheory_8h.html#a637fa2abf1a48bc38f3c0d7c7edd679a">RabinMillerTest</a>(rng, p, 1);</div><div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  <span class="keywordflow">if</span> (level >= 1)</div><div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  pass = pass && <a class="code" href="nbtheory_8h.html#a637fa2abf1a48bc38f3c0d7c7edd679a">RabinMillerTest</a>(rng, p, 10);</div><div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  <span class="keywordflow">return</span> pass;</div><div class="line"><a name="l00253"></a><span class="lineno"> 253</span> }</div><div class="line"><a name="l00254"></a><span class="lineno"> 254</span> </div><div class="line"><a name="l00255"></a><span class="lineno"> 255</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> PrimeSearchInterval(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &max)</div><div class="line"><a name="l00256"></a><span class="lineno"> 256</span> {</div><div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  <span class="keywordflow">return</span> max.<a class="code" href="class_integer.html#a867356d88074424328d0ebb9bea63254">BitCount</a>();</div><div class="line"><a name="l00258"></a><span class="lineno"> 258</span> }</div><div class="line"><a name="l00259"></a><span class="lineno"> 259</span> </div><div class="line"><a name="l00260"></a><span class="lineno"> 260</span> <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> FastProbablePrimeTest(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &n)</div><div class="line"><a name="l00261"></a><span class="lineno"> 261</span> {</div><div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  <span class="keywordflow">return</span> <a class="code" href="nbtheory_8h.html#a97c6199f98f7c5174373422d1e1c39af">IsStrongProbablePrime</a>(n,2);</div><div class="line"><a name="l00263"></a><span class="lineno"> 263</span> }</div><div class="line"><a name="l00264"></a><span class="lineno"> 264</span> </div><div class="line"><a name="l00265"></a><span class="lineno"> 265</span> <a class="code" href="class_algorithm_parameters.html">AlgorithmParameters</a> MakeParametersForTwoPrimesOfEqualSize(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> productBitLength)</div><div class="line"><a name="l00266"></a><span class="lineno"> 266</span> {</div><div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  <span class="keywordflow">if</span> (productBitLength < 16)</div><div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  <span class="keywordflow">throw</span> <a class="code" href="class_invalid_argument.html">InvalidArgument</a>(<span class="stringliteral">"invalid bit length"</span>);</div><div class="line"><a name="l00269"></a><span class="lineno"> 269</span> </div><div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  <a class="code" href="class_integer.html">Integer</a> minP, maxP;</div><div class="line"><a name="l00271"></a><span class="lineno"> 271</span> </div><div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  <span class="keywordflow">if</span> (productBitLength%2==0)</div><div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  {</div><div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  minP = <a class="code" href="class_integer.html">Integer</a>(182) << (productBitLength/2-8);</div><div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  maxP = <a class="code" href="class_integer.html#ade53248f5dbb520273a70856b975417c">Integer::Power2</a>(productBitLength/2)-1;</div><div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  }</div><div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  {</div><div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  minP = <a class="code" href="class_integer.html#ade53248f5dbb520273a70856b975417c">Integer::Power2</a>((productBitLength-1)/2);</div><div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  maxP = <a class="code" href="class_integer.html">Integer</a>(181) << ((productBitLength+1)/2-8);</div><div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  }</div><div class="line"><a name="l00282"></a><span class="lineno"> 282</span> </div><div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  <span class="keywordflow">return</span> <a class="code" href="algparam_8h.html#aa13eee74de98cf8aaa7e83f4fae7f28b">MakeParameters</a>(<span class="stringliteral">"RandomNumberType"</span>, <a class="code" href="class_integer.html#a9b4088ac01abf76b9ba60060abccb7a3afe686f55e5b6768b20009a12522bd0d9">Integer::PRIME</a>)(<span class="stringliteral">"Min"</span>, minP)(<span class="stringliteral">"Max"</span>, maxP);</div><div class="line"><a name="l00284"></a><span class="lineno"> 284</span> }</div><div class="line"><a name="l00285"></a><span class="lineno"> 285</span> </div><div class="line"><a name="l00286"></a><span class="lineno"><a class="line" href="class_prime_sieve.html"> 286</a></span> <span class="keyword">class </span><a class="code" href="class_prime_sieve.html">PrimeSieve</a></div><div class="line"><a name="l00287"></a><span class="lineno"> 287</span> {</div><div class="line"><a name="l00288"></a><span class="lineno"> 288</span> <span class="keyword">public</span>:</div><div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  <span class="comment">// delta == 1 or -1 means double sieve with p = 2*q + delta</span></div><div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  <a class="code" href="class_prime_sieve.html">PrimeSieve</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &first, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &last, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &step, <span class="keywordtype">signed</span> <span class="keywordtype">int</span> delta=0);</div><div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  <span class="keywordtype">bool</span> NextCandidate(<a class="code" href="class_integer.html">Integer</a> &c);</div><div class="line"><a name="l00292"></a><span class="lineno"> 292</span> </div><div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  <span class="keywordtype">void</span> DoSieve();</div><div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  <span class="keyword">static</span> <span class="keywordtype">void</span> SieveSingle(std::vector<bool> &sieve, word16 p, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &first, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &step, word16 stepInv);</div><div class="line"><a name="l00295"></a><span class="lineno"> 295</span> </div><div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  <a class="code" href="class_integer.html">Integer</a> m_first, m_last, m_step;</div><div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  <span class="keywordtype">signed</span> <span class="keywordtype">int</span> m_delta;</div><div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  word m_next;</div><div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  std::vector<bool> m_sieve;</div><div class="line"><a name="l00300"></a><span class="lineno"> 300</span> };</div><div class="line"><a name="l00301"></a><span class="lineno"> 301</span> </div><div class="line"><a name="l00302"></a><span class="lineno"> 302</span> PrimeSieve::PrimeSieve(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &first, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &last, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &step, <span class="keywordtype">signed</span> <span class="keywordtype">int</span> delta)</div><div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  : m_first(first), m_last(last), m_step(step), m_delta(delta), m_next(0)</div><div class="line"><a name="l00304"></a><span class="lineno"> 304</span> {</div><div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  DoSieve();</div><div class="line"><a name="l00306"></a><span class="lineno"> 306</span> }</div><div class="line"><a name="l00307"></a><span class="lineno"> 307</span> </div><div class="line"><a name="l00308"></a><span class="lineno"> 308</span> <span class="keywordtype">bool</span> PrimeSieve::NextCandidate(<a class="code" href="class_integer.html">Integer</a> &c)</div><div class="line"><a name="l00309"></a><span class="lineno"> 309</span> {</div><div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  <span class="keywordtype">bool</span> safe = <a class="code" href="misc_8h.html#a8a2ce94589bb74164d809f4675bd23dd">SafeConvert</a>(std::find(m_sieve.begin()+m_next, m_sieve.end(), <span class="keyword">false</span>) - m_sieve.begin(), m_next);</div><div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  CRYPTOPP_UNUSED(safe); <a class="code" href="trap_8h.html#adf3b392588bc94cbeae9f415a78c7b95">CRYPTOPP_ASSERT</a>(safe);</div><div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  <span class="keywordflow">if</span> (m_next == m_sieve.size())</div><div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  {</div><div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  m_first += long(m_sieve.size())*m_step;</div><div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  <span class="keywordflow">if</span> (m_first > m_last)</div><div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  {</div><div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  m_next = 0;</div><div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  DoSieve();</div><div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  <span class="keywordflow">return</span> NextCandidate(c);</div><div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  }</div><div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  }</div><div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  {</div><div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  c = m_first + long(m_next)*m_step;</div><div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  ++m_next;</div><div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div><div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  }</div><div class="line"><a name="l00330"></a><span class="lineno"> 330</span> }</div><div class="line"><a name="l00331"></a><span class="lineno"> 331</span> </div><div class="line"><a name="l00332"></a><span class="lineno"> 332</span> <span class="keywordtype">void</span> PrimeSieve::SieveSingle(std::vector<bool> &sieve, word16 p, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &first, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &step, word16 stepInv)</div><div class="line"><a name="l00333"></a><span class="lineno"> 333</span> {</div><div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  <span class="keywordflow">if</span> (stepInv)</div><div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  {</div><div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  <span class="keywordtype">size_t</span> sieveSize = sieve.size();</div><div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  <span class="keywordtype">size_t</span> j = (word32(p-(first%p))*stepInv) % p;</div><div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  <span class="comment">// if the first multiple of p is p, skip it</span></div><div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  <span class="keywordflow">if</span> (first.<a class="code" href="class_integer.html#a8c04a3308dd546cac819835922ee8db6">WordCount</a>() <= 1 && first + step*long(j) == p)</div><div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  j += p;</div><div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  <span class="keywordflow">for</span> (; j < sieveSize; j += p)</div><div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  sieve[j] = <span class="keyword">true</span>;</div><div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  }</div><div class="line"><a name="l00344"></a><span class="lineno"> 344</span> }</div><div class="line"><a name="l00345"></a><span class="lineno"> 345</span> </div><div class="line"><a name="l00346"></a><span class="lineno"> 346</span> <span class="keywordtype">void</span> PrimeSieve::DoSieve()</div><div class="line"><a name="l00347"></a><span class="lineno"> 347</span> {</div><div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> primeTableSize;</div><div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  <span class="keyword">const</span> word16 * primeTable = <a class="code" href="nbtheory_8h.html#aa41f53fa846ea7546d7269b5d5c6a29f">GetPrimeTable</a>(primeTableSize);</div><div class="line"><a name="l00350"></a><span class="lineno"> 350</span> </div><div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  <span class="keyword">const</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> maxSieveSize = 32768;</div><div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> sieveSize = <a class="code" href="misc_8h.html#abe412b0409249cb54899e97bc7d86424">STDMIN</a>(<a class="code" href="class_integer.html">Integer</a>(maxSieveSize), (m_last-m_first)/m_step+1).ConvertToLong();</div><div class="line"><a name="l00353"></a><span class="lineno"> 353</span> </div><div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  m_sieve.clear();</div><div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  m_sieve.resize(sieveSize, <span class="keyword">false</span>);</div><div class="line"><a name="l00356"></a><span class="lineno"> 356</span> </div><div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  <span class="keywordflow">if</span> (m_delta == 0)</div><div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  {</div><div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i = 0; i < primeTableSize; ++i)</div><div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  SieveSingle(m_sieve, primeTable[i], m_first, m_step, (word16)m_step.<a class="code" href="class_integer.html#af805574831ce19221692966e6217e6e0">InverseMod</a>(primeTable[i]));</div><div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  }</div><div class="line"><a name="l00362"></a><span class="lineno"> 362</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  {</div><div class="line"><a name="l00364"></a><span class="lineno"> 364</span>  <a class="code" href="trap_8h.html#adf3b392588bc94cbeae9f415a78c7b95">CRYPTOPP_ASSERT</a>(m_step%2==0);</div><div class="line"><a name="l00365"></a><span class="lineno"> 365</span>  <a class="code" href="class_integer.html">Integer</a> qFirst = (m_first-m_delta) >> 1;</div><div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  <a class="code" href="class_integer.html">Integer</a> halfStep = m_step >> 1;</div><div class="line"><a name="l00367"></a><span class="lineno"> 367</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i = 0; i < primeTableSize; ++i)</div><div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  {</div><div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  word16 p = primeTable[i];</div><div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  word16 stepInv = (word16)m_step.<a class="code" href="class_integer.html#af805574831ce19221692966e6217e6e0">InverseMod</a>(p);</div><div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  SieveSingle(m_sieve, p, m_first, m_step, stepInv);</div><div class="line"><a name="l00372"></a><span class="lineno"> 372</span> </div><div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  word16 halfStepInv = 2*stepInv < p ? 2*stepInv : 2*stepInv-p;</div><div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  SieveSingle(m_sieve, p, qFirst, halfStep, halfStepInv);</div><div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  }</div><div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  }</div><div class="line"><a name="l00377"></a><span class="lineno"> 377</span> }</div><div class="line"><a name="l00378"></a><span class="lineno"> 378</span> </div><div class="line"><a name="l00379"></a><span class="lineno"><a class="line" href="nbtheory_8h.html#aaef9ef9567713cd9935e468309ebcc9d"> 379</a></span> <span class="keywordtype">bool</span> <a class="code" href="nbtheory_8h.html#aaef9ef9567713cd9935e468309ebcc9d">FirstPrime</a>(<a class="code" href="class_integer.html">Integer</a> &p, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &max, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &equiv, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &mod, <span class="keyword">const</span> <a class="code" href="class_prime_selector.html">PrimeSelector</a> *pSelector)</div><div class="line"><a name="l00380"></a><span class="lineno"> 380</span> {</div><div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  <a class="code" href="trap_8h.html#adf3b392588bc94cbeae9f415a78c7b95">CRYPTOPP_ASSERT</a>(!equiv.<a class="code" href="class_integer.html#ad767ae81c89be3804da8785e132d2d1f">IsNegative</a>() && equiv < mod);</div><div class="line"><a name="l00382"></a><span class="lineno"> 382</span> </div><div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  <a class="code" href="class_integer.html">Integer</a> gcd = <a class="code" href="nbtheory_8h.html#ac1d98aa1d0ed1df97bf0dc194da5169a">GCD</a>(equiv, mod);</div><div class="line"><a name="l00384"></a><span class="lineno"> 384</span>  <span class="keywordflow">if</span> (gcd != <a class="code" href="class_integer.html#a8c070592581bf6c2f928c72bfa1c1638">Integer::One</a>())</div><div class="line"><a name="l00385"></a><span class="lineno"> 385</span>  {</div><div class="line"><a name="l00386"></a><span class="lineno"> 386</span>  <span class="comment">// the only possible prime p such that p%mod==equiv where GCD(mod,equiv)!=1 is GCD(mod,equiv)</span></div><div class="line"><a name="l00387"></a><span class="lineno"> 387</span>  <span class="keywordflow">if</span> (p <= gcd && gcd <= max && <a class="code" href="nbtheory_8h.html#ae8442dd787d99d3604436a91799552bf">IsPrime</a>(gcd) && (!pSelector || pSelector->IsAcceptable(gcd)))</div><div class="line"><a name="l00388"></a><span class="lineno"> 388</span>  {</div><div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  p = gcd;</div><div class="line"><a name="l00390"></a><span class="lineno"> 390</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div><div class="line"><a name="l00391"></a><span class="lineno"> 391</span>  }</div><div class="line"><a name="l00392"></a><span class="lineno"> 392</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  }</div><div class="line"><a name="l00395"></a><span class="lineno"> 395</span> </div><div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> primeTableSize;</div><div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  <span class="keyword">const</span> word16 * primeTable = <a class="code" href="nbtheory_8h.html#aa41f53fa846ea7546d7269b5d5c6a29f">GetPrimeTable</a>(primeTableSize);</div><div class="line"><a name="l00398"></a><span class="lineno"> 398</span> </div><div class="line"><a name="l00399"></a><span class="lineno"> 399</span>  <span class="keywordflow">if</span> (p <= primeTable[primeTableSize-1])</div><div class="line"><a name="l00400"></a><span class="lineno"> 400</span>  {</div><div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  <span class="keyword">const</span> word16 *pItr;</div><div class="line"><a name="l00402"></a><span class="lineno"> 402</span> </div><div class="line"><a name="l00403"></a><span class="lineno"> 403</span>  --p;</div><div class="line"><a name="l00404"></a><span class="lineno"> 404</span>  <span class="keywordflow">if</span> (p.