<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
<meta http-equiv="X-UA-Compatible" content="IE=9"/>
<meta name="generator" content="Doxygen 1.8.14"/>
<meta name="viewport" content="width=device-width, initial-scale=1"/>
<title>Crypto++: modarith.h Source File</title>
<link href="tabs.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="jquery.js"></script>
<script type="text/javascript" src="dynsections.js"></script>
<link href="doxygen.css" rel="stylesheet" type="text/css" />
</head>
<body>
<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
<div id="titlearea">
<table cellspacing="0" cellpadding="0">
<tbody>
<tr style="height: 56px;">
<td id="projectalign" style="padding-left: 0.5em;">
<div id="projectname">Crypto++
 <span id="projectnumber">7.0</span>
</div>
<div id="projectbrief">Free C++ class library of cryptographic schemes</div>
</td>
</tr>
</tbody>
</table>
</div>
<!-- end header part -->
<!-- Generated by Doxygen 1.8.14 -->
<script type="text/javascript" src="menudata.js"></script>
<script type="text/javascript" src="menu.js"></script>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&dn=gpl-2.0.txt GPL-v2 */
$(function() {
initMenu('',false,false,'search.php','Search');
});
/* @license-end */</script>
<div id="main-nav"></div>
</div><!-- top -->
<div class="header">
<div class="headertitle">
<div class="title">modarith.h</div> </div>
</div><!--header-->
<div class="contents">
<a href="modarith_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// modarith.h - 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> <span class="comment"></span></div><div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">/// \file modarith.h</span></div><div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">/// \brief Class file for performing modular arithmetic.</span></div><div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment"></span></div><div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="preprocessor">#ifndef CRYPTOPP_MODARITH_H</span></div><div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="preprocessor">#define CRYPTOPP_MODARITH_H</span></div><div class="line"><a name="l00008"></a><span class="lineno"> 8</span> </div><div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">// implementations are in integer.cpp</span></div><div class="line"><a name="l00010"></a><span class="lineno"> 10</span> </div><div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="preprocessor">#include "<a class="code" href="cryptlib_8h.html">cryptlib.h</a>"</span></div><div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor">#include "<a class="code" href="integer_8h.html">integer.h</a>"</span></div><div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="preprocessor">#include "<a class="code" href="algebra_8h.html">algebra.h</a>"</span></div><div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="preprocessor">#include "<a class="code" href="secblock_8h.html">secblock.h</a>"</span></div><div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="preprocessor">#include "<a class="code" href="misc_8h.html">misc.h</a>"</span></div><div class="line"><a name="l00016"></a><span class="lineno"> 16</span> </div><div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="preprocessor">#if CRYPTOPP_MSC_VERSION</span></div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="preprocessor"># pragma warning(push)</span></div><div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="preprocessor"># pragma warning(disable: 4231 4275)</span></div><div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00021"></a><span class="lineno"> 21</span> </div><div class="line"><a name="l00022"></a><span class="lineno"> 22</span> NAMESPACE_BEGIN(<a class="code" href="namespace_crypto_p_p.html">CryptoPP</a>)</div><div class="line"><a name="l00023"></a><span class="lineno"> 23</span> </div><div class="line"><a name="l00024"></a><span class="lineno"> 24</span> CRYPTOPP_DLL_TEMPLATE_CLASS <a class="code" href="class_abstract_group.html">AbstractGroup<Integer></a>;</div><div class="line"><a name="l00025"></a><span class="lineno"> 25</span> CRYPTOPP_DLL_TEMPLATE_CLASS <a class="code" href="class_abstract_ring.html">AbstractRing<Integer></a>;</div><div class="line"><a name="l00026"></a><span class="lineno"> 26</span> CRYPTOPP_DLL_TEMPLATE_CLASS <a class="code" href="class_abstract_euclidean_domain.html">AbstractEuclideanDomain<Integer></a>;</div><div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment"></span></div><div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="comment">/// \brief Ring of congruence classes modulo n</span></div><div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="comment">/// \details This implementation represents each congruence class as the smallest</span></div><div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="comment">/// non-negative integer in that class.</span></div><div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="comment">/// \details <tt>const Element&</tt> returned by member functions are references</span></div><div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="comment">/// to internal data members. Since each object may have only</span></div><div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="comment">/// one such data member for holding results, the following code</span></div><div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment">/// will produce incorrect results:</span></div><div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment">/// <pre> abcd = group.Add(group.Add(a,b), group.Add(c,d));</pre></span></div><div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment">/// But this should be fine:</span></div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment">/// <pre> abcd = group.Add(a, group.Add(b, group.Add(c,d));</pre></span></div><div class="line"><a name="l00038"></a><span class="lineno"><a class="line" href="class_modular_arithmetic.html"> 38</a></span> <span class="comment"></span><span class="keyword">class </span>CRYPTOPP_DLL <a class="code" href="class_modular_arithmetic.html">ModularArithmetic</a> : <span class="keyword">public</span> <a class="code" href="class_abstract_ring.html">AbstractRing</a><Integer></div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span> {</div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="keyword">public</span>:</div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span> </div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  <span class="keyword">typedef</span> <span class="keywordtype">int</span> RandomizationParameter;</div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  <span class="keyword">typedef</span> <a class="code" href="class_integer.html">Integer</a> <a class="code" href="class_integer.html">Element</a>;</div><div class="line"><a name="l00044"></a><span class="lineno"> 44</span> </div><div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  <span class="keyword">virtual</span> ~<a class="code" href="class_modular_arithmetic.html">ModularArithmetic</a>() {}</div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="comment"></span></div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="comment"> /// \brief Construct a ModularArithmetic</span></div><div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="comment"> /// \param modulus congruence class modulus</span></div><div class="line"><a name="l00049"></a><span class="lineno"><a class="line" href="class_modular_arithmetic.html#a1cdfc924e8d11f9620bd826535aabb62"> 49</a></span> <span class="comment"></span> <a class="code" href="class_modular_arithmetic.html#a1cdfc924e8d11f9620bd826535aabb62">ModularArithmetic</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &modulus = <a class="code" href="class_integer.html#a8c070592581bf6c2f928c72bfa1c1638">Integer::One</a>())</div><div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  : <a class="code" href="class_abstract_ring.html">AbstractRing</a><<a class="code" href="class_integer.html">Integer</a>>(), m_modulus(modulus), m_result((word)0, modulus.reg.size()) {}</div><div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="comment"></span></div><div class="line"><a name="l00052"></a><span class="lineno"> 52</span> <span class="comment"> /// \brief Copy construct a ModularArithmetic</span></div><div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="comment"> /// \param ma other ModularArithmetic</span></div><div class="line"><a name="l00054"></a><span class="lineno"><a class="line" href="class_modular_arithmetic.html#a7a7bf808b07baa755ed9ce9f300ce743"> 54</a></span> <span class="comment"></span> <a class="code" href="class_modular_arithmetic.html#a7a7bf808b07baa755ed9ce9f300ce743">ModularArithmetic</a>(<span class="keyword">const</span> <a class="code" href="class_modular_arithmetic.html">ModularArithmetic</a> &ma)</div><div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  : <a class="code" href="class_abstract_ring.html">AbstractRing</a><<a class="code" href="class_integer.html">Integer</a>>(), m_modulus(ma.m_modulus), m_result((word)0, ma.m_modulus.reg.size()) {}</div><div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <span class="comment"></span></div><div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="comment"> /// \brief Construct a ModularArithmetic</span></div><div class="line"><a name="l00058"></a><span class="lineno"> 58</span> <span class="comment"> /// \param bt BER encoded ModularArithmetic</span></div><div class="line"><a name="l00059"></a><span class="lineno"> 59</span> <span class="comment"></span> <a class="code" href="class_modular_arithmetic.html">ModularArithmetic</a>(<a class="code" href="class_buffered_transformation.html">BufferedTransformation</a> &bt); <span class="comment">// construct from BER encoded parameters</span></div><div class="line"><a name="l00060"></a><span class="lineno"> 60</span> <span class="comment"></span></div><div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="comment"> /// \brief Clone a ModularArithmetic</span></div><div class="line"><a name="l00062"></a><span class="lineno"> 62</span> <span class="comment"> /// \returns pointer to a new ModularArithmetic</span></div><div class="line"><a name="l00063"></a><span class="lineno"> 63</span> <span class="comment"> /// \details Clone effectively copy constructs a new ModularArithmetic. The caller is</span></div><div class="line"><a name="l00064"></a><span class="lineno"> 64</span> <span class="comment"> /// responsible for deleting the pointer returned from this method.</span></div><div class="line"><a name="l00065"></a><span class="lineno"><a class="line" href="class_modular_arithmetic.html#a2ea01ae9e84d5392a8781b99d5cba83f"> 65</a></span> <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="class_modular_arithmetic.html">ModularArithmetic</a> * <a class="code" href="class_modular_arithmetic.html#a2ea01ae9e84d5392a8781b99d5cba83f">Clone</a>()<span class="keyword"> const </span>{<span class="keywordflow">return</span> <span class="keyword">new</span> <a class="code" href="class_modular_arithmetic.html">ModularArithmetic</a>(*<span class="keyword">this</span>);}</div><div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <span class="comment"></span></div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span> <span class="comment"> /// \brief Encodes in DER format</span></div><div class="line"><a name="l00068"></a><span class="lineno"> 68</span> <span class="comment"> /// \param bt BufferedTransformation object</span></div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span> <span class="comment"></span> <span class="keywordtype">void</span> DEREncode(<a class="code" href="class_buffered_transformation.html">BufferedTransformation</a> &bt) <span class="keyword">const</span>;</div><div class="line"><a name="l00070"></a><span class="lineno"> 70</span> <span class="comment"></span></div><div class="line"><a name="l00071"></a><span class="lineno"> 71</span> <span class="comment"> /// \brief Encodes element in DER format</span></div><div class="line"><a name="l00072"></a><span class="lineno"> 72</span> <span class="comment"> /// \param out BufferedTransformation object</span></div><div class="line"><a name="l00073"></a><span class="lineno"> 73</span> <span class="comment"> /// \param a Element to encode</span></div><div class="line"><a name="l00074"></a><span class="lineno"> 74</span> <span class="comment"></span> <span class="keywordtype">void</span> DEREncodeElement(<a class="code" href="class_buffered_transformation.html">BufferedTransformation</a> &out, <span class="keyword">const</span> Element &a) <span class="keyword">const</span>;</div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span> <span class="comment"></span></div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span> <span class="comment"> /// \brief Decodes element in DER format</span></div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="comment"> /// \param in BufferedTransformation object</span></div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span> <span class="comment"> /// \param a Element to decode</span></div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span> <span class="comment"></span> <span class="keywordtype">void</span> BERDecodeElement(<a class="code" href="class_buffered_transformation.html">BufferedTransformation</a> &in, Element &a) <span class="keyword">const</span>;</div><div class="line"><a name="l00080"></a><span class="lineno"> 80</span> <span class="comment"></span></div><div class="line"><a name="l00081"></a><span class="lineno"> 81</span> <span class="comment"> /// \brief Retrieves the modulus</span></div><div class="line"><a name="l00082"></a><span class="lineno"> 82</span> <span class="comment"> /// \returns the modulus</span></div><div class="line"><a name="l00083"></a><span class="lineno"><a class="line" href="class_modular_arithmetic.html#a71a51e5b665bf7fb89af2ccba19f0043"> 83</a></span> <span class="comment"></span> <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a>& <a class="code" href="class_modular_arithmetic.html#a71a51e5b665bf7fb89af2ccba19f0043">GetModulus</a>()<span class="keyword"> const </span>{<span class="keywordflow">return</span> m_modulus;}</div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span> <span class="comment"></span></div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span> <span class="comment"> /// \brief Sets the modulus</span></div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span> <span class="comment"> /// \param newModulus the new modulus</span></div><div class="line"><a name="l00087"></a><span class="lineno"><a class="line" href="class_modular_arithmetic.html#a2d7a07fd3831386eb9315c4e1f5fcf25"> 87</a></span> <span class="comment"></span> <span class="keywordtype">void</span> <a class="code" href="class_modular_arithmetic.html#a2d7a07fd3831386eb9315c4e1f5fcf25">SetModulus</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &newModulus)</div><div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  {m_modulus = newModulus; m_result.reg.