<a class="code" href="class_integer.html#a13ddbfd8e9729932c2a99b0dff530978">IsPositive</a>())</div><div class="line"><a name="l00405"></a><span class="lineno"> 405</span>  pItr = std::upper_bound(primeTable, primeTable+primeTableSize, (word)p.<a class="code" href="class_integer.html#a2e90d8f4c5a13e203b94f9abc24d733f">ConvertToLong</a>());</div><div class="line"><a name="l00406"></a><span class="lineno"> 406</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l00407"></a><span class="lineno"> 407</span>  pItr = primeTable;</div><div class="line"><a name="l00408"></a><span class="lineno"> 408</span> </div><div class="line"><a name="l00409"></a><span class="lineno"> 409</span>  <span class="keywordflow">while</span> (pItr < primeTable+primeTableSize && !(*pItr%mod == equiv && (!pSelector || pSelector->IsAcceptable(*pItr))))</div><div class="line"><a name="l00410"></a><span class="lineno"> 410</span>  ++pItr;</div><div class="line"><a name="l00411"></a><span class="lineno"> 411</span> </div><div class="line"><a name="l00412"></a><span class="lineno"> 412</span>  <span class="keywordflow">if</span> (pItr < primeTable+primeTableSize)</div><div class="line"><a name="l00413"></a><span class="lineno"> 413</span>  {</div><div class="line"><a name="l00414"></a><span class="lineno"> 414</span>  p = *pItr;</div><div class="line"><a name="l00415"></a><span class="lineno"> 415</span>  <span class="keywordflow">return</span> p <= max;</div><div class="line"><a name="l00416"></a><span class="lineno"> 416</span>  }</div><div class="line"><a name="l00417"></a><span class="lineno"> 417</span> </div><div class="line"><a name="l00418"></a><span class="lineno"> 418</span>  p = primeTable[primeTableSize-1]+1;</div><div class="line"><a name="l00419"></a><span class="lineno"> 419</span>  }</div><div class="line"><a name="l00420"></a><span class="lineno"> 420</span> </div><div class="line"><a name="l00421"></a><span class="lineno"> 421</span>  <a class="code" href="trap_8h.html#adf3b392588bc94cbeae9f415a78c7b95">CRYPTOPP_ASSERT</a>(p > primeTable[primeTableSize-1]);</div><div class="line"><a name="l00422"></a><span class="lineno"> 422</span> </div><div class="line"><a name="l00423"></a><span class="lineno"> 423</span>  <span class="keywordflow">if</span> (mod.<a class="code" href="class_integer.html#aed4bb7208a18b986ef3e1a7d92e06d1d">IsOdd</a>())</div><div class="line"><a name="l00424"></a><span class="lineno"> 424</span>  <span class="keywordflow">return</span> <a class="code" href="nbtheory_8h.html#aaef9ef9567713cd9935e468309ebcc9d">FirstPrime</a>(p, max, <a class="code" href="nbtheory_8h.html#ab3fae49135264b5b5afecd0331915040">CRT</a>(equiv, mod, 1, 2, 1), mod<<1, pSelector);</div><div class="line"><a name="l00425"></a><span class="lineno"> 425</span> </div><div class="line"><a name="l00426"></a><span class="lineno"> 426</span>  p += (equiv-p)%mod;</div><div class="line"><a name="l00427"></a><span class="lineno"> 427</span> </div><div class="line"><a name="l00428"></a><span class="lineno"> 428</span>  <span class="keywordflow">if</span> (p>max)</div><div class="line"><a name="l00429"></a><span class="lineno"> 429</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00430"></a><span class="lineno"> 430</span> </div><div class="line"><a name="l00431"></a><span class="lineno"> 431</span>  <a class="code" href="class_prime_sieve.html">PrimeSieve</a> sieve(p, max, mod);</div><div class="line"><a name="l00432"></a><span class="lineno"> 432</span> </div><div class="line"><a name="l00433"></a><span class="lineno"> 433</span>  <span class="keywordflow">while</span> (sieve.NextCandidate(p))</div><div class="line"><a name="l00434"></a><span class="lineno"> 434</span>  {</div><div class="line"><a name="l00435"></a><span class="lineno"> 435</span>  <span class="keywordflow">if</span> ((!pSelector || pSelector->IsAcceptable(p)) && FastProbablePrimeTest(p) && <a class="code" href="nbtheory_8h.html#ae8442dd787d99d3604436a91799552bf">IsPrime</a>(p))</div><div class="line"><a name="l00436"></a><span class="lineno"> 436</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div><div class="line"><a name="l00437"></a><span class="lineno"> 437</span>  }</div><div class="line"><a name="l00438"></a><span class="lineno"> 438</span> </div><div class="line"><a name="l00439"></a><span class="lineno"> 439</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00440"></a><span class="lineno"> 440</span> }</div><div class="line"><a name="l00441"></a><span class="lineno"> 441</span> </div><div class="line"><a name="l00442"></a><span class="lineno"> 442</span> <span class="comment">// the following two functions are based on code and comments provided by Preda Mihailescu</span></div><div class="line"><a name="l00443"></a><span class="lineno"> 443</span> <span class="keyword">static</span> <span class="keywordtype">bool</span> ProvePrime(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &p, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &q)</div><div class="line"><a name="l00444"></a><span class="lineno"> 444</span> {</div><div class="line"><a name="l00445"></a><span class="lineno"> 445</span>  <a class="code" href="trap_8h.html#adf3b392588bc94cbeae9f415a78c7b95">CRYPTOPP_ASSERT</a>(p < q*q*q);</div><div class="line"><a name="l00446"></a><span class="lineno"> 446</span>  <a class="code" href="trap_8h.html#adf3b392588bc94cbeae9f415a78c7b95">CRYPTOPP_ASSERT</a>(p % q == 1);</div><div class="line"><a name="l00447"></a><span class="lineno"> 447</span> </div><div class="line"><a name="l00448"></a><span class="lineno"> 448</span> <span class="comment">// this is the Quisquater test. Numbers p having passed the Lucas - Lehmer test</span></div><div class="line"><a name="l00449"></a><span class="lineno"> 449</span> <span class="comment">// for q and verifying p < q^3 can only be built up of two factors, both = 1 mod q,</span></div><div class="line"><a name="l00450"></a><span class="lineno"> 450</span> <span class="comment">// or be prime. The next two lines build the discriminant of a quadratic equation</span></div><div class="line"><a name="l00451"></a><span class="lineno"> 451</span> <span class="comment">// which holds iff p is built up of two factors (exercise ... )</span></div><div class="line"><a name="l00452"></a><span class="lineno"> 452</span> </div><div class="line"><a name="l00453"></a><span class="lineno"> 453</span>  <a class="code" href="class_integer.html">Integer</a> r = (p-1)/q;</div><div class="line"><a name="l00454"></a><span class="lineno"> 454</span>  <span class="keywordflow">if</span> (((r%q).Squared()-4*(r/q)).IsSquare())</div><div class="line"><a name="l00455"></a><span class="lineno"> 455</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00456"></a><span class="lineno"> 456</span> </div><div class="line"><a name="l00457"></a><span class="lineno"> 457</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> primeTableSize;</div><div class="line"><a name="l00458"></a><span class="lineno"> 458</span>  <span class="keyword">const</span> word16 * primeTable = <a class="code" href="nbtheory_8h.html#aa41f53fa846ea7546d7269b5d5c6a29f">GetPrimeTable</a>(primeTableSize);</div><div class="line"><a name="l00459"></a><span class="lineno"> 459</span> </div><div class="line"><a name="l00460"></a><span class="lineno"> 460</span>  <a class="code" href="trap_8h.html#adf3b392588bc94cbeae9f415a78c7b95">CRYPTOPP_ASSERT</a>(primeTableSize >= 50);</div><div class="line"><a name="l00461"></a><span class="lineno"> 461</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i=0; i<50; i++)</div><div class="line"><a name="l00462"></a><span class="lineno"> 462</span>  {</div><div class="line"><a name="l00463"></a><span class="lineno"> 463</span>  <a class="code" href="class_integer.html">Integer</a> b = a_exp_b_mod_c(primeTable[i], r, p);</div><div class="line"><a name="l00464"></a><span class="lineno"> 464</span>  <span class="keywordflow">if</span> (b != 1)</div><div class="line"><a name="l00465"></a><span class="lineno"> 465</span>  <span class="keywordflow">return</span> a_exp_b_mod_c(b, q, p) == 1;</div><div class="line"><a name="l00466"></a><span class="lineno"> 466</span>  }</div><div class="line"><a name="l00467"></a><span class="lineno"> 467</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00468"></a><span class="lineno"> 468</span> }</div><div class="line"><a name="l00469"></a><span class="lineno"> 469</span> </div><div class="line"><a name="l00470"></a><span class="lineno"><a class="line" href="nbtheory_8h.html#a40fab13239e32e04892023c81bb42597"> 470</a></span> <a class="code" href="class_integer.html">Integer</a> <a class="code" href="nbtheory_8h.html#a40fab13239e32e04892023c81bb42597">MihailescuProvablePrime</a>(<a class="code" href="class_random_number_generator.html">RandomNumberGenerator</a> &rng, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> pbits)</div><div class="line"><a name="l00471"></a><span class="lineno"> 471</span> {</div><div class="line"><a name="l00472"></a><span class="lineno"> 472</span>  <a class="code" href="class_integer.html">Integer</a> p;</div><div class="line"><a name="l00473"></a><span class="lineno"> 473</span>  <a class="code" href="class_integer.html">Integer</a> minP = <a class="code" href="class_integer.html#ade53248f5dbb520273a70856b975417c">Integer::Power2</a>(pbits-1);</div><div class="line"><a name="l00474"></a><span class="lineno"> 474</span>  <a class="code" href="class_integer.html">Integer</a> maxP = <a class="code" href="class_integer.html#ade53248f5dbb520273a70856b975417c">Integer::Power2</a>(pbits) - 1;</div><div class="line"><a name="l00475"></a><span class="lineno"> 475</span> </div><div class="line"><a name="l00476"></a><span class="lineno"> 476</span>  <span class="keywordflow">if</span> (maxP <= <a class="code" href="class_integer.html">Integer</a>(s_lastSmallPrime).Squared())</div><div class="line"><a name="l00477"></a><span class="lineno"> 477</span>  {</div><div class="line"><a name="l00478"></a><span class="lineno"> 478</span>  <span class="comment">// Randomize() will generate a prime provable by trial division</span></div><div class="line"><a name="l00479"></a><span class="lineno"> 479</span>  p.<a class="code" href="class_integer.html#a62a8829c926b4e421183e76ea4233702">Randomize</a>(rng, minP, maxP, <a class="code" href="class_integer.html#a9b4088ac01abf76b9ba60060abccb7a3afe686f55e5b6768b20009a12522bd0d9">Integer::PRIME</a>);</div><div class="line"><a name="l00480"></a><span class="lineno"> 480</span>  <span class="keywordflow">return</span> p;</div><div class="line"><a name="l00481"></a><span class="lineno"> 481</span>  }</div><div class="line"><a name="l00482"></a><span class="lineno"> 482</span> </div><div class="line"><a name="l00483"></a><span class="lineno"> 483</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> qbits = (pbits+2)/3 + 1 + rng.<a class="code" href="class_random_number_generator.html#a96a3eec202b6251f5c94136ab7edbde1">GenerateWord32</a>(0, pbits/36);</div><div class="line"><a name="l00484"></a><span class="lineno"> 484</span>  <a class="code" href="class_integer.html">Integer</a> q = <a class="code" href="nbtheory_8h.html#a40fab13239e32e04892023c81bb42597">MihailescuProvablePrime</a>(rng, qbits);</div><div class="line"><a name="l00485"></a><span class="lineno"> 485</span>  <a class="code" href="class_integer.html">Integer</a> q2 = q<<1;</div><div class="line"><a name="l00486"></a><span class="lineno"> 486</span> </div><div class="line"><a name="l00487"></a><span class="lineno"> 487</span>  <span class="keywordflow">while</span> (<span class="keyword">true</span>)</div><div class="line"><a name="l00488"></a><span class="lineno"> 488</span>  {</div><div class="line"><a name="l00489"></a><span class="lineno"> 489</span>  <span class="comment">// this initializes the sieve to search in the arithmetic</span></div><div class="line"><a name="l00490"></a><span class="lineno"> 490</span>  <span class="comment">// progression p = p_0 + \lambda * q2 = p_0 + 2 * \lambda * q,</span></div><div class="line"><a name="l00491"></a><span class="lineno"> 491</span>  <span class="comment">// with q the recursively generated prime above. We will be able</span></div><div class="line"><a name="l00492"></a><span class="lineno"> 492</span>  <span class="comment">// to use Lucas tets for proving primality. A trick of Quisquater</span></div><div class="line"><a name="l00493"></a><span class="lineno"> 493</span>  <span class="comment">// allows taking q > cubic_root(p) rather then square_root: this</span></div><div class="line"><a name="l00494"></a><span class="lineno"> 494</span>  <span class="comment">// decreases the recursion.</span></div><div class="line"><a name="l00495"></a><span class="lineno"> 495</span> </div><div class="line"><a name="l00496"></a><span class="lineno"> 496</span>  p.<a class="code" href="class_integer.html#a62a8829c926b4e421183e76ea4233702">Randomize</a>(rng, minP, maxP, <a class="code" href="class_integer.html#a9b4088ac01abf76b9ba60060abccb7a3ad9b396a7ba736a4ca02db0125cc8c6a4">Integer::ANY</a>, 1, q2);</div><div class="line"><a name="l00497"></a><span class="lineno"> 497</span>  <a class="code" href="class_prime_sieve.html">PrimeSieve</a> sieve(p, <a class="code" href="misc_8h.html#abe412b0409249cb54899e97bc7d86424">STDMIN</a>(p+PrimeSearchInterval(maxP)*q2, maxP), q2);</div><div class="line"><a name="l00498"></a><span class="lineno"> 498</span> </div><div class="line"><a name="l00499"></a><span class="lineno"> 499</span>  <span class="keywordflow">while</span> (sieve.NextCandidate(p))</div><div class="line"><a name="l00500"></a><span class="lineno"> 500</span>  {</div><div class="line"><a name="l00501"></a><span class="lineno"> 501</span>  <span class="keywordflow">if</span> (FastProbablePrimeTest(p) && ProvePrime(p, q))</div><div class="line"><a name="l00502"></a><span class="lineno"> 502</span>  <span class="keywordflow">return</span> p;</div><div class="line"><a name="l00503"></a><span class="lineno"> 503</span>  }</div><div class="line"><a name="l00504"></a><span class="lineno"> 504</span>  }</div><div class="line"><a name="l00505"></a><span class="lineno"> 505</span> </div><div class="line"><a name="l00506"></a><span class="lineno"> 506</span>  <span class="comment">// not reached</span></div><div class="line"><a name="l00507"></a><span class="lineno"> 507</span>  <span class="keywordflow">return</span> p;</div><div class="line"><a name="l00508"></a><span class="lineno"> 508</span> }</div><div class="line"><a name="l00509"></a><span class="lineno"> 509</span> </div><div class="line"><a name="l00510"></a><span class="lineno"><a class="line" href="nbtheory_8h.html#a4f5215dbaaf83eacf300ef54f0e941fc"> 510</a></span> <a class="code" href="class_integer.html">Integer</a> <a class="code" href="nbtheory_8h.html#a4f5215dbaaf83eacf300ef54f0e941fc">MaurerProvablePrime</a>(<a class="code" href="class_random_number_generator.html">RandomNumberGenerator</a> &rng, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> bits)</div><div class="line"><a name="l00511"></a><span class="lineno"> 511</span> {</div><div class="line"><a name="l00512"></a><span class="lineno"> 512</span>  <span class="keyword">const</span> <span class="keywordtype">unsigned</span> smallPrimeBound = 29, c_opt=10;</div><div class="line"><a name="l00513"></a><span class="lineno"> 513</span>  <a class="code" href="class_integer.html">Integer</a> p;</div><div class="line"><a name="l00514"></a><span class="lineno"> 514</span> </div><div class="line"><a name="l00515"></a><span class="lineno"> 515</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> primeTableSize;</div><div class="line"><a name="l00516"></a><span class="lineno"> 516</span>  <span class="keyword">const</span> word16 * primeTable = <a class="code" href="nbtheory_8h.html#aa41f53fa846ea7546d7269b5d5c6a29f">GetPrimeTable</a>(primeTableSize);</div><div class="line"><a name="l00517"></a><span class="lineno"> 517</span> </div><div class="line"><a name="l00518"></a><span class="lineno"> 518</span>  <span class="keywordflow">if</span> (bits < smallPrimeBound)</div><div class="line"><a name="l00519"></a><span class="lineno"> 519</span>  {</div><div class="line"><a name="l00520"></a><span class="lineno"> 520</span>  <span class="keywordflow">do</span></div><div class="line"><a name="l00521"></a><span class="lineno"> 521</span>  p.<a class="code" href="class_integer.html#a62a8829c926b4e421183e76ea4233702">Randomize</a>(rng, <a class="code" href="class_integer.html#ade53248f5dbb520273a70856b975417c">Integer::Power2</a>(bits-1), <a class="code" href="class_integer.html#ade53248f5dbb520273a70856b975417c">Integer::Power2</a>(bits)-1, <a class="code" href="class_integer.html#a9b4088ac01abf76b9ba60060abccb7a3ad9b396a7ba736a4ca02db0125cc8c6a4">Integer::ANY</a>, 1, 2);</div><div class="line"><a name="l00522"></a><span class="lineno"> 522</span>  <span class="keywordflow">while</span> (<a class="code" href="nbtheory_8h.html#aef5a456e724cba394ff8ad788eae777d">TrialDivision</a>(p, 1 << ((bits+1)/2)));</div><div class="line"><a name="l00523"></a><span class="lineno"> 523</span>  }</div><div class="line"><a name="l00524"></a><span class="lineno"> 524</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l00525"></a><span class="lineno"> 525</span>  {</div><div class="line"><a name="l00526"></a><span class="lineno"> 526</span>  <span class="keyword">const</span> <span class="keywordtype">unsigned</span> margin = bits > 50 ? 20 : (bits-10)/2;</div><div class="line"><a name="l00527"></a><span class="lineno"> 527</span>  <span class="keywordtype">double</span> relativeSize;</div><div class="line"><a name="l00528"></a><span class="lineno"> 528</span>  <span class="keywordflow">do</span></div><div class="line"><a name="l00529"></a><span class="lineno"> 529</span>  relativeSize = std::pow(2.0, <span class="keywordtype">double</span>(rng.