<a class="code" href="class_sec_block.html#af9e98d3f4a7af1156fcf3e6e68f4ae5a">resize</a>(m_modulus.reg.size());}</div><div class="line"><a name="l00089"></a><span class="lineno"> 89</span> <span class="comment"></span></div><div class="line"><a name="l00090"></a><span class="lineno"> 90</span> <span class="comment"> /// \brief Retrieves the representation</span></div><div class="line"><a name="l00091"></a><span class="lineno"> 91</span> <span class="comment"> /// \returns true if the if the modulus is in Montgomery form for multiplication, false otherwise</span></div><div class="line"><a name="l00092"></a><span class="lineno"><a class="line" href="class_modular_arithmetic.html#a7a93adfe41f5545dcfaf3ee9f2b49bc3"> 92</a></span> <span class="comment"></span> <span class="keyword">virtual</span> <span class="keywordtype">bool</span> <a class="code" href="class_modular_arithmetic.html#a7a93adfe41f5545dcfaf3ee9f2b49bc3">IsMontgomeryRepresentation</a>()<span class="keyword"> const </span>{<span class="keywordflow">return</span> <span class="keyword">false</span>;}</div><div class="line"><a name="l00093"></a><span class="lineno"> 93</span> <span class="comment"></span></div><div class="line"><a name="l00094"></a><span class="lineno"> 94</span> <span class="comment"> /// \brief Reduces an element in the congruence class</span></div><div class="line"><a name="l00095"></a><span class="lineno"> 95</span> <span class="comment"> /// \param a element to convert</span></div><div class="line"><a name="l00096"></a><span class="lineno"> 96</span> <span class="comment"> /// \returns the reduced element</span></div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span> <span class="comment"> /// \details ConvertIn is useful for derived classes, like MontgomeryRepresentation, which</span></div><div class="line"><a name="l00098"></a><span class="lineno"> 98</span> <span class="comment"> /// must convert between representations.</span></div><div class="line"><a name="l00099"></a><span class="lineno"><a class="line" href="class_modular_arithmetic.html#afc5cb8d95e05c9f8975b1b940218d07c"> 99</a></span> <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="class_integer.html">Integer</a> <a class="code" href="class_modular_arithmetic.html#afc5cb8d95e05c9f8975b1b940218d07c">ConvertIn</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &a)<span class="keyword"> const</span></div><div class="line"><a name="l00100"></a><span class="lineno"> 100</span> <span class="keyword"> </span>{<span class="keywordflow">return</span> a%m_modulus;}</div><div class="line"><a name="l00101"></a><span class="lineno"> 101</span> <span class="comment"></span></div><div class="line"><a name="l00102"></a><span class="lineno"> 102</span> <span class="comment"> /// \brief Reduces an element in the congruence class</span></div><div class="line"><a name="l00103"></a><span class="lineno"> 103</span> <span class="comment"> /// \param a element to convert</span></div><div class="line"><a name="l00104"></a><span class="lineno"> 104</span> <span class="comment"> /// \returns the reduced element</span></div><div class="line"><a name="l00105"></a><span class="lineno"> 105</span> <span class="comment"> /// \details ConvertOut is useful for derived classes, like MontgomeryRepresentation, which</span></div><div class="line"><a name="l00106"></a><span class="lineno"> 106</span> <span class="comment"> /// must convert between representations.</span></div><div class="line"><a name="l00107"></a><span class="lineno"><a class="line" href="class_modular_arithmetic.html#ac97e7eea935290b4af9e89591f06f4cf"> 107</a></span> <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="class_integer.html">Integer</a> <a class="code" href="class_modular_arithmetic.html#ac97e7eea935290b4af9e89591f06f4cf">ConvertOut</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &a)<span class="keyword"> const</span></div><div class="line"><a name="l00108"></a><span class="lineno"> 108</span> <span class="keyword"> </span>{<span class="keywordflow">return</span> a;}</div><div class="line"><a name="l00109"></a><span class="lineno"> 109</span> <span class="comment"></span></div><div class="line"><a name="l00110"></a><span class="lineno"> 110</span> <span class="comment"> /// \brief Divides an element by 2</span></div><div class="line"><a name="l00111"></a><span class="lineno"> 111</span> <span class="comment"> /// \param a element to convert</span></div><div class="line"><a name="l00112"></a><span class="lineno"> 112</span> <span class="comment"></span> <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a>& Half(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &a) <span class="keyword">const</span>;</div><div class="line"><a name="l00113"></a><span class="lineno"> 113</span> <span class="comment"></span></div><div class="line"><a name="l00114"></a><span class="lineno"> 114</span> <span class="comment"> /// \brief Compare two elements for equality</span></div><div class="line"><a name="l00115"></a><span class="lineno"> 115</span> <span class="comment"> /// \param a first element</span></div><div class="line"><a name="l00116"></a><span class="lineno"> 116</span> <span class="comment"> /// \param b second element</span></div><div class="line"><a name="l00117"></a><span class="lineno"> 117</span> <span class="comment"> /// \returns true if the elements are equal, false otherwise</span></div><div class="line"><a name="l00118"></a><span class="lineno"> 118</span> <span class="comment"> /// \details Equal() tests the elements for equality using <tt>a==b</tt></span></div><div class="line"><a name="l00119"></a><span class="lineno"><a class="line" href="class_modular_arithmetic.html#a89c5edea6e87341761c35ab03a46bcc0"> 119</a></span> <span class="comment"></span> <span class="keywordtype">bool</span> <a class="code" href="class_modular_arithmetic.html#a89c5edea6e87341761c35ab03a46bcc0">Equal</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> &b)<span class="keyword"> const</span></div><div class="line"><a name="l00120"></a><span class="lineno"> 120</span> <span class="keyword"> </span>{<span class="keywordflow">return</span> a==b;}</div><div class="line"><a name="l00121"></a><span class="lineno"> 121</span> <span class="comment"></span></div><div class="line"><a name="l00122"></a><span class="lineno"> 122</span> <span class="comment"> /// \brief Provides the Identity element</span></div><div class="line"><a name="l00123"></a><span class="lineno"> 123</span> <span class="comment"> /// \returns the Identity element</span></div><div class="line"><a name="l00124"></a><span class="lineno"><a class="line" href="class_modular_arithmetic.html#abd2425e1caf5af1a290b424cadb1517c"> 124</a></span> <span class="comment"></span> <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a>& <a class="code" href="class_modular_arithmetic.html#abd2425e1caf5af1a290b424cadb1517c">Identity</a>()<span class="keyword"> const</span></div><div class="line"><a name="l00125"></a><span class="lineno"> 125</span> <span class="keyword"> </span>{<span class="keywordflow">return</span> <a class="code" href="class_integer.html#a19b7e6d48b1b57bd4846160ea2928175">Integer::Zero</a>();}</div><div class="line"><a name="l00126"></a><span class="lineno"> 126</span> <span class="comment"></span></div><div class="line"><a name="l00127"></a><span class="lineno"> 127</span> <span class="comment"> /// \brief Adds elements in the ring</span></div><div class="line"><a name="l00128"></a><span class="lineno"> 128</span> <span class="comment"> /// \param a first element</span></div><div class="line"><a name="l00129"></a><span class="lineno"> 129</span> <span class="comment"> /// \param b second element</span></div><div class="line"><a name="l00130"></a><span class="lineno"> 130</span> <span class="comment"> /// \returns the sum of <tt>a</tt> and <tt>b</tt></span></div><div class="line"><a name="l00131"></a><span class="lineno"> 131</span> <span class="comment"></span> <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a>& <a class="code" href="class_abstract_group.html#aa813430d9e4244de24c487d090eb5797">Add</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> &b) <span class="keyword">const</span>;</div><div class="line"><a name="l00132"></a><span class="lineno"> 132</span> <span class="comment"></span></div><div class="line"><a name="l00133"></a><span class="lineno"> 133</span> <span class="comment"> /// \brief TODO</span></div><div class="line"><a name="l00134"></a><span class="lineno"> 134</span> <span class="comment"> /// \param a first element</span></div><div class="line"><a name="l00135"></a><span class="lineno"> 135</span> <span class="comment"> /// \param b second element</span></div><div class="line"><a name="l00136"></a><span class="lineno"> 136</span> <span class="comment"> /// \returns TODO</span></div><div class="line"><a name="l00137"></a><span class="lineno"> 137</span> <span class="comment"></span> <a class="code" href="class_integer.html">Integer</a>& <a class="code" href="class_abstract_group.html#ab03cc0a23f23c6aa1c003e11f9abb8c5">Accumulate</a>(<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>;</div><div class="line"><a name="l00138"></a><span class="lineno"> 138</span> <span class="comment"></span></div><div class="line"><a name="l00139"></a><span class="lineno"> 139</span> <span class="comment"> /// \brief Inverts the element in the ring</span></div><div class="line"><a name="l00140"></a><span class="lineno"> 140</span> <span class="comment"> /// \param a first element</span></div><div class="line"><a name="l00141"></a><span class="lineno"> 141</span> <span class="comment"> /// \returns the inverse of the element</span></div><div class="line"><a name="l00142"></a><span class="lineno"> 142</span> <span class="comment"></span> <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a>& <a class="code" href="class_abstract_group.html#ab22563bc0dcb544399d7e22b3589e165">Inverse</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &a) <span class="keyword">const</span>;</div><div class="line"><a name="l00143"></a><span class="lineno"> 143</span> <span class="comment"></span></div><div class="line"><a name="l00144"></a><span class="lineno"> 144</span> <span class="comment"> /// \brief Subtracts elements in the ring</span></div><div class="line"><a name="l00145"></a><span class="lineno"> 145</span> <span class="comment"> /// \param a first element</span></div><div class="line"><a name="l00146"></a><span class="lineno"> 146</span> <span class="comment"> /// \param b second element</span></div><div class="line"><a name="l00147"></a><span class="lineno"> 147</span> <span class="comment"> /// \returns the difference of <tt>a</tt> and <tt>b</tt>. The element <tt>a</tt> must provide a Subtract member function.</span></div><div class="line"><a name="l00148"></a><span class="lineno"> 148</span> <span class="comment"></span> <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a>& <a class="code" href="class_abstract_group.html#aa19e1bef00198fb30eb01df3f7076717">Subtract</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> &b) <span class="keyword">const</span>;</div><div class="line"><a name="l00149"></a><span class="lineno"> 149</span> <span class="comment"></span></div><div class="line"><a name="l00150"></a><span class="lineno"> 150</span> <span class="comment"> /// \brief TODO</span></div><div class="line"><a name="l00151"></a><span class="lineno"> 151</span> <span class="comment"> /// \param a first element</span></div><div class="line"><a name="l00152"></a><span class="lineno"> 152</span> <span class="comment"> /// \param b second element</span></div><div class="line"><a name="l00153"></a><span class="lineno"> 153</span> <span class="comment"> /// \returns TODO</span></div><div class="line"><a name="l00154"></a><span class="lineno"> 154</span> <span class="comment"></span> <a class="code" href="class_integer.html">Integer</a>& <a class="code" href="class_abstract_group.html#a40f7de55eddc193e07a7c3b5acad781a">Reduce</a>(<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>;</div><div class="line"><a name="l00155"></a><span class="lineno"> 155</span> <span class="comment"></span></div><div class="line"><a name="l00156"></a><span class="lineno"> 156</span> <span class="comment"> /// \brief Doubles an element in the ring</span></div><div class="line"><a name="l00157"></a><span class="lineno"> 157</span> <span class="comment"> /// \param a the element</span></div><div class="line"><a name="l00158"></a><span class="lineno"> 158</span> <span class="comment"> /// \returns the element doubled</span></div><div class="line"><a name="l00159"></a><span class="lineno"> 159</span> <span class="comment"> /// \details Double returns <tt>Add(a, a)</tt>. The element <tt>a</tt> must provide an Add member function.</span></div><div class="line"><a name="l00160"></a><span class="lineno"><a class="line" href="class_modular_arithmetic.html#a042dc36ae961ede73694e4c5dcf7cbbc"> 160</a></span> <span class="comment"></span> <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a>& <a class="code" href="class_modular_arithmetic.html#a042dc36ae961ede73694e4c5dcf7cbbc">Double</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &a)<span class="keyword"> const</span></div><div class="line"><a name="l00161"></a><span class="lineno"> 161</span> <span class="keyword"> </span>{<span class="keywordflow">return</span> <a class="code" href="class_abstract_group.html#aa813430d9e4244de24c487d090eb5797">Add</a>(a, a);}</div><div class="line"><a name="l00162"></a><span class="lineno"> 162</span> <span class="comment"></span></div><div class="line"><a name="l00163"></a><span class="lineno"> 163</span> <span class="comment"> /// \brief Retrieves the multiplicative identity</span></div><div class="line"><a name="l00164"></a><span class="lineno"> 164</span> <span class="comment"> /// \returns the multiplicative identity</span></div><div class="line"><a name="l00165"></a><span class="lineno"> 165</span> <span class="comment"> /// \details the base class implementations returns 1.