<a class="code" href="class_random_number_generator.html#a96a3eec202b6251f5c94136ab7edbde1">GenerateWord32</a>())/0xffffffff - 1);</div><div class="line"><a name="l00530"></a><span class="lineno"> 530</span>  <span class="keywordflow">while</span> (bits * relativeSize >= bits - margin);</div><div class="line"><a name="l00531"></a><span class="lineno"> 531</span> </div><div class="line"><a name="l00532"></a><span class="lineno"> 532</span>  <a class="code" href="class_integer.html">Integer</a> a,b;</div><div class="line"><a name="l00533"></a><span class="lineno"> 533</span>  <a class="code" href="class_integer.html">Integer</a> q = <a class="code" href="nbtheory_8h.html#a4f5215dbaaf83eacf300ef54f0e941fc">MaurerProvablePrime</a>(rng, <span class="keywordtype">unsigned</span>(bits*relativeSize));</div><div class="line"><a name="l00534"></a><span class="lineno"> 534</span>  <a class="code" href="class_integer.html">Integer</a> I = <a class="code" href="class_integer.html#ade53248f5dbb520273a70856b975417c">Integer::Power2</a>(bits-2)/q;</div><div class="line"><a name="l00535"></a><span class="lineno"> 535</span>  <a class="code" href="class_integer.html">Integer</a> I2 = I << 1;</div><div class="line"><a name="l00536"></a><span class="lineno"> 536</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> trialDivisorBound = (<span class="keywordtype">unsigned</span> int)<a class="code" href="misc_8h.html#abe412b0409249cb54899e97bc7d86424">STDMIN</a>((<span class="keywordtype">unsigned</span> <span class="keywordtype">long</span>)primeTable[primeTableSize-1], (<span class="keywordtype">unsigned</span> long)bits*bits/c_opt);</div><div class="line"><a name="l00537"></a><span class="lineno"> 537</span>  <span class="keywordtype">bool</span> success = <span class="keyword">false</span>;</div><div class="line"><a name="l00538"></a><span class="lineno"> 538</span>  <span class="keywordflow">while</span> (!success)</div><div class="line"><a name="l00539"></a><span class="lineno"> 539</span>  {</div><div class="line"><a name="l00540"></a><span class="lineno"> 540</span>  p.<a class="code" href="class_integer.html#a62a8829c926b4e421183e76ea4233702">Randomize</a>(rng, I, I2, <a class="code" href="class_integer.html#a9b4088ac01abf76b9ba60060abccb7a3ad9b396a7ba736a4ca02db0125cc8c6a4">Integer::ANY</a>);</div><div class="line"><a name="l00541"></a><span class="lineno"> 541</span>  p *= q; p <<= 1; ++p;</div><div class="line"><a name="l00542"></a><span class="lineno"> 542</span>  <span class="keywordflow">if</span> (!<a class="code" href="nbtheory_8h.html#aef5a456e724cba394ff8ad788eae777d">TrialDivision</a>(p, trialDivisorBound))</div><div class="line"><a name="l00543"></a><span class="lineno"> 543</span>  {</div><div class="line"><a name="l00544"></a><span class="lineno"> 544</span>  a.Randomize(rng, 2, p-1, <a class="code" href="class_integer.html#a9b4088ac01abf76b9ba60060abccb7a3ad9b396a7ba736a4ca02db0125cc8c6a4">Integer::ANY</a>);</div><div class="line"><a name="l00545"></a><span class="lineno"> 545</span>  b = a_exp_b_mod_c(a, (p-1)/q, p);</div><div class="line"><a name="l00546"></a><span class="lineno"> 546</span>  success = (<a class="code" href="nbtheory_8h.html#ac1d98aa1d0ed1df97bf0dc194da5169a">GCD</a>(b-1, p) == 1) && (a_exp_b_mod_c(b, q, p) == 1);</div><div class="line"><a name="l00547"></a><span class="lineno"> 547</span>  }</div><div class="line"><a name="l00548"></a><span class="lineno"> 548</span>  }</div><div class="line"><a name="l00549"></a><span class="lineno"> 549</span>  }</div><div class="line"><a name="l00550"></a><span class="lineno"> 550</span>  <span class="keywordflow">return</span> p;</div><div class="line"><a name="l00551"></a><span class="lineno"> 551</span> }</div><div class="line"><a name="l00552"></a><span class="lineno"> 552</span> </div><div class="line"><a name="l00553"></a><span class="lineno"><a class="line" href="nbtheory_8h.html#ab3fae49135264b5b5afecd0331915040"> 553</a></span> <a class="code" href="class_integer.html">Integer</a> <a class="code" href="nbtheory_8h.html#ab3fae49135264b5b5afecd0331915040">CRT</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &xp, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &p, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &xq, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &q, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &u)</div><div class="line"><a name="l00554"></a><span class="lineno"> 554</span> {</div><div class="line"><a name="l00555"></a><span class="lineno"> 555</span>  <span class="comment">// isn't operator overloading great?</span></div><div class="line"><a name="l00556"></a><span class="lineno"> 556</span>  <span class="keywordflow">return</span> p * (u * (xq-xp) % q) + xp;</div><div class="line"><a name="l00557"></a><span class="lineno"> 557</span> <span class="comment">/*</span></div><div class="line"><a name="l00558"></a><span class="lineno"> 558</span> <span class="comment"> Integer t1 = xq-xp;</span></div><div class="line"><a name="l00559"></a><span class="lineno"> 559</span> <span class="comment"> cout << hex << t1 << endl;</span></div><div class="line"><a name="l00560"></a><span class="lineno"> 560</span> <span class="comment"> Integer t2 = u * t1;</span></div><div class="line"><a name="l00561"></a><span class="lineno"> 561</span> <span class="comment"> cout << hex << t2 << endl;</span></div><div class="line"><a name="l00562"></a><span class="lineno"> 562</span> <span class="comment"> Integer t3 = t2 % q;</span></div><div class="line"><a name="l00563"></a><span class="lineno"> 563</span> <span class="comment"> cout << hex << t3 << endl;</span></div><div class="line"><a name="l00564"></a><span class="lineno"> 564</span> <span class="comment"> Integer t4 = p * t3;</span></div><div class="line"><a name="l00565"></a><span class="lineno"> 565</span> <span class="comment"> cout << hex << t4 << endl;</span></div><div class="line"><a name="l00566"></a><span class="lineno"> 566</span> <span class="comment"> Integer t5 = t4 + xp;</span></div><div class="line"><a name="l00567"></a><span class="lineno"> 567</span> <span class="comment"> cout << hex << t5 << endl;</span></div><div class="line"><a name="l00568"></a><span class="lineno"> 568</span> <span class="comment"> return t5;</span></div><div class="line"><a name="l00569"></a><span class="lineno"> 569</span> <span class="comment">*/</span></div><div class="line"><a name="l00570"></a><span class="lineno"> 570</span> }</div><div class="line"><a name="l00571"></a><span class="lineno"> 571</span> </div><div class="line"><a name="l00572"></a><span class="lineno"><a class="line" href="nbtheory_8h.html#abb83c7bbd49b1761028d08a9a1016e68"> 572</a></span> <a class="code" href="class_integer.html">Integer</a> <a class="code" href="nbtheory_8h.html#abb83c7bbd49b1761028d08a9a1016e68">ModularSquareRoot</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &a, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &p)</div><div class="line"><a name="l00573"></a><span class="lineno"> 573</span> {</div><div class="line"><a name="l00574"></a><span class="lineno"> 574</span>  <span class="keywordflow">if</span> (p%4 == 3)</div><div class="line"><a name="l00575"></a><span class="lineno"> 575</span>  <span class="keywordflow">return</span> a_exp_b_mod_c(a, (p+1)/4, p);</div><div class="line"><a name="l00576"></a><span class="lineno"> 576</span> </div><div class="line"><a name="l00577"></a><span class="lineno"> 577</span>  <a class="code" href="class_integer.html">Integer</a> q=p-1;</div><div class="line"><a name="l00578"></a><span class="lineno"> 578</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> r=0;</div><div class="line"><a name="l00579"></a><span class="lineno"> 579</span>  <span class="keywordflow">while</span> (q.<a class="code" href="class_integer.html#afedf9af097a3417d8bd3742ec53f9593">IsEven</a>())</div><div class="line"><a name="l00580"></a><span class="lineno"> 580</span>  {</div><div class="line"><a name="l00581"></a><span class="lineno"> 581</span>  r++;</div><div class="line"><a name="l00582"></a><span class="lineno"> 582</span>  q >>= 1;</div><div class="line"><a name="l00583"></a><span class="lineno"> 583</span>  }</div><div class="line"><a name="l00584"></a><span class="lineno"> 584</span> </div><div class="line"><a name="l00585"></a><span class="lineno"> 585</span>  <a class="code" href="class_integer.html">Integer</a> n=2;</div><div class="line"><a name="l00586"></a><span class="lineno"> 586</span>  <span class="keywordflow">while</span> (<a class="code" href="nbtheory_8h.html#abffe3c03543252f53fcf59fdb2df765c">Jacobi</a>(n, p) != -1)</div><div class="line"><a name="l00587"></a><span class="lineno"> 587</span>  ++n;</div><div class="line"><a name="l00588"></a><span class="lineno"> 588</span> </div><div class="line"><a name="l00589"></a><span class="lineno"> 589</span>  <a class="code" href="class_integer.html">Integer</a> y = a_exp_b_mod_c(n, q, p);</div><div class="line"><a name="l00590"></a><span class="lineno"> 590</span>  <a class="code" href="class_integer.html">Integer</a> x = a_exp_b_mod_c(a, (q-1)/2, p);</div><div class="line"><a name="l00591"></a><span class="lineno"> 591</span>  <a class="code" href="class_integer.html">Integer</a> b = (x.Squared()%p)*a%p;</div><div class="line"><a name="l00592"></a><span class="lineno"> 592</span>  x = a*x%p;</div><div class="line"><a name="l00593"></a><span class="lineno"> 593</span>  <a class="code" href="class_integer.html">Integer</a> tempb, t;</div><div class="line"><a name="l00594"></a><span class="lineno"> 594</span> </div><div class="line"><a name="l00595"></a><span class="lineno"> 595</span>  <span class="keywordflow">while</span> (b != 1)</div><div class="line"><a name="l00596"></a><span class="lineno"> 596</span>  {</div><div class="line"><a name="l00597"></a><span class="lineno"> 597</span>  <span class="keywordtype">unsigned</span> m=0;</div><div class="line"><a name="l00598"></a><span class="lineno"> 598</span>  tempb = b;</div><div class="line"><a name="l00599"></a><span class="lineno"> 599</span>  <span class="keywordflow">do</span></div><div class="line"><a name="l00600"></a><span class="lineno"> 600</span>  {</div><div class="line"><a name="l00601"></a><span class="lineno"> 601</span>  m++;</div><div class="line"><a name="l00602"></a><span class="lineno"> 602</span>  b = b.Squared()%p;</div><div class="line"><a name="l00603"></a><span class="lineno"> 603</span>  <span class="keywordflow">if</span> (m==r)</div><div class="line"><a name="l00604"></a><span class="lineno"> 604</span>  <span class="keywordflow">return</span> <a class="code" href="class_integer.html#a19b7e6d48b1b57bd4846160ea2928175">Integer::Zero</a>();</div><div class="line"><a name="l00605"></a><span class="lineno"> 605</span>  }</div><div class="line"><a name="l00606"></a><span class="lineno"> 606</span>  <span class="keywordflow">while</span> (b != 1);</div><div class="line"><a name="l00607"></a><span class="lineno"> 607</span> </div><div class="line"><a name="l00608"></a><span class="lineno"> 608</span>  t = y;</div><div class="line"><a name="l00609"></a><span class="lineno"> 609</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> i=0; i<r-m-1; i++)</div><div class="line"><a name="l00610"></a><span class="lineno"> 610</span>  t = t.<a class="code" href="class_integer.html#a7b5e639045868c5ac338f4180e1c7efa">Squared</a>()%p;</div><div class="line"><a name="l00611"></a><span class="lineno"> 611</span>  y = t.<a class="code" href="class_integer.html#a7b5e639045868c5ac338f4180e1c7efa">Squared</a>()%p;</div><div class="line"><a name="l00612"></a><span class="lineno"> 612</span>  r = m;</div><div class="line"><a name="l00613"></a><span class="lineno"> 613</span>  x = x*t%p;</div><div class="line"><a name="l00614"></a><span class="lineno"> 614</span>  b = tempb*y%p;</div><div class="line"><a name="l00615"></a><span class="lineno"> 615</span>  }</div><div class="line"><a name="l00616"></a><span class="lineno"> 616</span> </div><div class="line"><a name="l00617"></a><span class="lineno"> 617</span>  <a class="code" href="trap_8h.html#adf3b392588bc94cbeae9f415a78c7b95">CRYPTOPP_ASSERT</a>(x.Squared()%p == a);</div><div class="line"><a name="l00618"></a><span class="lineno"> 618</span>  <span class="keywordflow">return</span> x;</div><div class="line"><a name="l00619"></a><span class="lineno"> 619</span> }</div><div class="line"><a name="l00620"></a><span class="lineno"> 620</span> </div><div class="line"><a name="l00621"></a><span class="lineno"><a class="line" href="nbtheory_8h.html#aa308ad452a47cf22de4ac3204ab09e7d"> 621</a></span> <span class="keywordtype">bool</span> <a class="code" href="nbtheory_8h.html#aa308ad452a47cf22de4ac3204ab09e7d">SolveModularQuadraticEquation</a>(<a class="code" href="class_integer.html">Integer</a> &r1, <a class="code" href="class_integer.html">Integer</a> &r2, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &a, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &b, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &c, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &p)</div><div class="line"><a name="l00622"></a><span class="lineno"> 622</span> {</div><div class="line"><a name="l00623"></a><span class="lineno"> 623</span>  <a class="code" href="class_integer.html">Integer</a> D = (b.Squared() - 4*a*c) % p;</div><div class="line"><a name="l00624"></a><span class="lineno"> 624</span>  <span class="keywordflow">switch</span> (<a class="code" href="nbtheory_8h.html#abffe3c03543252f53fcf59fdb2df765c">Jacobi</a>(D, p))</div><div class="line"><a name="l00625"></a><span class="lineno"> 625</span>  {</div><div class="line"><a name="l00626"></a><span class="lineno"> 626</span>  <span class="keywordflow">default</span>:</div><div class="line"><a name="l00627"></a><span class="lineno"> 627</span>  <a class="code" href="trap_8h.html#adf3b392588bc94cbeae9f415a78c7b95">CRYPTOPP_ASSERT</a>(<span class="keyword">false</span>); <span class="comment">// not reached</span></div><div class="line"><a name="l00628"></a><span class="lineno"> 628</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00629"></a><span class="lineno"> 629</span>  <span class="keywordflow">case</span> -1:</div><div class="line"><a name="l00630"></a><span class="lineno"> 630</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00631"></a><span class="lineno"> 631</span>  <span class="keywordflow">case</span> 0:</div><div class="line"><a name="l00632"></a><span class="lineno"> 632</span>  r1 = r2 = (-b*(a+a).InverseMod(p)) % p;</div><div class="line"><a name="l00633"></a><span class="lineno"> 633</span>  <a class="code" href="trap_8h.html#adf3b392588bc94cbeae9f415a78c7b95">CRYPTOPP_ASSERT</a>(((r1.Squared()*a + r1*b + c) % p).IsZero());</div><div class="line"><a name="l00634"></a><span class="lineno"> 634</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div><div class="line"><a name="l00635"></a><span class="lineno"> 635</span>  <span class="keywordflow">case</span> 1:</div><div class="line"><a name="l00636"></a><span class="lineno"> 636</span>  <a class="code" href="class_integer.html">Integer</a> s = <a class="code" href="nbtheory_8h.html#abb83c7bbd49b1761028d08a9a1016e68">ModularSquareRoot</a>(D, p);</div><div class="line"><a name="l00637"></a><span class="lineno"> 637</span>  <a class="code" href="class_integer.html">Integer</a> t = (a+a).InverseMod(p);</div><div class="line"><a name="l00638"></a><span class="lineno"> 638</span>  r1 = (s-b)*t % p;</div><div class="line"><a name="l00639"></a><span class="lineno"> 639</span>  r2 = (-s-b)*t % p;</div><div class="line"><a name="l00640"></a><span class="lineno"> 640</span>  <a class="code" href="trap_8h.html#adf3b392588bc94cbeae9f415a78c7b95">CRYPTOPP_ASSERT</a>(((r1.Squared()*a + r1*b + c) % p).IsZero());</div><div class="line"><a name="l00641"></a><span class="lineno"> 641</span>  <a class="code" href="trap_8h.html#adf3b392588bc94cbeae9f415a78c7b95">CRYPTOPP_ASSERT</a>(((r2.Squared()*a + r2*b + c) % p).IsZero());</div><div class="line"><a name="l00642"></a><span class="lineno"> 642</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div><div class="line"><a name="l00643"></a><span class="lineno"> 643</span>  }</div><div class="line"><a name="l00644"></a><span class="lineno"> 644</span> }</div><div class="line"><a name="l00645"></a><span class="lineno"> 645</span> </div><div class="line"><a name="l00646"></a><span class="lineno"><a class="line" href="nbtheory_8h.html#aad7ca1c53c38a93997327226eddc0240"> 646</a></span> <a class="code" href="class_integer.html">Integer</a> <a class="code" href="nbtheory_8h.html#aad7ca1c53c38a93997327226eddc0240">ModularRoot</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &a, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &dp, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &dq,</div><div class="line"><a name="l00647"></a><span class="lineno"> 647</span>  <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &p, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &q, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &u)</div><div class="line"><a name="l00648"></a><span class="lineno"> 648</span> {</div><div class="line"><a name="l00649"></a><span class="lineno"> 649</span>  <a class="code" href="class_integer.html">Integer</a> p2, q2;</div><div class="line"><a name="l00650"></a><span class="lineno"> 650</span> <span class="preprocessor"> #pragma omp parallel</span></div><div class="line"><a name="l00651"></a><span class="lineno"> 651</span> <span class="preprocessor"> #pragma omp sections</span></div><div class="line"><a name="l00652"></a><span class="lineno"> 652</span>  {</div><div class="line"><a name="l00653"></a><span class="lineno"> 653</span> <span class="preprocessor"> #pragma omp section</span></div><div class="line"><a name="l00654"></a><span class="lineno"> 654</span>  p2 = <a class="code" href="nbtheory_8h.html#a5365cc677fbc93221d9bdfaec442ca3d">ModularExponentiation</a>((a % p), dp, p);</div><div class="line"><a name="l00655"></a><span class="lineno"> 655</span> <span class="preprocessor"> #pragma omp section</span></div><div class="line"><a name="l00656"></a><span class="lineno"> 656</span>  q2 = <a class="code" href="nbtheory_8h.html#a5365cc677fbc93221d9bdfaec442ca3d">ModularExponentiation</a>((a % q), dq, q);</div><div class="line"><a name="l00657"></a><span