</span></div><div class="line"><a name="l00166"></a><span class="lineno"><a class="line" href="class_modular_arithmetic.html#af942a7ca057b363cb7a4c74f15a9530e"> 166</a></span> <span class="comment"></span> <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a>& <a class="code" href="class_modular_arithmetic.html#af942a7ca057b363cb7a4c74f15a9530e">MultiplicativeIdentity</a>()<span class="keyword"> const</span></div><div class="line"><a name="l00167"></a><span class="lineno"> 167</span> <span class="keyword"> </span>{<span class="keywordflow">return</span> <a class="code" href="class_integer.html#a8c070592581bf6c2f928c72bfa1c1638">Integer::One</a>();}</div><div class="line"><a name="l00168"></a><span class="lineno"> 168</span> <span class="comment"></span></div><div class="line"><a name="l00169"></a><span class="lineno"> 169</span> <span class="comment"> /// \brief Multiplies elements in the ring</span></div><div class="line"><a name="l00170"></a><span class="lineno"> 170</span> <span class="comment"> /// \param a the multiplicand</span></div><div class="line"><a name="l00171"></a><span class="lineno"> 171</span> <span class="comment"> /// \param b the multiplier</span></div><div class="line"><a name="l00172"></a><span class="lineno"> 172</span> <span class="comment"> /// \returns the product of a and b</span></div><div class="line"><a name="l00173"></a><span class="lineno"> 173</span> <span class="comment"> /// \details Multiply returns <tt>a*b\%n</tt>.</span></div><div class="line"><a name="l00174"></a><span class="lineno"><a class="line" href="class_modular_arithmetic.html#a3b88a85b11eb1a826d26d01bdaafbf0a"> 174</a></span> <span class="comment"></span> <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a>& <a class="code" href="class_modular_arithmetic.html#a3b88a85b11eb1a826d26d01bdaafbf0a">Multiply</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> &b)<span class="keyword"> const</span></div><div class="line"><a name="l00175"></a><span class="lineno"> 175</span> <span class="keyword"> </span>{<span class="keywordflow">return</span> m_result1 = a*b%m_modulus;}</div><div class="line"><a name="l00176"></a><span class="lineno"> 176</span> <span class="comment"></span></div><div class="line"><a name="l00177"></a><span class="lineno"> 177</span> <span class="comment"> /// \brief Square an element in the ring</span></div><div class="line"><a name="l00178"></a><span class="lineno"> 178</span> <span class="comment"> /// \param a the element</span></div><div class="line"><a name="l00179"></a><span class="lineno"> 179</span> <span class="comment"> /// \returns the element squared</span></div><div class="line"><a name="l00180"></a><span class="lineno"> 180</span> <span class="comment"> /// \details Square returns <tt>a*a\%n</tt>. The element <tt>a</tt> must provide a Square member function.</span></div><div class="line"><a name="l00181"></a><span class="lineno"><a class="line" href="class_modular_arithmetic.html#a7f74883ad789f0db51ed9b45385c14db"> 181</a></span> <span class="comment"></span> <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a>& <a class="code" href="class_modular_arithmetic.html#a7f74883ad789f0db51ed9b45385c14db">Square</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &a)<span class="keyword"> const</span></div><div class="line"><a name="l00182"></a><span class="lineno"> 182</span> <span class="keyword"> </span>{<span class="keywordflow">return</span> m_result1 = a.Squared()%m_modulus;}</div><div class="line"><a name="l00183"></a><span class="lineno"> 183</span> <span class="comment"></span></div><div class="line"><a name="l00184"></a><span class="lineno"> 184</span> <span class="comment"> /// \brief Determines whether an element is a unit in the ring</span></div><div class="line"><a name="l00185"></a><span class="lineno"> 185</span> <span class="comment"> /// \param a the element</span></div><div class="line"><a name="l00186"></a><span class="lineno"> 186</span> <span class="comment"> /// \returns true if the element is a unit after reduction, false otherwise.</span></div><div class="line"><a name="l00187"></a><span class="lineno"><a class="line" href="class_modular_arithmetic.html#a0d8edd3e4ff60627b92e93ebd00cdfb3"> 187</a></span> <span class="comment"></span> <span class="keywordtype">bool</span> <a class="code" href="class_modular_arithmetic.html#a0d8edd3e4ff60627b92e93ebd00cdfb3">IsUnit</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &a)<span class="keyword"> const</span></div><div class="line"><a name="l00188"></a><span class="lineno"> 188</span> <span class="keyword"> </span>{<span class="keywordflow">return</span> <a class="code" href="class_integer.html#a2d4d29937f8ef666717530b30f137c37">Integer::Gcd</a>(a, m_modulus).<a class="code" href="class_integer.html#aea313b73beda59a8c4ee2de11d637412">IsUnit</a>();}</div><div class="line"><a name="l00189"></a><span class="lineno"> 189</span> <span class="comment"></span></div><div class="line"><a name="l00190"></a><span class="lineno"> 190</span> <span class="comment"> /// \brief Calculate the multiplicative inverse of an element in the ring</span></div><div class="line"><a name="l00191"></a><span class="lineno"> 191</span> <span class="comment"> /// \param a the element</span></div><div class="line"><a name="l00192"></a><span class="lineno"> 192</span> <span class="comment"> /// \details MultiplicativeInverse returns <tt>a<sup>-1</sup>\%n</tt>. The element <tt>a</tt> must</span></div><div class="line"><a name="l00193"></a><span class="lineno"> 193</span> <span class="comment"> /// provide a InverseMod member function.</span></div><div class="line"><a name="l00194"></a><span class="lineno"><a class="line" href="class_modular_arithmetic.html#a149c6c7abe3e1729880658db5650e48a"> 194</a></span> <span class="comment"></span> <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a>& <a class="code" href="class_modular_arithmetic.html#a149c6c7abe3e1729880658db5650e48a">MultiplicativeInverse</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &a)<span class="keyword"> const</span></div><div class="line"><a name="l00195"></a><span class="lineno"> 195</span> <span class="keyword"> </span>{<span class="keywordflow">return</span> m_result1 = a.InverseMod(m_modulus);}</div><div class="line"><a name="l00196"></a><span class="lineno"> 196</span> <span class="comment"></span></div><div class="line"><a name="l00197"></a><span class="lineno"> 197</span> <span class="comment"> /// \brief Divides elements in the ring</span></div><div class="line"><a name="l00198"></a><span class="lineno"> 198</span> <span class="comment"> /// \param a the dividend</span></div><div class="line"><a name="l00199"></a><span class="lineno"> 199</span> <span class="comment"> /// \param b the divisor</span></div><div class="line"><a name="l00200"></a><span class="lineno"> 200</span> <span class="comment"> /// \returns the quotient</span></div><div class="line"><a name="l00201"></a><span class="lineno"> 201</span> <span class="comment"> /// \details Divide returns <tt>a*b<sup>-1</sup>\%n</tt>.</span></div><div class="line"><a name="l00202"></a><span class="lineno"><a class="line" href="class_modular_arithmetic.html#a584d214676856d1463e14c6407d1cd31"> 202</a></span> <span class="comment"></span> <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a>& <a class="code" href="class_modular_arithmetic.html#a584d214676856d1463e14c6407d1cd31">Divide</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> &b)<span class="keyword"> const</span></div><div class="line"><a name="l00203"></a><span class="lineno"> 203</span> <span class="keyword"> </span>{<span class="keywordflow">return</span> <a class="code" href="class_abstract_ring.html#a4ba8818fc72fa298cd52fd483bdd6ad4">Multiply</a>(a, <a class="code" href="class_abstract_ring.html#aba109f4e7932d77a8251c1ec20627571">MultiplicativeInverse</a>(b));}</div><div class="line"><a name="l00204"></a><span class="lineno"> 204</span> <span class="comment"></span></div><div class="line"><a name="l00205"></a><span class="lineno"> 205</span> <span class="comment"> /// \brief TODO</span></div><div class="line"><a name="l00206"></a><span class="lineno"> 206</span> <span class="comment"> /// \param x first element</span></div><div class="line"><a name="l00207"></a><span class="lineno"> 207</span> <span class="comment"> /// \param e1 first exponent</span></div><div class="line"><a name="l00208"></a><span class="lineno"> 208</span> <span class="comment"> /// \param y second element</span></div><div class="line"><a name="l00209"></a><span class="lineno"> 209</span> <span class="comment"> /// \param e2 second exponent</span></div><div class="line"><a name="l00210"></a><span class="lineno"> 210</span> <span class="comment"> /// \returns TODO</span></div><div class="line"><a name="l00211"></a><span class="lineno"> 211</span> <span class="comment"></span> <a class="code" href="class_integer.html">Integer</a> <a class="code" href="class_abstract_ring.html#adb4d33ac59a8f8bff1752b75809136e6">CascadeExponentiate</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &x, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &e1, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &y, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &e2) <span class="keyword">const</span>;</div><div class="line"><a name="l00212"></a><span class="lineno"> 212</span> <span class="comment"></span></div><div class="line"><a name="l00213"></a><span class="lineno"> 213</span> <span class="comment"> /// \brief Exponentiates a base to multiple exponents in the ring</span></div><div class="line"><a name="l00214"></a><span class="lineno"> 214</span> <span class="comment"> /// \param results an array of Elements</span></div><div class="line"><a name="l00215"></a><span class="lineno"> 215</span> <span class="comment"> /// \param base the base to raise to the exponents</span></div><div class="line"><a name="l00216"></a><span class="lineno"> 216</span> <span class="comment"> /// \param exponents an array of exponents</span></div><div class="line"><a name="l00217"></a><span class="lineno"> 217</span> <span class="comment"> /// \param exponentsCount the number of exponents in the array</span></div><div class="line"><a name="l00218"></a><span class="lineno"> 218</span> <span class="comment"> /// \details SimultaneousExponentiate() raises the base to each exponent in the exponents array and stores the</span></div><div class="line"><a name="l00219"></a><span class="lineno"> 219</span> <span class="comment"> /// result at the respective position in the results array.</span></div><div class="line"><a name="l00220"></a><span class="lineno"> 220</span> <span class="comment"> /// \details SimultaneousExponentiate() must be implemented in a derived class.</span></div><div class="line"><a name="l00221"></a><span class="lineno"> 221</span> <span class="comment"> /// \pre <tt>COUNTOF(results) == exponentsCount</tt></span></div><div class="line"><a name="l00222"></a><span class="lineno"> 222</span> <span class="comment"> /// \pre <tt>COUNTOF(exponents) == exponentsCount</tt></span></div><div class="line"><a name="l00223"></a><span class="lineno"> 223</span> <span class="comment"></span> <span class="keywordtype">void</span> <a class="code" href="class_abstract_ring.html#a63530b69e7bfa78e5ee7b072cc798f0a">SimultaneousExponentiate</a>(Element *results, <span class="keyword">const</span> Element &base, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> *exponents, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> exponentsCount) <span class="keyword">const</span>;</div><div class="line"><a name="l00224"></a><span class="lineno"> 224</span> <span class="comment"></span></div><div class="line"><a name="l00225"></a><span class="lineno"> 225</span> <span class="comment"> /// \brief Provides the maximum bit size of an element in the ring</span></div><div class="line"><a name="l00226"></a><span class="lineno"> 226</span> <span class="comment"> /// \returns maximum bit size of an element</span></div><div class="line"><a name="l00227"></a><span class="lineno"><a class="line" href="class_modular_arithmetic.html#a3c802233b0edf8df4228d65082ff37fa"> 227</a></span> <span class="comment"></span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> <a class="code" href="class_modular_arithmetic.html#a3c802233b0edf8df4228d65082ff37fa">MaxElementBitLength</a>()<span class="keyword"> const</span></div><div class="line"><a name="l00228"></a><span class="lineno"> 228</span> <span class="keyword"> </span>{<span class="keywordflow">return</span> (m_modulus-1).BitCount();}</div><div class="line"><a name="l00229"></a><span class="lineno"> 229</span> <span class="comment"></span></div><div class="line"><a name="l00230"></a><span class="lineno"> 230</span> <span class="comment"> /// \brief Provides the maximum byte size of an element in the ring</span></div><div class="line"><a name="l00231"></a><span class="lineno"> 231</span> <span class="comment"> /// \returns maximum byte size of an element</span></div><div class="line"><a name="l00232"></a><span class="lineno"><a class="line" href="class_modular_arithmetic.html#a5897aea2ee78595979f8f261130c93ee"> 232</a></span> <span class="comment"></span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> <a class="code" href="class_modular_arithmetic.html#a5897aea2ee78595979f8f261130c93ee">MaxElementByteLength</a>()<span class="keyword"> const</span></div><div class="line"><a name="l00233"></a><span class="lineno"> 233</span> <span class="keyword"> </span>{<span class="keywordflow">return</span> (m_modulus-1).ByteCount();}</div><div class="line"><a name="l00234"></a><span class="lineno"> 234</span> <span class="comment"></span></div><div class="line"><a name="l00235"></a><span class="lineno"> 235</span> <span class="comment"> /// \brief Provides a random element in the ring</span></div><div class="line"><a name="l00236"></a><span class="lineno"> 236</span> <span class="comment"> /// \param rng RandomNumberGenerator used to generate material</span></div><div class="line"><a name="l00237"></a><span class="lineno"> 237</span> <span class="comment"> /// \param ignore_for_now unused</span></div><div class="line"><a name="l00238"></a><span class="lineno"> 238</span> <span class="comment"> /// \returns a random element that is uniformly distributed</span></div><div class="line"><a name="l00239"></a><span class="lineno"> 239</span> <span class="comment"> /// \details RandomElement constructs a new element in the range <tt>[0,n-1]</tt>, inclusive.</span></div><div class="line"><a name="l00240"></a><span class="lineno"> 240</span> <span class="comment"> /// The element's class must provide a constructor with the signature <tt>Element(RandomNumberGenerator rng,</span></div><div class="line"><a name="l00241"></a><span class="lineno"> 241</span> <span class="comment"> /// Element min, Element max)</tt>.