class="lineno"> 657</span>  }</div><div class="line"><a name="l00658"></a><span class="lineno"> 658</span>  <span class="keywordflow">return</span> <a class="code" href="nbtheory_8h.html#ab3fae49135264b5b5afecd0331915040">CRT</a>(p2, p, q2, q, u);</div><div class="line"><a name="l00659"></a><span class="lineno"> 659</span> }</div><div class="line"><a name="l00660"></a><span class="lineno"> 660</span> </div><div class="line"><a name="l00661"></a><span class="lineno"> 661</span> <a class="code" href="class_integer.html">Integer</a> <a class="code" href="nbtheory_8h.html#aad7ca1c53c38a93997327226eddc0240">ModularRoot</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &a, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &e,</div><div class="line"><a name="l00662"></a><span class="lineno"> 662</span>  <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &p, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &q)</div><div class="line"><a name="l00663"></a><span class="lineno"> 663</span> {</div><div class="line"><a name="l00664"></a><span class="lineno"> 664</span>  <a class="code" href="class_integer.html">Integer</a> dp = <a class="code" href="nbtheory_8h.html#aa88bcc8ea0e0608098a17bec60abe61e">EuclideanMultiplicativeInverse</a>(e, p-1);</div><div class="line"><a name="l00665"></a><span class="lineno"> 665</span>  <a class="code" href="class_integer.html">Integer</a> dq = <a class="code" href="nbtheory_8h.html#aa88bcc8ea0e0608098a17bec60abe61e">EuclideanMultiplicativeInverse</a>(e, q-1);</div><div class="line"><a name="l00666"></a><span class="lineno"> 666</span>  <a class="code" href="class_integer.html">Integer</a> u = <a class="code" href="nbtheory_8h.html#aa88bcc8ea0e0608098a17bec60abe61e">EuclideanMultiplicativeInverse</a>(p, q);</div><div class="line"><a name="l00667"></a><span class="lineno"> 667</span>  <a class="code" href="trap_8h.html#adf3b392588bc94cbeae9f415a78c7b95">CRYPTOPP_ASSERT</a>(!!dp && !!dq && !!u);</div><div class="line"><a name="l00668"></a><span class="lineno"> 668</span>  <span class="keywordflow">return</span> <a class="code" href="nbtheory_8h.html#aad7ca1c53c38a93997327226eddc0240">ModularRoot</a>(a, dp, dq, p, q, u);</div><div class="line"><a name="l00669"></a><span class="lineno"> 669</span> }</div><div class="line"><a name="l00670"></a><span class="lineno"> 670</span> </div><div class="line"><a name="l00671"></a><span class="lineno"> 671</span> <span class="comment">/*</span></div><div class="line"><a name="l00672"></a><span class="lineno"> 672</span> <span class="comment">Integer GCDI(const Integer &x, const Integer &y)</span></div><div class="line"><a name="l00673"></a><span class="lineno"> 673</span> <span class="comment">{</span></div><div class="line"><a name="l00674"></a><span class="lineno"> 674</span> <span class="comment"> Integer a=x, b=y;</span></div><div class="line"><a name="l00675"></a><span class="lineno"> 675</span> <span class="comment"> unsigned k=0;</span></div><div class="line"><a name="l00676"></a><span class="lineno"> 676</span> <span class="comment"></span></div><div class="line"><a name="l00677"></a><span class="lineno"> 677</span> <span class="comment"> CRYPTOPP_ASSERT(!!a && !!b);</span></div><div class="line"><a name="l00678"></a><span class="lineno"> 678</span> <span class="comment"></span></div><div class="line"><a name="l00679"></a><span class="lineno"> 679</span> <span class="comment"> while (a[0]==0 && b[0]==0)</span></div><div class="line"><a name="l00680"></a><span class="lineno"> 680</span> <span class="comment"> {</span></div><div class="line"><a name="l00681"></a><span class="lineno"> 681</span> <span class="comment"> a >>= 1;</span></div><div class="line"><a name="l00682"></a><span class="lineno"> 682</span> <span class="comment"> b >>= 1;</span></div><div class="line"><a name="l00683"></a><span class="lineno"> 683</span> <span class="comment"> k++;</span></div><div class="line"><a name="l00684"></a><span class="lineno"> 684</span> <span class="comment"> }</span></div><div class="line"><a name="l00685"></a><span class="lineno"> 685</span> <span class="comment"></span></div><div class="line"><a name="l00686"></a><span class="lineno"> 686</span> <span class="comment"> while (a[0]==0)</span></div><div class="line"><a name="l00687"></a><span class="lineno"> 687</span> <span class="comment"> a >>= 1;</span></div><div class="line"><a name="l00688"></a><span class="lineno"> 688</span> <span class="comment"></span></div><div class="line"><a name="l00689"></a><span class="lineno"> 689</span> <span class="comment"> while (b[0]==0)</span></div><div class="line"><a name="l00690"></a><span class="lineno"> 690</span> <span class="comment"> b >>= 1;</span></div><div class="line"><a name="l00691"></a><span class="lineno"> 691</span> <span class="comment"></span></div><div class="line"><a name="l00692"></a><span class="lineno"> 692</span> <span class="comment"> while (1)</span></div><div class="line"><a name="l00693"></a><span class="lineno"> 693</span> <span class="comment"> {</span></div><div class="line"><a name="l00694"></a><span class="lineno"> 694</span> <span class="comment"> switch (a.Compare(b))</span></div><div class="line"><a name="l00695"></a><span class="lineno"> 695</span> <span class="comment"> {</span></div><div class="line"><a name="l00696"></a><span class="lineno"> 696</span> <span class="comment"> case -1:</span></div><div class="line"><a name="l00697"></a><span class="lineno"> 697</span> <span class="comment"> b -= a;</span></div><div class="line"><a name="l00698"></a><span class="lineno"> 698</span> <span class="comment"> while (b[0]==0)</span></div><div class="line"><a name="l00699"></a><span class="lineno"> 699</span> <span class="comment"> b >>= 1;</span></div><div class="line"><a name="l00700"></a><span class="lineno"> 700</span> <span class="comment"> break;</span></div><div class="line"><a name="l00701"></a><span class="lineno"> 701</span> <span class="comment"></span></div><div class="line"><a name="l00702"></a><span class="lineno"> 702</span> <span class="comment"> case 0:</span></div><div class="line"><a name="l00703"></a><span class="lineno"> 703</span> <span class="comment"> return (a <<= k);</span></div><div class="line"><a name="l00704"></a><span class="lineno"> 704</span> <span class="comment"></span></div><div class="line"><a name="l00705"></a><span class="lineno"> 705</span> <span class="comment"> case 1:</span></div><div class="line"><a name="l00706"></a><span class="lineno"> 706</span> <span class="comment"> a -= b;</span></div><div class="line"><a name="l00707"></a><span class="lineno"> 707</span> <span class="comment"> while (a[0]==0)</span></div><div class="line"><a name="l00708"></a><span class="lineno"> 708</span> <span class="comment"> a >>= 1;</span></div><div class="line"><a name="l00709"></a><span class="lineno"> 709</span> <span class="comment"> break;</span></div><div class="line"><a name="l00710"></a><span class="lineno"> 710</span> <span class="comment"></span></div><div class="line"><a name="l00711"></a><span class="lineno"> 711</span> <span class="comment"> default:</span></div><div class="line"><a name="l00712"></a><span class="lineno"> 712</span> <span class="comment"> CRYPTOPP_ASSERT(false);</span></div><div class="line"><a name="l00713"></a><span class="lineno"> 713</span> <span class="comment"> }</span></div><div class="line"><a name="l00714"></a><span class="lineno"> 714</span> <span class="comment"> }</span></div><div class="line"><a name="l00715"></a><span class="lineno"> 715</span> <span class="comment">}</span></div><div class="line"><a name="l00716"></a><span class="lineno"> 716</span> <span class="comment"></span></div><div class="line"><a name="l00717"></a><span class="lineno"> 717</span> <span class="comment">Integer EuclideanMultiplicativeInverse(const Integer &a, const Integer &b)</span></div><div class="line"><a name="l00718"></a><span class="lineno"> 718</span> <span class="comment">{</span></div><div class="line"><a name="l00719"></a><span class="lineno"> 719</span> <span class="comment"> CRYPTOPP_ASSERT(b.Positive());</span></div><div class="line"><a name="l00720"></a><span class="lineno"> 720</span> <span class="comment"></span></div><div class="line"><a name="l00721"></a><span class="lineno"> 721</span> <span class="comment"> if (a.Negative())</span></div><div class="line"><a name="l00722"></a><span class="lineno"> 722</span> <span class="comment"> return EuclideanMultiplicativeInverse(a%b, b);</span></div><div class="line"><a name="l00723"></a><span class="lineno"> 723</span> <span class="comment"></span></div><div class="line"><a name="l00724"></a><span class="lineno"> 724</span> <span class="comment"> if (b[0]==0)</span></div><div class="line"><a name="l00725"></a><span class="lineno"> 725</span> <span class="comment"> {</span></div><div class="line"><a name="l00726"></a><span class="lineno"> 726</span> <span class="comment"> if (!b || a[0]==0)</span></div><div class="line"><a name="l00727"></a><span class="lineno"> 727</span> <span class="comment"> return Integer::Zero(); // no inverse</span></div><div class="line"><a name="l00728"></a><span class="lineno"> 728</span> <span class="comment"> if (a==1)</span></div><div class="line"><a name="l00729"></a><span class="lineno"> 729</span> <span class="comment"> return 1;</span></div><div class="line"><a name="l00730"></a><span class="lineno"> 730</span> <span class="comment"> Integer u = EuclideanMultiplicativeInverse(b, a);</span></div><div class="line"><a name="l00731"></a><span class="lineno"> 731</span> <span class="comment"> if (!u)</span></div><div class="line"><a name="l00732"></a><span class="lineno"> 732</span> <span class="comment"> return Integer::Zero(); // no inverse</span></div><div class="line"><a name="l00733"></a><span class="lineno"> 733</span> <span class="comment"> else</span></div><div class="line"><a name="l00734"></a><span class="lineno"> 734</span> <span class="comment"> return (b*(a-u)+1)/a;</span></div><div class="line"><a name="l00735"></a><span class="lineno"> 735</span> <span class="comment"> }</span></div><div class="line"><a name="l00736"></a><span class="lineno"> 736</span> <span class="comment"></span></div><div class="line"><a name="l00737"></a><span class="lineno"> 737</span> <span class="comment"> Integer u=1, d=a, v1=b, v3=b, t1, t3, b2=(b+1)>>1;</span></div><div class="line"><a name="l00738"></a><span class="lineno"> 738</span> <span class="comment"></span></div><div class="line"><a name="l00739"></a><span class="lineno"> 739</span> <span class="comment"> if (a[0])</span></div><div class="line"><a name="l00740"></a><span class="lineno"> 740</span> <span class="comment"> {</span></div><div class="line"><a name="l00741"></a><span class="lineno"> 741</span> <span class="comment"> t1 = Integer::Zero();</span></div><div class="line"><a name="l00742"></a><span class="lineno"> 742</span> <span class="comment"> t3 = -b;</span></div><div class="line"><a name="l00743"></a><span class="lineno"> 743</span> <span class="comment"> }</span></div><div class="line"><a name="l00744"></a><span class="lineno"> 744</span> <span class="comment"> else</span></div><div class="line"><a name="l00745"></a><span class="lineno"> 745</span> <span class="comment"> {</span></div><div class="line"><a name="l00746"></a><span class="lineno"> 746</span> <span class="comment"> t1 = b2;</span></div><div class="line"><a name="l00747"></a><span class="lineno"> 747</span> <span class="comment"> t3 = a>>1;</span></div><div class="line"><a name="l00748"></a><span class="lineno"> 748</span> <span class="comment"> }</span></div><div class="line"><a name="l00749"></a><span class="lineno"> 749</span> <span class="comment"></span></div><div class="line"><a name="l00750"></a><span class="lineno"> 750</span> <span class="comment"> while (!!t3)</span></div><div class="line"><a name="l00751"></a><span class="lineno"> 751</span> <span class="comment"> {</span></div><div class="line"><a name="l00752"></a><span class="lineno"> 752</span> <span class="comment"> while (t3[0]==0)</span></div><div class="line"><a name="l00753"></a><span class="lineno"> 753</span> <span class="comment"> {</span></div><div class="line"><a name="l00754"></a><span class="lineno"> 754</span> <span class="comment"> t3 >>= 1;</span></div><div class="line"><a name="l00755"></a><span class="lineno"> 755</span> <span class="comment"> if (t1[0]==0)</span></div><div class="line"><a name="l00756"></a><span class="lineno"> 756</span> <span class="comment"> t1 >>= 1;</span></div><div class="line"><a name="l00757"></a><span class="lineno"> 757</span> <span class="comment"> else</span></div><div class="line"><a name="l00758"></a><span class="lineno"> 758</span> <span class="comment"> {</span></div><div class="line"><a name="l00759"></a><span class="lineno"> 759</span> <span class="comment"> t1 >>= 1;</span></div><div class="line"><a name="l00760"></a><span class="lineno"> 760</span> <span class="comment"> t1 += b2;</span></div><div class="line"><a name="l00761"></a><span class="lineno"> 761</span> <span class="comment"> }</span></div><div class="line"><a name="l00762"></a><span class="lineno"> 762</span> <span class="comment"> }</span></div><div class="line"><a name="l00763"></a><span class="lineno"> 763</span> <span class="comment"> if (t3.Positive())</span></div><div class="line"><a name="l00764"></a><span class="lineno"> 764</span> <span class="comment"> {</span></div><div class="line"><a name="l00765"></a><span class="lineno"> 765</span> <span class="comment"> u = t1;</span></div><div class="line"><a name="l00766"></a><span class="lineno"> 766</span> <span class="comment"> d = t3;</span></div><div class="line"><a name="l00767"></a><span class="lineno"> 767</span> <span class="comment"> }</span></div><div class="line"><a name="l00768"></a><span class="lineno"> 768</span> <span class="comment"> else</span></div><div class="line"><a name="l00769"></a><span class="lineno"> 769</span> <span class="comment"> {</span></div><div class="line"><a name="l00770"></a><span class="lineno"> 770</span> <span class="comment"> v1 = b-t1;</span></div><div class="line"><a name="l00771"></a><span class="lineno"> 771</span> <span class="comment"> v3 = -t3;</span></div><div class="line"><a name="l00772"></a><span class="lineno"> 772</span> <span class="comment"> }</span></div><div class="line"><a name="l00773"></a><span class="lineno"> 773</span> <span class="comment"> t1 = u-v1;</span></div><div class="line"><a name="l00774"></a><span class="lineno"> 774</span> <span class="comment"> t3 = d-v3;</span></div><div class="line"><a name="l00775"></a><span class="lineno"> 775</span> <span class="comment"> if (t1.Negative())</span></div><div class="line"><a name="l00776"></a><span class="lineno"> 776</span> <span class="comment"> t1 += b;</span></div><div class="line"><a name="l00777"></a><span class="lineno"> 777</span> <span class="comment"> }</span></div><div class="line"><a name="l00778"></a><span class="lineno"> 778</span> <span class="comment"> if (d==1)</span></div><div class="line"><a name="l00779"></a><span class="lineno"> 779</span> <span class="comment"> return u;</span></div><div class="line"><a name="l00780"></a><span class="lineno"> 780</span> <span class="comment"> else</span></div><div class="line"><a name="l00781"></a><span class="lineno"> 781</span> <span class="comment"> return Integer::Zero(); // no inverse</span></div><div class="line"><a name="l00782"></a><span class="lineno"> 782</span> <span class="comment">}</span></div><div class="line"><a name="l00783"></a><span class="lineno"> 783</span> <span class="comment">*/</span></div><div class="line"><a name="l00784"></a><span class="lineno"> 784</span> </div><div class="line"><a name="l00785"></a><span class="lineno"><a class="line" href="nbtheory_8h.html#abffe3c03543252f53fcf59fdb2df765c"> 785</a></span> <span class="keywordtype">int</span> <a class="code" href="nbtheory_8h.html#abffe3c03543252f53fcf59fdb2df765c">Jacobi</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &aIn, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &bIn)</div><div class="line"><a name="l00786"></a><span class="lineno"> 786</span> {</div><div class="line"><a name="l00787"></a><span class="lineno"> 787</span>  <a class="code" href="trap_8h.html#adf3b392588bc94cbeae9f415a78c7b95">CRYPTOPP_ASSERT</a>(bIn.<a class="code" href="class_integer.html#aed4bb7208a18b986ef3e1a7d92e06d1d">IsOdd</a>());</div><div class="line"><a name="l00788"></a><span class="lineno"> 788</span> </div><div class="line"><a name="l00789"></a><span class="lineno"> 789</span>  <a class="code" href="class_integer.html">Integer</a> b = bIn, a = aIn%bIn;</div><div class="line"><a name="l00790"></a><span class="lineno"> 790</span>  <span class="keywordtype">int</span> result = 1;</div><div class="line"><a name="l00791"></a><span class="lineno"> 791</span> </div><div class="line"><a name="l00792"></a><span class="lineno"> 792</span>  <span class="keywordflow">while</span> (!!a)</div><div class="line"><a name="l00793"></a><span class="lineno"> 793</span>  {</div><div class="line"><a name="l00794"></a><span class="lineno"> 794</span>  <span class="keywordtype">unsigned</span> i=0;</div><div class="line"><a name="l00795"></a><span class="lineno"> 795</span>  <span class="keywordflow">while</span> (a.GetBit(i)==0)</div><div class="line"><a name="l00796"></a><span class="lineno"> 796</span>  i++;</div><div class="line"><a name="l00797"></a><span class="lineno"> 797</span>  a>>=i;</div><div class="line"><a name="l00798"></a><span class="lineno"> 798</span> </div><div class="line"><a name="l00799"></a><span class="lineno"> 799</span>  <span class="keywordflow">if</span> (i%2==1 && (b%8==3 || b%8==5))</div><div class="line"><a name="l00800"></a><span class="lineno"> 800</span>  result = -result;</div><div class="line"><a name="l00801"></a><span class="lineno"> 801</span> </div><div class="line"><a name="l00802"></a><span class="lineno"> 802</span>  <span class="keywordflow">if</span> (a%4==3 && b%4==3)</div><div class="line"><a name="l00803"></a><span class="lineno"> 803</span>  result = -result;</div><div class="line"><a name="l00804"></a><span class="lineno"> 804</span> </div><div class="line"><a name="l00805"></a><span class="lineno"> 805</span>  std::swap(a, b);</div><div class="line"><a name="l00806"></a><span class="lineno"> 806</span>  a %= b;</div><div class="line"><a name="l00807"></a><span class="lineno"> 807</span>  }</div><div class="line"><a name="l00808"></a><span class="lineno"> 808</span> </div><div class="line"><a name="l00809"></a><span class="lineno"> 809</span>  <span class="keywordflow">return</span> (b==1) ? result : 0;</div><div class="line"><a name="l00810"></a><span class="lineno"> 810</span> }</div><div class="line"><a name="l00811"></a><span class="lineno"> 811</span> </div><div class="line"><a name="l00812"></a><span class="lineno"><a class="line" href="nbtheory_8h.html#a6f8b2f16d9cb4cdc4bfa5a785928044a"> 812</a></span> <a class="code" href="class_integer.html">Integer</a> <a class="code" href="nbtheory_8h.html#a6f8b2f16d9cb4cdc4bfa5a785928044a">Lucas</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &e, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &pIn, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &n)</div><div class="line"><a name="l00813"></a><span class="lineno"> 813</span> {</div><div class="line"><a name="l00814"></a><span class="lineno"> 814</span>  <span class="keywordtype">unsigned</span> i = e.BitCount();</div><div class="line"><a name="l00815"></a><span class="lineno"> 815</span>  <span class="keywordflow">if</span> (i==0)</div><div class="line"><a name="l00816"></a><span class="lineno"> 816</span>  <span class="keywordflow">return</span> <a class="code" href="class_integer.html#af0cb74a45a48e677952166bdac9d82d7">Integer::Two</a>();</div><div class="line"><a name="l00817"></a><span class="lineno"> 817</span> </div><div class="line"><a name="l00818"></a><span class="lineno"> 818</span>  <a class="code" href="class_montgomery_representation.html">MontgomeryRepresentation</a> m(n);</div><div class="line"><a name="l00819"></a><span class="lineno"> 819</span>  <a class="code" href="class_integer.html">Integer</a> p=m.<a class="code" href="class_montgomery_representation.html#a502f8e7355d1eb252159c0d6e149379a">ConvertIn</a>(pIn%n), two=m.<a class="code" href="class_montgomery_representation.html#a502f8e7355d1eb252159c0d6e149379a">ConvertIn</a>(<a class="code" href="class_integer.html#af0cb74a45a48e677952166bdac9d82d7">Integer::Two</a>());</div><div class="line"><a name="l00820"></a><span class="lineno"> 820</span>  <a class="code" href="class_integer.html">Integer</a> v=p, v1=m.<a class="code" href="class_modular_arithmetic.html#ae4705633e8ca4308894f9a26c6f2881c">Subtract</a>(m.<a class="code" href="class_montgomery_representation.html#a2f24e4fb6d9b9fc9c6b363d41e7ee449">Square</a>(p), two);</div><div class="line"><a name="l00821"></a><span class="lineno"> 821</span> </div><div class="line"><a name="l00822"></a><span class="lineno"> 822</span>  i--;</div><div class="line"><a name="l00823"></a><span class="lineno"> 823</span>  <span class="keywordflow">while</span> (i--)</div><div class="line"><a name="l00824"></a><span class="lineno"> 824</span>  {</div><div class="line"><a name="l00825"></a><span class="lineno"> 825</span>  <span class="keywordflow">if</span> (e.GetBit(i))</div><div class="line"><a name="l00826"></a><span class="lineno"> 826</span>  {</div><div class="line"><a name="l00827"></a><span class="lineno"> 827</span>  <span class="comment">// v = (v*v1 - p) % m;</span></div><div class="line"><a name="l00828"></a><span class="lineno"> 828</span>  v = m.<a class="code" href="class_modular_arithmetic.html#ae4705633e8ca4308894f9a26c6f2881c">Subtract</a>(m.<a class="code" href="class_montgomery_representation.html#a793d265b8165135e2e972bf333ac5a49">Multiply</a>(v,v1), p);</div><div class="line"><a name="l00829"></a><span class="lineno"> 829</span>  <span class="comment">// v1 = (v1*v1 - 2) % m;</span></div><div class="line"><a name="l00830"></a><span class="lineno"> 830</span>  v1 = m.<a class="code" href="class_modular_arithmetic.html#ae4705633e8ca4308894f9a26c6f2881c">Subtract</a>(m.<a class="code" href="class_montgomery_representation.html#a2f24e4fb6d9b9fc9c6b363d41e7ee449">Square</a>(v1), two);</div><div class="line"><a name="l00831"></a><span class="lineno"> 831</span>  }</div><div class="line"><a name="l00832"></a><span class="lineno"> 832</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l00833"></a><span class="lineno"> 833</span>  {</div><div class="line"><a name="l00834"></a><span class="lineno"> 834</span>  <span class="comment">// v1 = (v*v1 - p) % m;</span></div><div class="line"><a name="l00835"></a><span class="lineno"> 835</span>  v1 = m.<a class="code" href="class_modular_arithmetic.html#ae4705633e8ca4308894f9a26c6f2881c">Subtract</a>(m.<a class="code" href="class_montgomery_representation.html#a793d265b8165135e2e972bf333ac5a49">Multiply</a>(v,v1), p);</div><div class="line"><a name="l00836"></a><span class="lineno"> 836</span>  <span class="comment">// v = (v*v - 2) % m;</span></div><div class="line"><a name="l00837"></a><span class="lineno"> 837</span>  v = m.<a class="code" href="class_modular_arithmetic.html#ae4705633e8ca4308894f9a26c6f2881c">Subtract</a>(m.<a class="code" href="class_montgomery_representation.html#a2f24e4fb6d9b9fc9c6b363d41e7ee449">Square</a>(v), two);</div><div class="line"><a name="l00838"></a><span class="lineno"> 838</span>  }</div><div class="line"><a name="l00839"></a><span class="lineno"> 839</span>  }</div><div class="line"><a name="l00840"></a><span class="lineno"> 840</span>  <span class="keywordflow">return</span> m.<a class="code" href="class_montgomery_representation.html#a2591b1df42db492ab9792bbe1fc9bf5e">ConvertOut</a>(v);</div><div class="line"><a name="l00841"></a><span class="lineno"> 841</span> }</div><div class="line"><a name="l00842"></a><span class="lineno"> 842</span> </div><div class="line"><a name="l00843"></a><span class="lineno"> 843</span> <span class="comment">// This is Peter Montgomery's unpublished Lucas sequence evalutation algorithm.</span></div><div class="line"><a name="l00844"></a><span class="lineno"> 844</span> <span class="comment">// The total number of multiplies and squares used is less than the binary</span></div><div class="line"><a name="l00845"></a><span class="lineno"> 845</span> <span class="comment">// algorithm (see above). Unfortunately I can't get it to run as fast as</span></div><div class="line"><a name="l00846"></a><span class="lineno"> 846</span> <span class="comment">// the binary algorithm because of the extra overhead.</span></div><div class="line"><a name="l00847"></a><span class="lineno"> 847</span> <span class="comment">/*</span></div><div class="line"><a name="l00848"></a><span class="lineno"> 848</span> <span class="comment">Integer Lucas(const Integer &n, const Integer &P, const Integer &modulus)</span></div><div class="line"><a name="l00849"></a><span class="lineno"> 849</span> <span class="comment">{</span></div><div class="line"><a name="l00850"></a><span class="lineno"> 850</span> <span class="comment"> if (!n)</span></div><div class="line"><a name="l00851"></a><span class="lineno"> 851</span> <span class="comment"> return 2;</span></div><div class="line"><a name="l00852"></a><span class="lineno"> 852</span> <span class="comment"></span></div><div class="line"><a name="l00853"></a><span class="lineno"> 853</span> <span class="comment">#define f(A, B, C) m.Subtract(m.Multiply(A, B), C)</span></div><div class="line"><a name="l00854"></a><span class="lineno"> 854</span> <span class="comment">#define X2(A) m.Subtract(m.Square(A), two)</span></div><div class="line"><a name="l00855"></a><span class="lineno"> 855</span> <span class="comment">#define X3(A) m.Multiply(A, m.Subtract(m.Square(A), three))</span></div><div class="line"><a name="l00856"></a><span class="lineno"> 856</span> <span class="comment"></span></div><div class="line"><a name="l00857"></a><span class="lineno"> 857</span> <span class="comment"> MontgomeryRepresentation m(modulus);</span></div><div class="line"><a name="l00858"></a><span class="lineno"> 858</span> <span class="comment"> Integer two=m.ConvertIn(2), three=m.ConvertIn(3);</span></div><div class="line"><a name="l00859"></a><span class="lineno"> 859</span> <span class="comment"> Integer A=m.ConvertIn(P), B, C, p, d=n, e, r, t, T, U;</span></div><div class="line"><a name="l00860"></a><span class="lineno"> 860</span> <span class="comment"></span></div><div class="line"><a name="l00861"></a><span class="lineno"> 861</span> <span class="comment"> while (d!=1)</span></div><div class="line"><a name="l00862"></a><span class="lineno"> 862</span> <span class="comment"> {</span></div><div class="line"><a name="l00863"></a><span class="lineno"> 863</span> <span class="comment"> p = d;</span></div><div class="line"><a name="l00864"></a><span class="lineno"> 864</span> <span class="comment"> unsigned int b = WORD_BITS * p.WordCount();</span></div><div class="line"><a name="l00865"></a><span class="lineno"> 865</span> <span class="comment"> Integer alpha = (Integer(5)<<(2*b-2)).SquareRoot() - Integer::Power2(b-1);</span></div><div class="line"><a name="l00866"></a><span class="lineno"> 866</span> <span class="comment"> r = (p*alpha)>>b;</span></div><div class="line"><a name="l00867"></a><span class="lineno"> 867</span> <span class="comment"> e = d-r;</span></div><div class="line"><a name="l00868"></a><span class="lineno"> 868</span> <span class="comment"> B = A;</span></div><div class="line"><a name="l00869"></a><span class="lineno"> 869</span> <span class="comment"> C = two;</span></div><div class="line"><a name="l00870"></a><span class="lineno"> 870</span> <span class="comment"> d = r;</span></div><div class="line"><a name="l00871"></a><span class="lineno"> 871</span> <span class="comment"></span></div><div class="line"><a name="l00872"></a><span class="lineno"> 872</span> <span class="comment"> while (d!=e)</span></div><div class="line"><a name="l00873"></a><span class="lineno"> 873</span> <span class="comment"> {</span></div><div class="line"><a name="l00874"></a><span class="lineno"> 874</span> <span class="comment"> if (d<e)</span></div><div class="line"><a name="l00875"></a><span class="lineno"> 875</span> <span class="comment"> {</span></div><div class="line"><a name="l00876"></a><span class="lineno"> 876</span> <span class="comment"> swap(d, e);</span></div><div class="line"><a name="l00877"></a><span class="lineno"> 877</span> <span class="comment"> swap(A, B);</span></div><div class="line"><a name="l00878"></a><span class="lineno"> 878</span> <span class="comment"> }</span></div><div class="line"><a name="l00879"></a><span class="lineno"> 879</span> <span class="comment"></span></div><div class="line"><a name="l00880"></a><span class="lineno"> 880</span> <span class="comment"> unsigned int dm2 = d[0], em2 = e[0];</span></div><div class="line"><a name="l00881"></a><span class="lineno"> 881</span> <span class="comment"> unsigned int dm3 = d%3, em3 = e%3;</span></div><div class="line"><a name="l00882"></a><span class="lineno"> 882</span> <span class="comment"></span></div><div class="line"><a name="l00883"></a><span class="lineno"> 883</span> <span class="comment">// if ((dm6+em6)%3 == 0 && d <= e + (e>>2))</span></div><div class="line"><a name="l00884"></a><span class="lineno"> 884</span> <span class="comment"> if ((dm3+em3==0 || dm3+em3==3) && (t = e, t >>= 2, t += e, d <= t))</span></div><div class="line"><a name="l00885"></a><span class="lineno"> 885</span> <span class="comment"> {</span></div><div class="line"><a name="l00886"></a><span class="lineno"> 886</span> <span class="comment"> // #1</span></div><div class="line"><a name="l00887"></a><span class="lineno"> 887</span> <span class="comment">// t = (d+d-e)/3;</span></div><div class="line"><a name="l00888"></a><span class="lineno"> 888</span> <span class="comment">// t = d; t += d; t -= e; t /= 3;</span></div><div class="line"><a name="l00889"></a><span class="lineno"> 889</span> <span class="comment">// e = (e+e-d)/3;</span></div><div class="line"><a name="l00890"></a><span class="lineno"> 890</span> <span class="comment">// e += e; e -= d; e /= 3;</span></div><div class="line"><a name="l00891"></a><span class="lineno"> 891</span> <span class="comment">// d = t;</span></div><div class="line"><a name="l00892"></a><span class="lineno"> 892</span> <span class="comment"></span></div><div class="line"><a name="l00893"></a><span class="lineno"> 893</span> <span class="comment">// t = (d+e)/3</span></div><div class="line"><a name="l00894"></a><span class="lineno"> 894</span> <span class="comment"> t = d; t += e; t /= 3;</span></div><div class="line"><a name="l00895"></a><span class="lineno"> 895</span> <span class="comment"> e -= t;</span></div><div class="line"><a name="l00896"></a><span class="lineno"> 896</span> <span class="comment"> d -= t;</span></div><div class="line"><a name="l00897"></a><span class="lineno"> 897</span> <span class="comment"></span></div><div class="line"><a name="l00898"></a><span class="lineno"> 898</span> <span class="comment"> T = f(A, B, C);</span></div><div class="line"><a name="l00899"></a><span class="lineno"> 899</span> <span class="comment"> U = f(T, A, B);</span></div><div class="line"><a name="l00900"></a><span class="lineno"> 900</span> <span class="comment"> B = f(T, B, A);</span></div><div class="line"><a name="l00901"></a><span class="lineno"> 901</span> <span class="comment"> A = U;</span></div><div class="line"><a name="l00902"></a><span class="lineno"> 902</span> <span class="comment"> continue;</span></div><div class="line"><a name="l00903"></a><span class="lineno"> 903</span> <span class="comment"> }</span></div><div class="line"><a name="l00904"></a><span class="lineno"> 904</span> <span class="comment"></span></div><div class="line"><a name="l00905"></a><span class="lineno"> 905</span> <span class="comment">// if (dm6 == em6 && d <= e + (e>>2))</span></div><div class="line"><a name="l00906"></a><span class="lineno"> 906</span> <span class="comment"> if (dm3 == em3 && dm2 == em2 && (t = e, t >>= 2, t += e, d <= t))</span></div><div class="line"><a name="l00907"></a><span class="lineno"> 907</span> <span class="comment"> {</span></div><div class="line"><a name="l00908"></a><span class="lineno"> 908</span> <span class="comment"> // #2</span></div><div class="line"><a name="l00909"></a><span class="lineno"> 909</span> <span class="comment">// d = (d-e)>>1;</span></div><div class="line"><a name="l00910"></a><span class="lineno"> 910</span> <span class="comment"> d -= e; d >>= 1;</span></div><div class="line"><a name="l00911"></a><span class="lineno"> 911</span> <span class="comment"> B = f(A, B, C);</span></div><div class="line"><a name="l00912"></a><span class="lineno"> 912</span> <span class="comment"> A = X2(A);</span></div><div class="line"><a name="l00913"></a><span class="lineno"> 913</span> <span class="comment"> continue;</span></div><div class="line"><a name="l00914"></a><span class="lineno"> 914</span> <span class="comment"> }</span></div><div class="line"><a name="l00915"></a><span class="lineno"> 915</span> <span class="comment"></span></div><div class="line"><a name="l00916"></a><span class="lineno"> 916</span> <span class="comment">// if (d <= (e<<2))</span></div><div class="line"><a name="l00917"></a><span class="lineno"> 917</span> <span class="comment"> if (d <= (t = e, t <<= 2))</span></div><div class="line"><a name="l00918"></a><span class="lineno"> 918</span> <span class="comment"> {</span></div><div class="line"><a name="l00919"></a><span class="lineno"> 919</span> <span class="comment"> // #3</span></div><div class="line"><a name="l00920"></a><span class="lineno"> 920</span> <span class="comment"> d -= e;</span></div><div class="line"><a name="l00921"></a><span class="lineno"> 921</span> <span class="comment"> C = f(A, B, C);</span></div><div class="line"><a name="l00922"></a><span class="lineno"> 922</span> <span class="comment"> swap(B, C);</span></div><div class="line"><a name="l00923"></a><span class="lineno"> 923</span> <span class="comment"> continue;</span></div><div class="line"><a name="l00924"></a><span class="lineno"> 924</span> <span class="comment"> }</span></div><div class="line"><a name="l00925"></a><span class="lineno"> 925</span> <span class="comment"></span></div><div class="line"><a name="l00926"></a><span class="lineno"> 926</span> <span class="comment"> if (dm2 == em2)</span></div><div class="line"><a name="l00927"></a><span class="lineno"> 927</span> <span class="comment"> {</span></div><div class="line"><a name="l00928"></a><span class="lineno"> 928</span> <span class="comment"> // #4</span></div><div class="line"><a name="l00929"></a><span class="lineno"> 929</span> <span class="comment">// d = (d-e)>>1;</span></div><div class="line"><a name="l00930"></a><span class="lineno"> 930</span> <span class="comment"> d -= e; d >>= 1;</span></div><div class="line"><a name="l00931"></a><span class="lineno"> 931</span> <span class="comment"> B = f(A, B, C);</span></div><div class="line"><a name="l00932"></a><span class="lineno"> 932</span> <span class="comment"> A = X2(A);</span></div><div class="line"><a name="l00933"></a><span class="lineno"> 933</span> <span class="comment"> continue;</span></div><div class="line"><a name="l00934"></a><span class="lineno"> 934</span> <span class="comment"> }</span></div><div class="line"><a name="l00935"></a><span class="lineno"> 935</span> <span class="comment"></span></div><div class="line"><a name="l00936"></a><span class="lineno"> 936</span> <span class="comment"> if (dm2 == 0)</span></div><div class="line"><a name="l00937"></a><span class="lineno"> 937</span> <span class="comment"> {</span></div><div class="line"><a name="l00938"></a><span class="lineno"> 938</span> <span class="comment"> // #5</span></div><div class="line"><a name="l00939"></a><span class="lineno"> 939</span> <span class="comment"> d >>= 1;</span></div><div class="line"><a name="l00940"></a><span class="lineno"> 940</span> <span class="comment"> C = f(A, C, B);</span></div><div class="line"><a name="l00941"></a><span class="lineno"> 941</span> <span class="comment"> A = X2(A);</span></div><div class="line"><a name="l00942"></a><span class="lineno"> 942</span> <span class="comment"> continue;</span></div><div class="line"><a name="l00943"></a><span class="lineno"> 943</span> <span class="comment"> }</span></div><div class="line"><a name="l00944"></a><span class="lineno"> 944</span> <span class="comment"></span></div><div class="line"><a name="l00945"></a><span class="lineno"> 945</span> <span class="comment"> if (dm3 == 0)</span></div><div class="line"><a name="l00946"></a><span class="lineno"> 946</span> <span class="comment"> {</span></div><div class="line"><a name="l00947"></a><span class="lineno"> 947</span> <span