</span></div><div class="line"><a name="l00242"></a><span class="lineno"><a class="line" href="class_modular_arithmetic.html#a6abf94f5924223c316c04752ba39795a"> 242</a></span> <span class="comment"></span> <a class="code" href="class_integer.html">Element</a> <a class="code" href="class_modular_arithmetic.html#a6abf94f5924223c316c04752ba39795a">RandomElement</a>(<a class="code" href="class_random_number_generator.html">RandomNumberGenerator</a> &rng , <span class="keyword">const</span> RandomizationParameter &ignore_for_now = 0) const</div><div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  <span class="comment">// left RandomizationParameter arg as ref in case RandomizationParameter becomes a more complicated struct</span></div><div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  {</div><div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  CRYPTOPP_UNUSED(ignore_for_now);</div><div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  <span class="keywordflow">return</span> <a class="code" href="class_integer.html">Element</a>(rng, <a class="code" href="class_integer.html#a19b7e6d48b1b57bd4846160ea2928175">Integer::Zero</a>(), m_modulus - <a class="code" href="class_integer.html#a8c070592581bf6c2f928c72bfa1c1638">Integer::One</a>()) ;</div><div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  }</div><div class="line"><a name="l00248"></a><span class="lineno"> 248</span> <span class="comment"></span></div><div class="line"><a name="l00249"></a><span class="lineno"> 249</span> <span class="comment"> /// \brief Compares two ModularArithmetic for equality</span></div><div class="line"><a name="l00250"></a><span class="lineno"> 250</span> <span class="comment"> /// \param rhs other ModularArithmetic</span></div><div class="line"><a name="l00251"></a><span class="lineno"> 251</span> <span class="comment"> /// \returns true if this is equal to the other, false otherwise</span></div><div class="line"><a name="l00252"></a><span class="lineno"> 252</span> <span class="comment"> /// \details The operator tests for equality using <tt>this.m_modulus == rhs.m_modulus</tt>.</span></div><div class="line"><a name="l00253"></a><span class="lineno"><a class="line" href="class_modular_arithmetic.html#a0ebc62368fdab13aae9521778beeea4c"> 253</a></span> <span class="comment"></span> <span class="keywordtype">bool</span> <a class="code" href="class_modular_arithmetic.html#a0ebc62368fdab13aae9521778beeea4c">operator==</a>(<span class="keyword">const</span> <a class="code" href="class_modular_arithmetic.html">ModularArithmetic</a> &rhs)<span class="keyword"> const</span></div><div class="line"><a name="l00254"></a><span class="lineno"> 254</span> <span class="keyword"> </span>{<span class="keywordflow">return</span> m_modulus == rhs.m_modulus;}</div><div class="line"><a name="l00255"></a><span class="lineno"> 255</span> </div><div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  <span class="keyword">static</span> <span class="keyword">const</span> RandomizationParameter DefaultRandomizationParameter ;</div><div class="line"><a name="l00257"></a><span class="lineno"> 257</span> </div><div class="line"><a name="l00258"></a><span class="lineno"> 258</span> <span class="keyword">protected</span>:</div><div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  <a class="code" href="class_integer.html">Integer</a> m_modulus;</div><div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  <span class="keyword">mutable</span> <a class="code" href="class_integer.html">Integer</a> m_result, m_result1;</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> </div><div class="line"><a name="l00263"></a><span class="lineno"> 263</span> <span class="comment">// const ModularArithmetic::RandomizationParameter ModularArithmetic::DefaultRandomizationParameter = 0 ;</span></div><div class="line"><a name="l00264"></a><span class="lineno"> 264</span> <span class="comment"></span></div><div class="line"><a name="l00265"></a><span class="lineno"> 265</span> <span class="comment">/// \brief Performs modular arithmetic in Montgomery representation for increased speed</span></div><div class="line"><a name="l00266"></a><span class="lineno"> 266</span> <span class="comment">/// \details The Montgomery representation represents each congruence class <tt>[a]</tt> as</span></div><div class="line"><a name="l00267"></a><span class="lineno"> 267</span> <span class="comment">/// <tt>a*r\%n</tt>, where <tt>r</tt> is a convenient power of 2.</span></div><div class="line"><a name="l00268"></a><span class="lineno"> 268</span> <span class="comment">/// \details <tt>const Element&</tt> returned by member functions are references to</span></div><div class="line"><a name="l00269"></a><span class="lineno"> 269</span> <span class="comment">/// internal data members. Since each object may have only one such data member for holding</span></div><div class="line"><a name="l00270"></a><span class="lineno"> 270</span> <span class="comment">/// results, the following code will produce incorrect results:</span></div><div class="line"><a name="l00271"></a><span class="lineno"> 271</span> <span class="comment">/// <pre> abcd = group.Add(group.Add(a,b), group.Add(c,d));</pre></span></div><div class="line"><a name="l00272"></a><span class="lineno"> 272</span> <span class="comment">/// But this should be fine:</span></div><div class="line"><a name="l00273"></a><span class="lineno"> 273</span> <span class="comment">/// <pre> abcd = group.Add(a, group.Add(b, group.Add(c,d));</pre></span></div><div class="line"><a name="l00274"></a><span class="lineno"><a class="line" href="class_montgomery_representation.html"> 274</a></span> <span class="comment"></span><span class="keyword">class </span>CRYPTOPP_DLL <a class="code" href="class_montgomery_representation.html">MontgomeryRepresentation</a> : <span class="keyword">public</span> <a class="code" href="class_modular_arithmetic.html">ModularArithmetic</a></div><div class="line"><a name="l00275"></a><span class="lineno"> 275</span> {</div><div class="line"><a name="l00276"></a><span class="lineno"> 276</span> <span class="keyword">public</span>:</div><div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  <span class="keyword">virtual</span> ~<a class="code" href="class_montgomery_representation.html">MontgomeryRepresentation</a>() {}</div><div class="line"><a name="l00278"></a><span class="lineno"> 278</span> <span class="comment"></span></div><div class="line"><a name="l00279"></a><span class="lineno"> 279</span> <span class="comment"> /// \brief Construct a MontgomeryRepresentation</span></div><div class="line"><a name="l00280"></a><span class="lineno"> 280</span> <span class="comment"> /// \param modulus congruence class modulus</span></div><div class="line"><a name="l00281"></a><span class="lineno"> 281</span> <span class="comment"> /// \note The modulus must be odd.