class="comment"> // #6</span></div><div class="line"><a name="l00948"></a><span class="lineno"> 948</span> <span class="comment">// d = d/3 - e;</span></div><div class="line"><a name="l00949"></a><span class="lineno"> 949</span> <span class="comment"> d /= 3; d -= e;</span></div><div class="line"><a name="l00950"></a><span class="lineno"> 950</span> <span class="comment"> T = X2(A);</span></div><div class="line"><a name="l00951"></a><span class="lineno"> 951</span> <span class="comment"> C = f(T, f(A, B, C), C);</span></div><div class="line"><a name="l00952"></a><span class="lineno"> 952</span> <span class="comment"> swap(B, C);</span></div><div class="line"><a name="l00953"></a><span class="lineno"> 953</span> <span class="comment"> A = f(T, A, A);</span></div><div class="line"><a name="l00954"></a><span class="lineno"> 954</span> <span class="comment"> continue;</span></div><div class="line"><a name="l00955"></a><span class="lineno"> 955</span> <span class="comment"> }</span></div><div class="line"><a name="l00956"></a><span class="lineno"> 956</span> <span class="comment"></span></div><div class="line"><a name="l00957"></a><span class="lineno"> 957</span> <span class="comment"> if (dm3+em3==0 || dm3+em3==3)</span></div><div class="line"><a name="l00958"></a><span class="lineno"> 958</span> <span class="comment"> {</span></div><div class="line"><a name="l00959"></a><span class="lineno"> 959</span> <span class="comment"> // #7</span></div><div class="line"><a name="l00960"></a><span class="lineno"> 960</span> <span class="comment">// d = (d-e-e)/3;</span></div><div class="line"><a name="l00961"></a><span class="lineno"> 961</span> <span class="comment"> d -= e; d -= e; d /= 3;</span></div><div class="line"><a name="l00962"></a><span class="lineno"> 962</span> <span class="comment"> T = f(A, B, C);</span></div><div class="line"><a name="l00963"></a><span class="lineno"> 963</span> <span class="comment"> B = f(T, A, B);</span></div><div class="line"><a name="l00964"></a><span class="lineno"> 964</span> <span class="comment"> A = X3(A);</span></div><div class="line"><a name="l00965"></a><span class="lineno"> 965</span> <span class="comment"> continue;</span></div><div class="line"><a name="l00966"></a><span class="lineno"> 966</span> <span class="comment"> }</span></div><div class="line"><a name="l00967"></a><span class="lineno"> 967</span> <span class="comment"></span></div><div class="line"><a name="l00968"></a><span class="lineno"> 968</span> <span class="comment"> if (dm3 == em3)</span></div><div class="line"><a name="l00969"></a><span class="lineno"> 969</span> <span class="comment"> {</span></div><div class="line"><a name="l00970"></a><span class="lineno"> 970</span> <span class="comment"> // #8</span></div><div class="line"><a name="l00971"></a><span class="lineno"> 971</span> <span class="comment">// d = (d-e)/3;</span></div><div class="line"><a name="l00972"></a><span class="lineno"> 972</span> <span class="comment"> d -= e; d /= 3;</span></div><div class="line"><a name="l00973"></a><span class="lineno"> 973</span> <span class="comment"> T = f(A, B, C);</span></div><div class="line"><a name="l00974"></a><span class="lineno"> 974</span> <span class="comment"> C = f(A, C, B);</span></div><div class="line"><a name="l00975"></a><span class="lineno"> 975</span> <span class="comment"> B = T;</span></div><div class="line"><a name="l00976"></a><span class="lineno"> 976</span> <span class="comment"> A = X3(A);</span></div><div class="line"><a name="l00977"></a><span class="lineno"> 977</span> <span class="comment"> continue;</span></div><div class="line"><a name="l00978"></a><span class="lineno"> 978</span> <span class="comment"> }</span></div><div class="line"><a name="l00979"></a><span class="lineno"> 979</span> <span class="comment"></span></div><div class="line"><a name="l00980"></a><span class="lineno"> 980</span> <span class="comment"> CRYPTOPP_ASSERT(em2 == 0);</span></div><div class="line"><a name="l00981"></a><span class="lineno"> 981</span> <span class="comment"> // #9</span></div><div class="line"><a name="l00982"></a><span class="lineno"> 982</span> <span class="comment"> e >>= 1;</span></div><div class="line"><a name="l00983"></a><span class="lineno"> 983</span> <span class="comment"> C = f(C, B, A);</span></div><div class="line"><a name="l00984"></a><span class="lineno"> 984</span> <span class="comment"> B = X2(B);</span></div><div class="line"><a name="l00985"></a><span class="lineno"> 985</span> <span class="comment"> }</span></div><div class="line"><a name="l00986"></a><span class="lineno"> 986</span> <span class="comment"></span></div><div class="line"><a name="l00987"></a><span class="lineno"> 987</span> <span class="comment"> A = f(A, B, C);</span></div><div class="line"><a name="l00988"></a><span class="lineno"> 988</span> <span class="comment"> }</span></div><div class="line"><a name="l00989"></a><span class="lineno"> 989</span> <span class="comment"></span></div><div class="line"><a name="l00990"></a><span class="lineno"> 990</span> <span class="comment">#undef f</span></div><div class="line"><a name="l00991"></a><span class="lineno"> 991</span> <span class="comment">#undef X2</span></div><div class="line"><a name="l00992"></a><span class="lineno"> 992</span> <span class="comment">#undef X3</span></div><div class="line"><a name="l00993"></a><span class="lineno"> 993</span> <span class="comment"></span></div><div class="line"><a name="l00994"></a><span class="lineno"> 994</span> <span class="comment"> return m.ConvertOut(A);</span></div><div class="line"><a name="l00995"></a><span class="lineno"> 995</span> <span class="comment">}</span></div><div class="line"><a name="l00996"></a><span class="lineno"> 996</span> <span class="comment">*/</span></div><div class="line"><a name="l00997"></a><span class="lineno"> 997</span> </div><div class="line"><a name="l00998"></a><span class="lineno"><a class="line" href="nbtheory_8h.html#a9b5b91490b1ae3357ab4f0d863f103c1"> 998</a></span> <a class="code" href="class_integer.html">Integer</a> <a class="code" href="nbtheory_8h.html#a9b5b91490b1ae3357ab4f0d863f103c1">InverseLucas</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &e, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &m, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &p, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &q, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &u)</div><div class="line"><a name="l00999"></a><span class="lineno"> 999</span> {</div><div class="line"><a name="l01000"></a><span class="lineno"> 1000</span>  <a class="code" href="class_integer.html">Integer</a> d = (m*m-4);</div><div class="line"><a name="l01001"></a><span class="lineno"> 1001</span>  <a class="code" href="class_integer.html">Integer</a> p2, q2;</div><div class="line"><a name="l01002"></a><span class="lineno"> 1002</span> <span class="preprocessor"> #pragma omp parallel</span></div><div class="line"><a name="l01003"></a><span class="lineno"> 1003</span> <span class="preprocessor"> #pragma omp sections</span></div><div class="line"><a name="l01004"></a><span class="lineno"> 1004</span>  {</div><div class="line"><a name="l01005"></a><span class="lineno"> 1005</span> <span class="preprocessor"> #pragma omp section</span></div><div class="line"><a name="l01006"></a><span class="lineno"> 1006</span>  {</div><div class="line"><a name="l01007"></a><span class="lineno"> 1007</span>  p2 = p-<a class="code" href="nbtheory_8h.html#abffe3c03543252f53fcf59fdb2df765c">Jacobi</a>(d,p);</div><div class="line"><a name="l01008"></a><span class="lineno"> 1008</span>  p2 = <a class="code" href="nbtheory_8h.html#a6f8b2f16d9cb4cdc4bfa5a785928044a">Lucas</a>(<a class="code" href="nbtheory_8h.html#aa88bcc8ea0e0608098a17bec60abe61e">EuclideanMultiplicativeInverse</a>(e,p2), m, p);</div><div class="line"><a name="l01009"></a><span class="lineno"> 1009</span>  }</div><div class="line"><a name="l01010"></a><span class="lineno"> 1010</span> <span class="preprocessor"> #pragma omp section</span></div><div class="line"><a name="l01011"></a><span class="lineno"> 1011</span>  {</div><div class="line"><a name="l01012"></a><span class="lineno"> 1012</span>  q2 = q-<a class="code" href="nbtheory_8h.html#abffe3c03543252f53fcf59fdb2df765c">Jacobi</a>(d,q);</div><div class="line"><a name="l01013"></a><span class="lineno"> 1013</span>  q2 = <a class="code" href="nbtheory_8h.html#a6f8b2f16d9cb4cdc4bfa5a785928044a">Lucas</a>(<a class="code" href="nbtheory_8h.html#aa88bcc8ea0e0608098a17bec60abe61e">EuclideanMultiplicativeInverse</a>(e,q2), m, q);</div><div class="line"><a name="l01014"></a><span class="lineno"> 1014</span>  }</div><div class="line"><a name="l01015"></a><span class="lineno"> 1015</span>  }</div><div class="line"><a name="l01016"></a><span class="lineno"> 1016</span>  <span class="keywordflow">return</span> <a class="code" href="nbtheory_8h.html#ab3fae49135264b5b5afecd0331915040">CRT</a>(p2, p, q2, q, u);</div><div class="line"><a name="l01017"></a><span class="lineno"> 1017</span> }</div><div class="line"><a name="l01018"></a><span class="lineno"> 1018</span> </div><div class="line"><a name="l01019"></a><span class="lineno"><a class="line" href="nbtheory_8h.html#a8e5a50115e2e7f5546884e4b9d9d1f30"> 1019</a></span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> <a class="code" href="nbtheory_8h.html#a8e5a50115e2e7f5546884e4b9d9d1f30">FactoringWorkFactor</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> n)</div><div class="line"><a name="l01020"></a><span class="lineno"> 1020</span> {</div><div class="line"><a name="l01021"></a><span class="lineno"> 1021</span>  <span class="comment">// extrapolated from the table in Odlyzko's "The Future of Integer Factorization"</span></div><div class="line"><a name="l01022"></a><span class="lineno"> 1022</span>  <span class="comment">// updated to reflect the factoring of RSA-130</span></div><div class="line"><a name="l01023"></a><span class="lineno"> 1023</span>  <span class="keywordflow">if</span> (n<5) <span class="keywordflow">return</span> 0;</div><div class="line"><a name="l01024"></a><span class="lineno"> 1024</span>  <span class="keywordflow">else</span> <span class="keywordflow">return</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span>)(2.4 * std::pow((<span class="keywordtype">double</span>)n, 1.0/3.0) * std::pow(log(<span class="keywordtype">double</span>(n)), 2.0/3.0) - 5);</div><div class="line"><a name="l01025"></a><span class="lineno"> 1025</span> }</div><div class="line"><a name="l01026"></a><span class="lineno"> 1026</span> </div><div class="line"><a name="l01027"></a><span class="lineno"><a class="line" href="nbtheory_8h.html#a0b8a9730d2aaeabc3c8582574ab9cf6d"> 1027</a></span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> <a class="code" href="nbtheory_8h.html#a0b8a9730d2aaeabc3c8582574ab9cf6d">DiscreteLogWorkFactor</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> n)</div><div class="line"><a name="l01028"></a><span class="lineno"> 1028</span> {</div><div class="line"><a name="l01029"></a><span class="lineno"> 1029</span>  <span class="comment">// assuming discrete log takes about the same time as factoring</span></div><div class="line"><a name="l01030"></a><span class="lineno"> 1030</span>  <span class="keywordflow">if</span> (n<5) <span class="keywordflow">return</span> 0;</div><div class="line"><a name="l01031"></a><span class="lineno"> 1031</span>  <span class="keywordflow">else</span> <span class="keywordflow">return</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span>)(2.4 * std::pow((<span class="keywordtype">double</span>)n, 1.0/3.0) * std::pow(log(<span class="keywordtype">double</span>(n)), 2.0/3.0) - 5);</div><div class="line"><a name="l01032"></a><span class="lineno"> 1032</span> }</div><div class="line"><a name="l01033"></a><span class="lineno"> 1033</span> </div><div class="line"><a name="l01034"></a><span class="lineno"> 1034</span> <span class="comment">// ********************************************************</span></div><div class="line"><a name="l01035"></a><span class="lineno"> 1035</span> </div><div class="line"><a name="l01036"></a><span class="lineno"><a class="line" href="class_prime_and_generator.html#a86de2822923f884d0d4285d7e6a47015"> 1036</a></span> <span class="keywordtype">void</span> <a class="code" href="class_prime_and_generator.html#a86de2822923f884d0d4285d7e6a47015">PrimeAndGenerator::Generate</a>(<span class="keywordtype">signed</span> <span class="keywordtype">int</span> delta, <a class="code" href="class_random_number_generator.html">RandomNumberGenerator</a> &rng, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> pbits, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> qbits)</div><div class="line"><a name="l01037"></a><span class="lineno"> 1037</span> {</div><div class="line"><a name="l01038"></a><span class="lineno"> 1038</span>  <span class="comment">// no prime exists for delta = -1, qbits = 4, and pbits = 5</span></div><div class="line"><a name="l01039"></a><span class="lineno"> 1039</span>  <a class="code" href="trap_8h.html#adf3b392588bc94cbeae9f415a78c7b95">CRYPTOPP_ASSERT</a>(qbits > 4);</div><div class="line"><a name="l01040"></a><span class="lineno"> 1040</span>  <a class="code" href="trap_8h.html#adf3b392588bc94cbeae9f415a78c7b95">CRYPTOPP_ASSERT</a>(pbits > qbits);</div><div class="line"><a name="l01041"></a><span class="lineno"> 1041</span> </div><div class="line"><a name="l01042"></a><span class="lineno"> 1042</span>  <span class="keywordflow">if</span> (qbits+1 == pbits)</div><div class="line"><a name="l01043"></a><span class="lineno"> 1043</span>  {</div><div class="line"><a name="l01044"></a><span class="lineno"> 1044</span>  <a class="code" href="class_integer.html">Integer</a> minP = <a class="code" href="class_integer.html#ade53248f5dbb520273a70856b975417c">Integer::Power2</a>(pbits-1);</div><div class="line"><a name="l01045"></a><span class="lineno"> 1045</span>  <a class="code" href="class_integer.html">Integer</a> maxP = <a class="code" href="class_integer.html#ade53248f5dbb520273a70856b975417c">Integer::Power2</a>(pbits) - 1;</div><div class="line"><a name="l01046"></a><span class="lineno"> 1046</span>  <span class="keywordtype">bool</span> success = <span class="keyword">false</span>;</div><div class="line"><a name="l01047"></a><span class="lineno"> 1047</span> </div><div class="line"><a name="l01048"></a><span class="lineno"> 1048</span>  <span class="keywordflow">while</span> (!success)</div><div class="line"><a name="l01049"></a><span class="lineno"> 1049</span>  {</div><div class="line"><a name="l01050"></a><span class="lineno"> 1050</span>  p.<a class="code" href="class_integer.html#a62a8829c926b4e421183e76ea4233702">Randomize</a>(rng, minP, maxP, <a class="code" href="class_integer.html#a9b4088ac01abf76b9ba60060abccb7a3ad9b396a7ba736a4ca02db0125cc8c6a4">Integer::ANY</a>, 6+5*delta, 12);</div><div class="line"><a name="l01051"></a><span class="lineno"> 1051</span>  <a class="code" href="class_prime_sieve.html">PrimeSieve</a> sieve(p, <a class="code" href="misc_8h.html#abe412b0409249cb54899e97bc7d86424">STDMIN</a>(p+PrimeSearchInterval(maxP)*12, maxP), 12, delta);</div><div class="line"><a name="l01052"></a><span class="lineno"> 1052</span> </div><div class="line"><a name="l01053"></a><span class="lineno"> 1053</span>  <span class="keywordflow">while</span> (sieve.NextCandidate(p))</div><div class="line"><a name="l01054"></a><span class="lineno"> 1054</span>  {</div><div class="line"><a name="l01055"></a><span class="lineno"> 1055</span>  <a class="code" href="trap_8h.html#adf3b392588bc94cbeae9f415a78c7b95">CRYPTOPP_ASSERT</a>(<a class="code" href="nbtheory_8h.html#a7bfb6022241ff5fb96250e366c68d49e">IsSmallPrime</a>(p) || <a class="code" href="nbtheory_8h.html#a7d7be62fa8075e10432f49cc08273707">SmallDivisorsTest</a>(p));</div><div class="line"><a name="l01056"></a><span class="lineno"> 1056</span>  q = (p-delta) >> 1;</div><div class="line"><a name="l01057"></a><span class="lineno"> 1057</span>  <a class="code" href="trap_8h.html#adf3b392588bc94cbeae9f415a78c7b95">CRYPTOPP_ASSERT</a>(<a class="code" href="nbtheory_8h.html#a7bfb6022241ff5fb96250e366c68d49e">IsSmallPrime</a>(q) || <a class="code" href="nbtheory_8h.html#a7d7be62fa8075e10432f49cc08273707">SmallDivisorsTest</a>(q));</div><div class="line"><a name="l01058"></a><span class="lineno"> 1058</span>  <span class="keywordflow">if</span> (FastProbablePrimeTest(q) && FastProbablePrimeTest(p) && <a class="code" href="nbtheory_8h.html#ae8442dd787d99d3604436a91799552bf">IsPrime</a>(q) && <a class="code" href="nbtheory_8h.html#ae8442dd787d99d3604436a91799552bf">IsPrime</a>(p))</div><div class="line"><a name="l01059"></a><span class="lineno"> 1059</span>  {</div><div class="line"><a name="l01060"></a><span class="lineno"> 1060</span>  success = <span class="keyword">true</span>;</div><div class="line"><a name="l01061"></a><span class="lineno"> 1061</span>  <span class="keywordflow">break</span>;</div><div class="line"><a name="l01062"></a><span class="lineno"> 1062</span>  }</div><div class="line"><a name="l01063"></a><span class="lineno"> 1063</span>  }</div><div class="line"><a name="l01064"></a><span class="lineno"> 1064</span>  }</div><div class="line"><a name="l01065"></a><span class="lineno"> 1065</span> </div><div class="line"><a name="l01066"></a><span class="lineno"> 1066</span>  <span class="keywordflow">if</span> (delta == 1)</div><div class="line"><a name="l01067"></a><span class="lineno"> 1067</span>  {</div><div class="line"><a name="l01068"></a><span class="lineno"> 1068</span>  <span class="comment">// find g such that g is a quadratic residue mod p, then g has order q</span></div><div class="line"><a name="l01069"></a><span class="lineno"> 1069</span>  <span class="comment">// g=4 always works, but this way we get the smallest quadratic residue (other than 1)</span></div><div class="line"><a name="l01070"></a><span class="lineno"> 1070</span>  <span class="keywordflow">for</span> (g=2; <a class="code" href="nbtheory_8h.html#abffe3c03543252f53fcf59fdb2df765c">Jacobi</a>(g, p) != 1; ++g) {}</div><div class="line"><a name="l01071"></a><span class="lineno"> 1071</span>  <span class="comment">// contributed by Walt Tuvell: g should be the following according to the Law of Quadratic Reciprocity</span></div><div class="line"><a name="l01072"></a><span class="lineno"> 1072</span>  <a class="code" href="trap_8h.html#adf3b392588bc94cbeae9f415a78c7b95">CRYPTOPP_ASSERT</a>((p%8==1 || p%8==7) ? g==2 : (p%12==1 || p%12==11) ? g==3 : g==4);</div><div class="line"><a name="l01073"></a><span class="lineno"> 1073</span>  }</div><div class="line"><a name="l01074"></a><span class="lineno"> 1074</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l01075"></a><span class="lineno"> 1075</span>  {</div><div class="line"><a name="l01076"></a><span class="lineno"> 1076</span>  <a class="code" href="trap_8h.html#adf3b392588bc94cbeae9f415a78c7b95">CRYPTOPP_ASSERT</a>(delta == -1);</div><div class="line"><a name="l01077"></a><span class="lineno"> 1077</span>  <span class="comment">// find g such that g*g-4 is a quadratic non-residue,</span></div><div class="line"><a name="l01078"></a><span class="lineno"> 1078</span>  <span class="comment">// and such that g has order q</span></div><div class="line"><a name="l01079"></a><span class="lineno"> 1079</span>  <span class="keywordflow">for</span> (g=3; ; ++g)</div><div class="line"><a name="l01080"></a><span class="lineno"> 1080</span>  <span class="keywordflow">if</span> (<a class="code" href="nbtheory_8h.html#abffe3c03543252f53fcf59fdb2df765c">Jacobi</a>(g*g-4, p)==-1 && <a class="code" href="nbtheory_8h.html#a6f8b2f16d9cb4cdc4bfa5a785928044a">Lucas</a>(q, g, p)==2)</div><div class="line"><a name="l01081"></a><span class="lineno"> 1081</span>  <span class="keywordflow">break</span>;</div><div class="line"><a name="l01082"></a><span class="lineno"> 1082</span>  }</div><div class="line"><a name="l01083"></a><span class="lineno"> 1083</span>  }</div><div class="line"><a name="l01084"></a><span class="lineno"> 1084</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l01085"></a><span class="lineno"> 1085</span>  {</div><div class="line"><a name="l01086"></a><span class="lineno"> 1086</span>  <a class="code" href="class_integer.html">Integer</a> minQ = <a class="code" href="class_integer.html#ade53248f5dbb520273a70856b975417c">Integer::Power2</a>(qbits-1);</div><div class="line"><a name="l01087"></a><span class="lineno"> 1087</span>  <a class="code" href="class_integer.html">Integer</a> maxQ = <a class="code" href="class_integer.html#ade53248f5dbb520273a70856b975417c">Integer::Power2</a>(qbits) - 1;</div><div class="line"><a name="l01088"></a><span class="lineno"> 1088</span>  <a class="code" href="class_integer.html">Integer</a> minP = <a class="code" href="class_integer.html#ade53248f5dbb520273a70856b975417c">Integer::Power2</a>(pbits-1);</div><div class="line"><a name="l01089"></a><span class="lineno"> 1089</span>  <a class="code" href="class_integer.html">Integer</a> maxP = <a class="code" href="class_integer.html#ade53248f5dbb520273a70856b975417c">Integer::Power2</a>(pbits) - 1;</div><div class="line"><a name="l01090"></a><span class="lineno"> 1090</span> </div><div class="line"><a name="l01091"></a><span class="lineno"> 1091</span>  <span class="keywordflow">do</span></div><div class="line"><a name="l01092"></a><span class="lineno"> 1092</span>  {</div><div class="line"><a name="l01093"></a><span class="lineno"> 1093</span>  q.<a class="code" href="class_integer.html#a62a8829c926b4e421183e76ea4233702">Randomize</a>(rng, minQ, maxQ, <a class="code" href="class_integer.html#a9b4088ac01abf76b9ba60060abccb7a3afe686f55e5b6768b20009a12522bd0d9">Integer::PRIME</a>);</div><div class="line"><a name="l01094"></a><span class="lineno"> 1094</span>  } <span class="keywordflow">while</span> (!p.<a class="code" href="class_integer.html#a62a8829c926b4e421183e76ea4233702">Randomize</a>(rng, minP, maxP, <a class="code" href="class_integer.html#a9b4088ac01abf76b9ba60060abccb7a3afe686f55e5b6768b20009a12522bd0d9">Integer::PRIME</a>, delta%q, q));</div><div class="line"><a name="l01095"></a><span class="lineno"> 1095</span> </div><div class="line"><a name="l01096"></a><span class="lineno"> 1096</span>  <span class="comment">// find a random g of order q</span></div><div class="line"><a name="l01097"></a><span class="lineno"> 1097</span>  <span class="keywordflow">if</span> (delta==1)</div><div class="line"><a name="l01098"></a><span class="lineno"> 1098</span>  {</div><div class="line"><a name="l01099"></a><span class="lineno"> 1099</span>  <span class="keywordflow">do</span></div><div class="line"><a name="l01100"></a><span class="lineno"> 1100</span>  {</div><div class="line"><a name="l01101"></a><span class="lineno"> 1101</span>  <a class="code" href="class_integer.html">Integer</a> h(rng, 2, p-2, <a class="code" href="class_integer.html#a9b4088ac01abf76b9ba60060abccb7a3ad9b396a7ba736a4ca02db0125cc8c6a4">Integer::ANY</a>);</div><div class="line"><a name="l01102"></a><span class="lineno"> 1102</span>  g = a_exp_b_mod_c(h, (p-1)/q, p);</div><div class="line"><a name="l01103"></a><span class="lineno"> 1103</span>  } <span class="keywordflow">while</span> (g <= 1);</div><div class="line"><a name="l01104"></a><span class="lineno"> 1104</span>  <a class="code" href="trap_8h.html#adf3b392588bc94cbeae9f415a78c7b95">CRYPTOPP_ASSERT</a>(a_exp_b_mod_c(g, q, p)==1);</div><div class="line"><a name="l01105"></a><span class="lineno"> 1105</span>  }</div><div class="line"><a name="l01106"></a><span class="lineno"> 1106</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l01107"></a><span class="lineno"> 1107</span>  {</div><div class="line"><a name="l01108"></a><span class="lineno"> 1108</span>  <a class="code" href="trap_8h.html#adf3b392588bc94cbeae9f415a78c7b95">CRYPTOPP_ASSERT</a>(delta==-1);</div><div class="line"><a name="l01109"></a><span class="lineno"> 1109</span>  <span class="keywordflow">do</span></div><div class="line"><a name="l01110"></a><span class="lineno"> 1110</span>  {</div><div class="line"><a name="l01111"></a><span class="lineno"> 1111</span>  <a class="code" href="class_integer.html">Integer</a> h(rng, 3, p-1, <a class="code" href="class_integer.html#a9b4088ac01abf76b9ba60060abccb7a3ad9b396a7ba736a4ca02db0125cc8c6a4">Integer::ANY</a>);</div><div class="line"><a name="l01112"></a><span class="lineno"> 1112</span>  <span class="keywordflow">if</span> (<a class="code" href="nbtheory_8h.html#abffe3c03543252f53fcf59fdb2df765c">Jacobi</a>(h*h-4, p)==1)</div><div class="line"><a name="l01113"></a><span class="lineno"> 1113</span>  <span class="keywordflow">continue</span>;</div><div class="line"><a name="l01114"></a><span class="lineno"> 1114</span>  g = <a class="code" href="nbtheory_8h.html#a6f8b2f16d9cb4cdc4bfa5a785928044a">Lucas</a>((p+1)/q, h, p);</div><div class="line"><a name="l01115"></a><span class="lineno"> 1115</span>  } <span class="keywordflow">while</span> (g <= 2);</div><div class="line"><a name="l01116"></a><span class="lineno"> 1116</span>  <a class="code" href="trap_8h.html#adf3b392588bc94cbeae9f415a78c7b95">CRYPTOPP_ASSERT</a>(<a class="code" href="nbtheory_8h.html#a6f8b2f16d9cb4cdc4bfa5a785928044a">Lucas</a>(q, g, p) == 2);</div><div class="line"><a name="l01117"></a><span class="lineno"> 1117</span>  }</div><div class="line"><a name="l01118"></a><span class="lineno"> 1118</span>  }</div><div class="line"><a name="l01119"></a><span class="lineno"> 1119</span> }</div><div class="line"><a name="l01120"></a><span class="lineno"> 1120</span> </div><div class="line"><a name="l01121"></a><span class="lineno"> 1121</span> NAMESPACE_END</div><div class="line"><a name="l01122"></a><span class="lineno"> 1122</span> </div><div class="line"><a name="l01123"></a><span class="lineno"> 1123</span> <span class="preprocessor">#endif</span></div><div class="ttc" id="nbtheory_8h_html_ab3fae49135264b5b5afecd0331915040"><div class="ttname"><a href="nbtheory_8h.html#ab3fae49135264b5b5afecd0331915040">CRT</a></div><div class="ttdeci">Integer CRT(const Integer &xp, const Integer &p, const Integer &xq, const Integer &q, const Integer &u)</div><div class="ttdoc">Chinese Remainder Theorem.</div><div class="ttdef"><b>Definition:</b> <a href="nbtheory_8cpp_source.html#l00553">nbtheory.cpp:553</a></div></div>
<div class="ttc" id="class_invalid_argument_html"><div class="ttname"><a href="class_invalid_argument.html">InvalidArgument</a></div><div class="ttdoc">An invalid argument was detected.</div><div class="ttdef"><b>Definition:</b> <a href="cryptlib_8h_source.html#l00199">cryptlib.h:199</a></div></div>
<div class="ttc" id="class_integer_html_a8c04a3308dd546cac819835922ee8db6"><div class="ttname"><a href="class_integer.html#a8c04a3308dd546cac819835922ee8db6">Integer::WordCount</a></div><div class="ttdeci">unsigned int WordCount() const</div><div class="ttdoc">Determines the number of words required to represent the Integer.</div><div class="ttdef"><b>Definition:</b> <a href="integer_8cpp_source.html#l03305">integer.cpp:3305</a></div></div>
<div class="ttc" id="nbtheory_8h_html_aa41f53fa846ea7546d7269b5d5c6a29f"><div class="ttname"><a href="nbtheory_8h.html#aa41f53fa846ea7546d7269b5d5c6a29f">GetPrimeTable</a></div><div class="ttdeci">const word16 * GetPrimeTable(unsigned int &size)</div><div class="ttdoc">The Small Prime table.</div><div class="ttdef"><b>Definition:</b> <a href="nbtheory_8cpp_source.html#l00053">nbtheory.cpp:53</a></div></div>
<div class="ttc" id="algparam_8h_html"><div class="ttname"><a href="algparam_8h.html">algparam.h</a></div><div class="ttdoc">Classes for working with NameValuePairs.</div></div>
<div class="ttc" id="nbtheory_8h_html_aada479f79cb8988f4df16df1e321fc7b"><div class="ttname"><a href="nbtheory_8h.html#aada479f79cb8988f4df16df1e321fc7b">IsLucasProbablePrime</a></div><div class="ttdeci">bool IsLucasProbablePrime(const Integer &n)</div><div class="ttdoc">Determine if a number is probably prime.</div><div class="ttdef"><b>Definition:</b> <a href="nbtheory_8cpp_source.html#l00155">nbtheory.cpp:155</a></div></div>
<div class="ttc" id="misc_8h_html_a8a2ce94589bb74164d809f4675bd23dd"><div class="ttname"><a href="misc_8h.html#a8a2ce94589bb74164d809f4675bd23dd">SafeConvert</a></div><div class="ttdeci">bool SafeConvert(T1 from, T2 &to)</div><div class="ttdoc">Tests whether a conversion from -> to is safe to perform.</div><div class="ttdef"><b>Definition:</b> <a href="misc_8h_source.html#l00562">misc.h:562</a></div></div>
<div class="ttc" id="struct_new_last_small_prime_squared_html"><div class="ttname"><a href="struct_new_last_small_prime_squared.html">NewLastSmallPrimeSquared</a></div><div class="ttdef"><b>Definition:</b> <a href="nbtheory_8cpp_source.html#l00229">nbtheory.cpp:229</a></div></div>
<div class="ttc" id="class_prime_sieve_html"><div class="ttname"><a href="class_prime_sieve.html">PrimeSieve</a></div><div class="ttdef"><b>Definition:</b> <a href="nbtheory_8cpp_source.html#l00286">nbtheory.cpp:286</a></div></div>
<div class="ttc" id="class_integer_html_a9b4088ac01abf76b9ba60060abccb7a3afe686f55e5b6768b20009a12522bd0d9"><div class="ttname"><a href="class_integer.html#a9b4088ac01abf76b9ba60060abccb7a3afe686f55e5b6768b20009a12522bd0d9">Integer::PRIME</a></div><div class="ttdoc">a number which is probabilistically prime</div><div class="ttdef"><b>Definition:</b> <a href="integer_8h_source.html#l00095">integer.h:95</a></div></div>
<div class="ttc" id="misc_8h_html"><div class="ttname"><a href="misc_8h.html">misc.h</a></div><div class="ttdoc">Utility functions for the Crypto++ library.</div></div>
<div class="ttc" id="class_singleton_html"><div class="ttname"><a href="class_singleton.html">Singleton</a></div><div class="ttdoc">Restricts the instantiation of a class to one static object without locks.</div><div class="ttdef"><b>Definition:</b> <a href="misc_8h_source.html#l00291">misc.h:291</a></div></div>
<div class="ttc" id="class_integer_html_a3acfdfd7aa905d2600073449c31eb3c4"><div class="ttname"><a href="class_integer.html#a3acfdfd7aa905d2600073449c31eb3c4">Integer::IsSquare</a></div><div class="ttdeci">bool IsSquare() const</div><div class="ttdoc">Determine whether this integer is a perfect square.</div><div class="ttdef"><b>Definition:</b> <a href="integer_8cpp_source.html#l04346">integer.cpp:4346</a></div></div>
<div class="ttc" id="nbtheory_8h_html_aaef9ef9567713cd9935e468309ebcc9d"><div class="ttname"><a href="nbtheory_8h.html#aaef9ef9567713cd9935e468309ebcc9d">FirstPrime</a></div><div class="ttdeci">bool FirstPrime(Integer &p, const Integer &max, const Integer &equiv, const Integer &mod, const PrimeSelector *pSelector)</div><div class="ttdoc">Finds a random prime of special form.</div><div class="ttdef"><b>Definition:</b> <a href="nbtheory_8cpp_source.html#l00379">nbtheory.cpp:379</a></div></div>
<div class="ttc" id="nbtheory_8h_html_a7d7be62fa8075e10432f49cc08273707"><div class="ttname"><a href="nbtheory_8h.html#a7d7be62fa8075e10432f49cc08273707">SmallDivisorsTest</a></div><div class="ttdeci">bool SmallDivisorsTest(const Integer &p)</div><div class="ttdoc">Tests whether a number is divisible by a small prime.</div><div class="ttdef"><b>Definition:</b> <a href="nbtheory_8cpp_source.html#l00089">nbtheory.cpp:89</a></div></div>
<div class="ttc" id="class_random_number_generator_html_a96a3eec202b6251f5c94136ab7edbde1"><div class="ttname"><a href="class_random_number_generator.html#a96a3eec202b6251f5c94136ab7edbde1">RandomNumberGenerator::GenerateWord32</a></div><div class="ttdeci">virtual word32 GenerateWord32(word32 min=0, word32 max=0xffffffffUL)</div><div class="ttdoc">Generate a random 32 bit word in the range min to max, inclusive.</div><div class="ttdef"><b>Definition:</b> <a href="cryptlib_8cpp_source.html#l00289">cryptlib.cpp:289</a></div></div>
<div class="ttc" id="nbtheory_8h_html_a9167952dad6998d1b854dee8355b53a0"><div class="ttname"><a href="nbtheory_8h.html#a9167952dad6998d1b854dee8355b53a0">IsStrongLucasProbablePrime</a></div><div class="ttdeci">bool IsStrongLucasProbablePrime(const Integer &n)</div><div class="ttdoc">Determine if a number is probably prime.</div><div class="ttdef"><b>Definition:</b> <a href="nbtheory_8cpp_source.html#l00182">nbtheory.cpp:182</a></div></div>
<div class="ttc" id="class_integer_html_a2e90d8f4c5a13e203b94f9abc24d733f"><div class="ttname"><a href="class_integer.html#a2e90d8f4c5a13e203b94f9abc24d733f">Integer::ConvertToLong</a></div><div class="ttdeci">signed long ConvertToLong() const</div><div class="ttdoc">Convert the Integer to Long.</div><div class="ttdef"><b>Definition:</b> <a href="integer_8cpp_source.html#l02988">integer.cpp:2988</a></div></div>
<div class="ttc" id="class_modular_arithmetic_html_ae4705633e8ca4308894f9a26c6f2881c"><div class="ttname"><a href="class_modular_arithmetic.html#ae4705633e8ca4308894f9a26c6f2881c">ModularArithmetic::Subtract</a></div><div class="ttdeci">const Integer & Subtract(const Integer &a, const Integer &b) const</div><div class="ttdoc">Subtracts elements in the ring.</div><div class="ttdef"><b>Definition:</b> <a href="integer_8cpp_source.html#l04534">integer.cpp:4534</a></div></div>
<div class="ttc" id="nbtheory_8h_html_a4f5215dbaaf83eacf300ef54f0e941fc"><div class="ttname"><a href="nbtheory_8h.html#a4f5215dbaaf83eacf300ef54f0e941fc">MaurerProvablePrime</a></div><div class="ttdeci">Integer MaurerProvablePrime(RandomNumberGenerator &rng, unsigned int bits)</div><div class="ttdoc">Generates a provable prime.</div><div class="ttdef"><b>Definition:</b> <a href="nbtheory_8cpp_source.html#l00510">nbtheory.cpp:510</a></div></div>
<div class="ttc" id="smartptr_8h_html"><div class="ttname"><a href="smartptr_8h.html">smartptr.h</a></div><div class="ttdoc">Classes for automatic resource management.</div></div>
<div class="ttc" id="nbtheory_8h_html_a7bfb6022241ff5fb96250e366c68d49e"><div class="ttname"><a href="nbtheory_8h.html#a7bfb6022241ff5fb96250e366c68d49e">IsSmallPrime</a></div><div class="ttdeci">bool IsSmallPrime(const Integer &p)</div><div class="ttdoc">Tests whether a number is a small prime.</div><div class="ttdef"><b>Definition:</b> <a href="nbtheory_8cpp_source.html#l00060">nbtheory.cpp:60</a></div></div>
<div class="ttc" id="class_integer_html_ad767ae81c89be3804da8785e132d2d1f"><div class="ttname"><a href="class_integer.html#ad767ae81c89be3804da8785e132d2d1f">Integer::IsNegative</a></div><div class="ttdeci">bool IsNegative() const</div><div class="ttdoc">Determines if the Integer is negative.</div><div class="ttdef"><b>Definition:</b> <a href="integer_8h_source.html#l00336">integer.h:336</a></div></div>
<div class="ttc" id="class_random_number_generator_html"><div class="ttname"><a href="class_random_number_generator.html">RandomNumberGenerator</a></div><div class="ttdoc">Interface for random number generators.</div><div class="ttdef"><b>Definition:</b> <a href="cryptlib_8h_source.html#l01330">cryptlib.h:1330</a></div></div>
<div class="ttc" id="stdcpp_8h_html"><div class="ttname"><a href="stdcpp_8h.html">stdcpp.h</a></div><div class="ttdoc">Common C++ header files.</div></div>
<div class="ttc" id="nbtheory_8h_html_abcaf62227292dc648e6f2f11f2a6e158"><div class="ttname"><a href="nbtheory_8h.html#abcaf62227292dc648e6f2f11f2a6e158">IsFermatProbablePrime</a></div><div class="ttdeci">bool IsFermatProbablePrime(const Integer &n, const Integer &b)</div><div class="ttdoc">Determine if a number is probably prime.</div><div class="ttdef"><b>Definition:</b> <a href="nbtheory_8cpp_source.html#l00096">nbtheory.cpp:96</a></div></div>
<div class="ttc" id="class_integer_html_a62a8829c926b4e421183e76ea4233702"><div class="ttname"><a href="class_integer.html#a62a8829c926b4e421183e76ea4233702">Integer::Randomize</a></div><div class="ttdeci">void Randomize(RandomNumberGenerator &rng, size_t bitCount)</div><div class="ttdoc">Set this Integer to random integer.</div><div class="ttdef"><b>Definition:</b> <a href="integer_8cpp_source.html#l03476">integer.cpp:3476</a></div></div>
<div class="ttc" id="nbtheory_8h_html_abffe3c03543252f53fcf59fdb2df765c"><div class="ttname"><a href="nbtheory_8h.html#abffe3c03543252f53fcf59fdb2df765c">Jacobi</a></div><div class="ttdeci">int Jacobi(const Integer &a, const Integer &b)</div><div class="ttdoc">Calculate the Jacobi symbol.</div><div class="ttdef"><b>Definition:</b> <a href="nbtheory_8cpp_source.html#l00785">nbtheory.cpp:785</a></div></div>
<div class="ttc" id="class_integer_html_af805574831ce19221692966e6217e6e0"><div class="ttname"><a href="class_integer.html#af805574831ce19221692966e6217e6e0">Integer::InverseMod</a></div><div class="ttdeci">Integer InverseMod(const Integer &n) const</div><div class="ttdoc">Calculate multiplicative inverse.</div><div class="ttdef"><b>Definition:</b> <a href="integer_8cpp_source.html#l04386">integer.cpp:4386</a></div></div>
<div class="ttc" id="nbtheory_8h_html_abb83c7bbd49b1761028d08a9a1016e68"><div class="ttname"><a href="nbtheory_8h.html#abb83c7bbd49b1761028d08a9a1016e68">ModularSquareRoot</a></div><div class="ttdeci">Integer ModularSquareRoot(const Integer &a, const Integer &p)</div><div class="ttdoc">Extract a modular square root.</div><div class="ttdef"><b>Definition:</b> <a href="nbtheory_8cpp_source.html#l00572">nbtheory.cpp:572</a></div></div>
<div class="ttc" id="class_integer_html_a13ddbfd8e9729932c2a99b0dff530978"><div class="ttname"><a href="class_integer.html#a13ddbfd8e9729932c2a99b0dff530978">Integer::IsPositive</a></div><div class="ttdeci">bool IsPositive() const</div><div class="ttdoc">Determines if the Integer is positive.</div><div class="ttdef"><b>Definition:</b> <a href="integer_8h_source.html#l00342">integer.h:342</a></div></div>
<div class="ttc" id="class_integer_html_a8c070592581bf6c2f928c72bfa1c1638"><div class="ttname"><a href="class_integer.html#a8c070592581bf6c2f928c72bfa1c1638">Integer::One</a></div><div class="ttdeci">static const Integer & One()</div><div class="ttdoc">Integer representing 1.</div><div class="ttdef"><b>Definition:</b> <a href="integer_8cpp_source.html#l04824">integer.cpp:4824</a></div></div>
<div class="ttc" id="nbtheory_8h_html_a9b5b91490b1ae3357ab4f0d863f103c1"><div class="ttname"><a href="nbtheory_8h.html#a9b5b91490b1ae3357ab4f0d863f103c1">InverseLucas</a></div><div class="ttdeci">Integer InverseLucas(const Integer &e, const Integer &m, const Integer &p, const Integer &q, const Integer &u)</div><div class="ttdoc">Calculate the inverse Lucas value.</div><div class="ttdef"><b>Definition:</b> <a href="nbtheory_8cpp_source.html#l00998">nbtheory.cpp:998</a></div></div>
<div class="ttc" id="nbtheory_8h_html_a97c6199f98f7c5174373422d1e1c39af"><div class="ttname"><a href="nbtheory_8h.html#a97c6199f98f7c5174373422d1e1c39af">IsStrongProbablePrime</a></div><div class="ttdeci">bool IsStrongProbablePrime(const Integer &n, const Integer &b)</div><div class="ttdoc">Determine if a number is probably prime.</div><div class="ttdef"><b>Definition:</b> <a href="nbtheory_8cpp_source.html#l00105">nbtheory.cpp:105</a></div></div>
<div class="ttc" id="class_montgomery_representation_html_a502f8e7355d1eb252159c0d6e149379a"><div class="ttname"><a href="class_montgomery_representation.html#a502f8e7355d1eb252159c0d6e149379a">MontgomeryRepresentation::ConvertIn</a></div><div class="ttdeci">Integer ConvertIn(const Integer &a) const</div><div class="ttdoc">Reduces an element in the congruence class.</div><div class="ttdef"><b>Definition:</b> <a href="modarith_8h_source.html#l00292">modarith.h:292</a></div></div>
<div class="ttc" id="classmember__ptr_html"><div class="ttname"><a href="classmember__ptr.html">member_ptr</a></div><div class="ttdoc">Pointer that overloads operator -></div><div class="ttdef"><b>Definition:</b> <a href="smartptr_8h_source.html#l00036">smartptr.h:36</a></div></div>
<div class="ttc" id="nbtheory_8h_html_a40fab13239e32e04892023c81bb42597"><div class="ttname"><a href="nbtheory_8h.html#a40fab13239e32e04892023c81bb42597">MihailescuProvablePrime</a></div><div class="ttdeci">Integer MihailescuProvablePrime(RandomNumberGenerator &rng, unsigned int bits)</div><div class="ttdoc">Generates a provable prime.</div><div class="ttdef"><b>Definition:</b> <a href="nbtheory_8cpp_source.html#l00470">nbtheory.cpp:470</a></div></div>
<div class="ttc" id="nbtheory_8h_html_ac1d98aa1d0ed1df97bf0dc194da5169a"><div class="ttname"><a href="nbtheory_8h.html#ac1d98aa1d0ed1df97bf0dc194da5169a">GCD</a></div><div class="ttdeci">Integer GCD(const Integer &a, const Integer &b)</div><div class="ttdoc">Calculate the greatest common divisor.</div><div class="ttdef"><b>Definition:</b> <a href="nbtheory_8h_source.html#l00142">nbtheory.h:142</a></div></div>
<div class="ttc" id="class_integer_html_a9b4088ac01abf76b9ba60060abccb7a3ad9b396a7ba736a4ca02db0125cc8c6a4"><div class="ttname"><a href="class_integer.html#a9b4088ac01abf76b9ba60060abccb7a3ad9b396a7ba736a4ca02db0125cc8c6a4">Integer::ANY</a></div><div class="ttdoc">a number with no special properties</div><div class="ttdef"><b>Definition:</b> <a href="integer_8h_source.html#l00093">integer.h:93</a></div></div>
<div class="ttc" id="nbtheory_8h_html_a6f8b2f16d9cb4cdc4bfa5a785928044a"><div class="ttname"><a href="nbtheory_8h.html#a6f8b2f16d9cb4cdc4bfa5a785928044a">Lucas</a></div><div class="ttdeci">Integer Lucas(const Integer &e, const Integer &p, const Integer &n)</div><div class="ttdoc">Calculate the Lucas value.</div><div class="ttdef"><b>Definition:</b> <a href="nbtheory_8cpp_source.html#l00812">nbtheory.cpp:812</a></div></div>
<div class="ttc" id="algparam_8h_html_aa13eee74de98cf8aaa7e83f4fae7f28b"><div class="ttname"><a href="algparam_8h.html#aa13eee74de98cf8aaa7e83f4fae7f28b">MakeParameters</a></div><div class="ttdeci">AlgorithmParameters MakeParameters(const char *name, const T &value, bool throwIfNotUsed=true)</div><div class="ttdoc">Create an object that implements NameValuePairs.</div><div class="ttdef"><b>Definition:</b> <a href="algparam_8h_source.html#l00502">algparam.h:502</a></div></div>
<div class="ttc" id="nbtheory_8h_html_a633d17045e229eccc3614426df054463"><div class="ttname"><a href="nbtheory_8h.html#a633d17045e229eccc3614426df054463">VerifyPrime</a></div><div class="ttdeci">bool VerifyPrime(RandomNumberGenerator &rng, const Integer &p, unsigned int level=1)</div><div class="ttdoc">Verifies a number is probably prime.</div><div class="ttdef"><b>Definition:</b> <a href="nbtheory_8cpp_source.html#l00247">nbtheory.cpp:247</a></div></div>
<div class="ttc" id="class_prime_selector_html"><div class="ttname"><a href="class_prime_selector.html">PrimeSelector</a></div><div class="ttdoc">Application callback to signal suitability of a cabdidate prime.</div><div class="ttdef"><b>Definition:</b> <a href="nbtheory_8h_source.html#l00113">nbtheory.h:113</a></div></div>
<div class="ttc" id="class_integer_html_ade53248f5dbb520273a70856b975417c"><div class="ttname"><a href="class_integer.html#ade53248f5dbb520273a70856b975417c">Integer::Power2</a></div><div class="ttdeci">static Integer Power2(size_t e)</div><div class="ttdoc">Exponentiates to a power of 2.</div><div class="ttdef"><b>Definition:</b> <a href="integer_8cpp_source.html#l03055">integer.cpp:3055</a></div></div>
<div class="ttc" id="class_integer_html"><div class="ttname"><a href="class_integer.html">Integer</a></div><div class="ttdoc">Multiple precision integer with arithmetic operations.</div><div class="ttdef"><b>Definition:</b> <a href="integer_8h_source.html#l00049">integer.h:49</a></div></div>
<div class="ttc" id="pch_8h_html"><div class="ttname"><a href="pch_8h.html">pch.h</a></div><div class="ttdoc">Precompiled header file.</div></div>
<div class="ttc" id="misc_8h_html_ac8391e7d9d613a6c401787d2cdab1f51"><div class="ttname"><a href="misc_8h.html#ac8391e7d9d613a6c401787d2cdab1f51">UnsignedMin</a></div><div class="ttdeci">const T1 UnsignedMin(const T1 &a, const T2 &b)</div><div class="ttdoc">Safe comparison of values that could be neagtive and incorrectly promoted.</div><div class="ttdef"><b>Definition:</b> <a href="misc_8h_source.html#l00546">misc.h:546</a></div></div>
<div class="ttc" id="class_montgomery_representation_html_a793d265b8165135e2e972bf333ac5a49"><div class="ttname"><a href="class_montgomery_representation.html#a793d265b8165135e2e972bf333ac5a49">MontgomeryRepresentation::Multiply</a></div><div class="ttdeci">const Integer & Multiply(const Integer &a, const Integer &b) const</div><div class="ttdoc">Multiplies elements in the ring.</div><div class="ttdef"><b>Definition:</b> <a href="integer_8cpp_source.html#l04615">integer.cpp:4615</a></div></div>
<div class="ttc" id="nbtheory_8h_html_ae8442dd787d99d3604436a91799552bf"><div class="ttname"><a href="nbtheory_8h.html#ae8442dd787d99d3604436a91799552bf">IsPrime</a></div><div class="ttdeci">bool IsPrime(const Integer &p)</div><div class="ttdoc">Verifies a number is probably prime.</div><div class="ttdef"><b>Definition:</b> <a href="nbtheory_8cpp_source.html#l00237">nbtheory.cpp:237</a></div></div>
<div class="ttc" id="class_integer_html_af0cb74a45a48e677952166bdac9d82d7"><div class="ttname"><a href="class_integer.html#af0cb74a45a48e677952166bdac9d82d7">Integer::Two</a></div><div class="ttdeci">static const Integer & Two()</div><div class="ttdoc">Integer representing 2.</div><div class="ttdef"><b>Definition:</b> <a href="integer_8cpp_source.html#l04836">integer.cpp:4836</a></div></div>
<div class="ttc" id="class_montgomery_representation_html_a2f24e4fb6d9b9fc9c6b363d41e7ee449"><div class="ttname"><a href="class_montgomery_representation.html#a2f24e4fb6d9b9fc9c6b363d41e7ee449">MontgomeryRepresentation::Square</a></div><div class="ttdeci">const Integer & Square(const Integer &a) const</div><div class="ttdoc">Square an element in the ring.</div><div class="ttdef"><b>Definition:</b> <a href="integer_8cpp_source.html#l04628">integer.cpp:4628</a></div></div>
<div class="ttc" id="class_integer_html_afedf9af097a3417d8bd3742ec53f9593"><div class="ttname"><a href="class_integer.html#afedf9af097a3417d8bd3742ec53f9593">Integer::IsEven</a></div><div class="ttdeci">bool IsEven() const</div><div class="ttdoc">Determines if the Integer is even parity.</div><div class="ttdef"><b>Definition:</b> <a href="integer_8h_source.html#l00348">integer.h:348</a></div></div>
<div class="ttc" id="misc_8h_html_abe412b0409249cb54899e97bc7d86424"><div class="ttname"><a href="misc_8h.html#abe412b0409249cb54899e97bc7d86424">STDMIN</a></div><div class="ttdeci">const T & STDMIN(const T &a, const T &b)</div><div class="ttdoc">Replacement function for std::min.</div><div class="ttdef"><b>Definition:</b> <a href="misc_8h_source.html#l00507">misc.h:507</a></div></div>
<div class="ttc" id="trap_8h_html_adf3b392588bc94cbeae9f415a78c7b95"><div class="ttname"><a href="trap_8h.html#adf3b392588bc94cbeae9f415a78c7b95">CRYPTOPP_ASSERT</a></div><div class="ttdeci">#define CRYPTOPP_ASSERT(exp)</div><div class="ttdoc">Debugging and diagnostic assertion.</div><div class="ttdef"><b>Definition:</b> <a href="trap_8h_source.html#l00060">trap.h:60</a></div></div>
<div class="ttc" id="nbtheory_8h_html_aef5a456e724cba394ff8ad788eae777d"><div class="ttname"><a href="nbtheory_8h.html#aef5a456e724cba394ff8ad788eae777d">TrialDivision</a></div><div class="ttdeci">bool TrialDivision(const Integer &p, unsigned bound)</div><div class="ttdoc">Tests whether a number is divisible by a small prime.</div><div class="ttdef"><b>Definition:</b> <a href="nbtheory_8cpp_source.html#l00071">nbtheory.cpp:71</a></div></div>
<div class="ttc" id="class_integer_html_a867356d88074424328d0ebb9bea63254"><div class="ttname"><a href="class_integer.html#a867356d88074424328d0ebb9bea63254">Integer::BitCount</a></div><div class="ttdeci">unsigned int BitCount() const</div><div class="ttdoc">Determines the number of bits required to represent the Integer.</div><div class="ttdef"><b>Definition:</b> <a href="integer_8cpp_source.html#l03319">integer.cpp:3319</a></div></div>
<div class="ttc" id="nbtheory_8h_html"><div class="ttname"><a href="nbtheory_8h.html">nbtheory.h</a></div><div class="ttdoc">Classes and functions for number theoretic operations.</div></div>
<div class="ttc" id="nbtheory_8h_html_a0b8a9730d2aaeabc3c8582574ab9cf6d"><div class="ttname"><a href="nbtheory_8h.html#a0b8a9730d2aaeabc3c8582574ab9cf6d">DiscreteLogWorkFactor</a></div><div class="ttdeci">unsigned int DiscreteLogWorkFactor(unsigned int bitlength)</div><div class="ttdoc">Estimate work factor.</div><div class="ttdef"><b>Definition:</b> <a href="nbtheory_8cpp_source.html#l01027">nbtheory.cpp:1027</a></div></div>
<div class="ttc" id="nbtheory_8h_html_aad7ca1c53c38a93997327226eddc0240"><div class="ttname"><a href="nbtheory_8h.html#aad7ca1c53c38a93997327226eddc0240">ModularRoot</a></div><div class="ttdeci">Integer ModularRoot(const Integer &a, const Integer &dp, const Integer &dq, const Integer &p, const Integer &q, const Integer &u)</div><div class="ttdoc">Extract a modular root.</div><div class="ttdef"><b>Definition:</b> <a href="nbtheory_8cpp_source.html#l00646">nbtheory.cpp:646</a></div></div>
<div class="ttc" id="nbtheory_8h_html_aa88bcc8ea0e0608098a17bec60abe61e"><div class="ttname"><a href="nbtheory_8h.html#aa88bcc8ea0e0608098a17bec60abe61e">EuclideanMultiplicativeInverse</a></div><div class="ttdeci">Integer EuclideanMultiplicativeInverse(const Integer &a, const Integer &b)</div><div class="ttdoc">Calculate multiplicative inverse.</div><div class="ttdef"><b>Definition:</b> <a href="nbtheory_8h_source.html#l00165">nbtheory.h:165</a></div></div>
<div class="ttc" id="class_integer_html_a7b5e639045868c5ac338f4180e1c7efa"><div class="ttname"><a href="class_integer.html#a7b5e639045868c5ac338f4180e1c7efa">Integer::Squared</a></div><div class="ttdeci">Integer Squared() const</div><div class="ttdoc">Multiply this integer by itself.</div><div class="ttdef"><b>Definition:</b> <a href="integer_8h_source.html#l00609">integer.h:609</a></div></div>
<div class="ttc" id="struct_new_prime_table_html"><div class="ttname"><a href="struct_new_prime_table.html">NewPrimeTable</a></div><div class="ttdef"><b>Definition:</b> <a href="nbtheory_8cpp_source.html#l00023">nbtheory.cpp:23</a></div></div>
<div class="ttc" id="class_montgomery_representation_html"><div class="ttname"><a href="class_montgomery_representation.html">MontgomeryRepresentation</a></div><div class="ttdoc">Performs modular arithmetic in Montgomery representation for increased speed.</div><div class="ttdef"><b>Definition:</b> <a href="modarith_8h_source.html#l00274">modarith.h:274</a></div></div>
<div class="ttc" id="class_algorithm_parameters_html"><div class="ttname"><a href="class_algorithm_parameters.html">AlgorithmParameters</a></div><div class="ttdoc">An object that implements NameValuePairs.</div><div class="ttdef"><b>Definition:</b> <a href="algparam_8h_source.html#l00419">algparam.h:419</a></div></div>
<div class="ttc" id="class_prime_and_generator_html_a86de2822923f884d0d4285d7e6a47015"><div class="ttname"><a href="class_prime_and_generator.html#a86de2822923f884d0d4285d7e6a47015">PrimeAndGenerator::Generate</a></div><div class="ttdeci">void Generate(signed int delta, RandomNumberGenerator &rng, unsigned int pbits, unsigned qbits)</div><div class="ttdoc">Generate a Prime and Generator.</div><div class="ttdef"><b>Definition:</b> <a href="nbtheory_8cpp_source.html#l01036">nbtheory.cpp:1036</a></div></div>
<div class="ttc" id="nbtheory_8h_html_a637fa2abf1a48bc38f3c0d7c7edd679a"><div class="ttname"><a href="nbtheory_8h.html#a637fa2abf1a48bc38f3c0d7c7edd679a">RabinMillerTest</a></div><div class="ttdeci">bool RabinMillerTest(RandomNumberGenerator &rng, const Integer &n, unsigned int rounds)</div><div class="ttdoc">Determine if a number is probably prime.</div><div class="ttdef"><b>Definition:</b> <a href="nbtheory_8cpp_source.html#l00138">nbtheory.cpp:138</a></div></div>
<div class="ttc" id="integer_8h_html"><div class="ttname"><a href="integer_8h.html">integer.h</a></div><div class="ttdoc">Multiple precision integer with arithmetic operations.</div></div>
<div class="ttc" id="class_integer_html_a19b7e6d48b1b57bd4846160ea2928175"><div class="ttname"><a href="class_integer.html#a19b7e6d48b1b57bd4846160ea2928175">Integer::Zero</a></div><div class="ttdeci">static const Integer & Zero()</div><div class="ttdoc">Integer representing 0.</div><div class="ttdef"><b>Definition:</b> <a href="integer_8cpp_source.html#l04812">integer.cpp:4812</a></div></div>
<div class="ttc" id="modarith_8h_html"><div class="ttname"><a href="modarith_8h.html">modarith.h</a></div><div class="ttdoc">Class file for performing modular arithmetic.</div></div>
<div class="ttc" id="namespace_crypto_p_p_html"><div class="ttname"><a href="namespace_crypto_p_p.html">CryptoPP</a></div><div class="ttdoc">Crypto++ library namespace.</div></div>
<div class="ttc" id="nbtheory_8h_html_aa308ad452a47cf22de4ac3204ab09e7d"><div class="ttname"><a href="nbtheory_8h.html#aa308ad452a47cf22de4ac3204ab09e7d">SolveModularQuadraticEquation</a></div><div class="ttdeci">bool SolveModularQuadraticEquation(Integer &r1, Integer &r2, const Integer &a, const Integer &b, const Integer &c, const Integer &p)</div><div class="ttdoc">Solve a Modular Quadratic Equation.</div><div class="ttdef"><b>Definition:</b> <a href="nbtheory_8cpp_source.html#l00621">nbtheory.cpp:621</a></div></div>
<div class="ttc" id="nbtheory_8h_html_a5365cc677fbc93221d9bdfaec442ca3d"><div class="ttname"><a href="nbtheory_8h.html#a5365cc677fbc93221d9bdfaec442ca3d">ModularExponentiation</a></div><div class="ttdeci">Integer ModularExponentiation(const Integer &x, const Integer &e, const Integer &m)</div><div class="ttdoc">Modular exponentiation.</div><div class="ttdef"><b>Definition:</b> <a href="nbtheory_8h_source.html#l00215">nbtheory.h:215</a></div></div>
<div class="ttc" id="class_integer_html_a0e377d23bde55fc7dc6ea2208c587d19"><div class="ttname"><a href="class_integer.html#a0e377d23bde55fc7dc6ea2208c587d19">Integer::GetBit</a></div><div class="ttdeci">bool GetBit(size_t i) const</div><div class="ttdoc">Provides the i-th bit of the Integer.</div><div class="ttdef"><b>Definition:</b> <a href="integer_8cpp_source.html#l03079">integer.cpp:3079</a></div></div>
<div class="ttc" id="nbtheory_8h_html_a8e5a50115e2e7f5546884e4b9d9d1f30"><div class="ttname"><a href="nbtheory_8h.html#a8e5a50115e2e7f5546884e4b9d9d1f30">FactoringWorkFactor</a></div><div class="ttdeci">unsigned int FactoringWorkFactor(unsigned int bitlength)</div><div class="ttdoc">Estimate work factor.</div><div class="ttdef"><b>Definition:</b> <a href="nbtheory_8cpp_source.html#l01019">nbtheory.cpp:1019</a></div></div>
<div class="ttc" id="class_integer_html_aed4bb7208a18b986ef3e1a7d92e06d1d"><div class="ttname"><a href="class_integer.html#aed4bb7208a18b986ef3e1a7d92e06d1d">Integer::IsOdd</a></div><div class="ttdeci">bool IsOdd() const</div><div class="ttdoc">Determines if the Integer is odd parity.</div><div class="ttdef"><b>Definition:</b> <a href="integer_8h_source.html#l00351">integer.h:351</a></div></div>
<div class="ttc" id="class_montgomery_representation_html_a2591b1df42db492ab9792bbe1fc9bf5e"><div class="ttname"><a href="class_montgomery_representation.html#a2591b1df42db492ab9792bbe1fc9bf5e">MontgomeryRepresentation::ConvertOut</a></div><div class="ttdeci">Integer ConvertOut(const Integer &a) const</div><div class="ttdoc">Reduces an element in the congruence class.</div><div class="ttdef"><b>Definition:</b> <a href="integer_8cpp_source.html#l04641">integer.cpp:4641</a></div></div>
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