</span></div><div class="line"><a name="l00282"></a><span class="lineno"> 282</span> <span class="comment"></span> <a class="code" href="class_montgomery_representation.html">MontgomeryRepresentation</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &modulus);</div><div class="line"><a name="l00283"></a><span class="lineno"> 283</span> <span class="comment"></span></div><div class="line"><a name="l00284"></a><span class="lineno"> 284</span> <span class="comment"> /// \brief Clone a MontgomeryRepresentation</span></div><div class="line"><a name="l00285"></a><span class="lineno"> 285</span> <span class="comment"> /// \returns pointer to a new MontgomeryRepresentation</span></div><div class="line"><a name="l00286"></a><span class="lineno"> 286</span> <span class="comment"> /// \details Clone effectively copy constructs a new MontgomeryRepresentation. The caller is</span></div><div class="line"><a name="l00287"></a><span class="lineno"> 287</span> <span class="comment"> /// responsible for deleting the pointer returned from this method.</span></div><div class="line"><a name="l00288"></a><span class="lineno"><a class="line" href="class_montgomery_representation.html#a4591893e6fb0e05f4d2585cddcc15201"> 288</a></span> <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="class_modular_arithmetic.html">ModularArithmetic</a> * <a class="code" href="class_montgomery_representation.html#a4591893e6fb0e05f4d2585cddcc15201">Clone</a>()<span class="keyword"> const </span>{<span class="keywordflow">return</span> <span class="keyword">new</span> <a class="code" href="class_montgomery_representation.html">MontgomeryRepresentation</a>(*<span class="keyword">this</span>);}</div><div class="line"><a name="l00289"></a><span class="lineno"> 289</span> </div><div class="line"><a name="l00290"></a><span class="lineno"><a class="line" href="class_montgomery_representation.html#a5e2e1914f195a03be80c58d62be84f5e"> 290</a></span>  <span class="keywordtype">bool</span> <a class="code" href="class_montgomery_representation.html#a5e2e1914f195a03be80c58d62be84f5e">IsMontgomeryRepresentation</a>()<span class="keyword"> const </span>{<span class="keywordflow">return</span> <span class="keyword">true</span>;}</div><div class="line"><a name="l00291"></a><span class="lineno"> 291</span> </div><div class="line"><a name="l00292"></a><span class="lineno"><a class="line" href="class_montgomery_representation.html#a502f8e7355d1eb252159c0d6e149379a"> 292</a></span>  <a class="code" href="class_integer.html">Integer</a> <a class="code" href="class_montgomery_representation.html#a502f8e7355d1eb252159c0d6e149379a">ConvertIn</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &a)<span class="keyword"> const</span></div><div class="line"><a name="l00293"></a><span class="lineno"> 293</span> <span class="keyword"> </span>{<span class="keywordflow">return</span> (a<<(WORD_BITS*m_modulus.reg.size()))%m_modulus;}</div><div class="line"><a name="l00294"></a><span class="lineno"> 294</span> </div><div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  <a class="code" href="class_integer.html">Integer</a> <a class="code" href="class_modular_arithmetic.html#ac97e7eea935290b4af9e89591f06f4cf">ConvertOut</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &a) <span class="keyword">const</span>;</div><div class="line"><a name="l00296"></a><span class="lineno"> 296</span> </div><div class="line"><a name="l00297"></a><span class="lineno"><a class="line" href="class_montgomery_representation.html#aebab2112b22e0af65d4d0048166ca432"> 297</a></span>  <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a>& <a class="code" href="class_montgomery_representation.html#aebab2112b22e0af65d4d0048166ca432">MultiplicativeIdentity</a>()<span class="keyword"> const</span></div><div class="line"><a name="l00298"></a><span class="lineno"> 298</span> <span class="keyword"> </span>{<span class="keywordflow">return</span> m_result1 = <a class="code" href="class_integer.html#ade53248f5dbb520273a70856b975417c">Integer::Power2</a>(WORD_BITS*m_modulus.reg.size())%m_modulus;}</div><div class="line"><a name="l00299"></a><span class="lineno"> 299</span> </div><div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a>& <a class="code" href="class_modular_arithmetic.html#a3b88a85b11eb1a826d26d01bdaafbf0a">Multiply</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> &b) <span class="keyword">const</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>  <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a>& <a class="code" href="class_modular_arithmetic.html#a7f74883ad789f0db51ed9b45385c14db">Square</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &a) <span class="keyword">const</span>;</div><div class="line"><a name="l00303"></a><span class="lineno"> 303</span> </div><div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a>& <a class="code" href="class_modular_arithmetic.html#a149c6c7abe3e1729880658db5650e48a">MultiplicativeInverse</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &a) <span class="keyword">const</span>;</div><div class="line"><a name="l00305"></a><span class="lineno"> 305</span> </div><div class="line"><a name="l00306"></a><span class="lineno"><a class="line" href="class_montgomery_representation.html#a63d9f4e3b09f34349fcc87059d86a77a"> 306</a></span>  <a class="code" href="class_integer.html">Integer</a> <a class="code" href="class_montgomery_representation.html#a63d9f4e3b09f34349fcc87059d86a77a">CascadeExponentiate</a>(<span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &x, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &e1, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &y, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> &e2)<span class="keyword"> const</span></div><div class="line"><a name="l00307"></a><span class="lineno"> 307</span> <span class="keyword"> </span>{<span class="keywordflow">return</span> <a class="code" href="class_abstract_ring.html#adb4d33ac59a8f8bff1752b75809136e6">AbstractRing<Integer>::CascadeExponentiate</a>(x, e1, y, e2);}</div><div class="line"><a name="l00308"></a><span class="lineno"> 308</span> </div><div class="line"><a name="l00309"></a><span class="lineno"><a class="line" href="class_montgomery_representation.html#a1b03500e21a63d27be5c137877b69d43"> 309</a></span>  <span class="keywordtype">void</span> <a class="code" href="class_montgomery_representation.html#a1b03500e21a63d27be5c137877b69d43">SimultaneousExponentiate</a>(<a class="code" href="class_integer.html">Element</a> *results, <span class="keyword">const</span> <a class="code" href="class_integer.html">Element</a> &base, <span class="keyword">const</span> <a class="code" href="class_integer.html">Integer</a> *exponents, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> exponentsCount)<span class="keyword"> const</span></div><div class="line"><a name="l00310"></a><span class="lineno"> 310</span> <span class="keyword"> </span>{<a class="code" href="class_abstract_ring.html#a63530b69e7bfa78e5ee7b072cc798f0a">AbstractRing<Integer>::SimultaneousExponentiate</a>(results, base, exponents, exponentsCount);}</div><div class="line"><a name="l00311"></a><span class="lineno"> 311</span> </div><div class="line"><a name="l00312"></a><span class="lineno"> 312</span> <span class="keyword">private</span>:</div><div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  <a class="code" href="class_integer.html">Integer</a> m_u;</div><div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  <span class="keyword">mutable</span> <a class="code" href="class_sec_block.html">IntegerSecBlock</a> m_workspace;</div><div class="line"><a name="l00315"></a><span class="lineno"> 315</span> };</div><div class="line"><a name="l00316"></a><span class="lineno"> 316</span> </div><div class="line"><a name="l00317"></a><span class="lineno"> 317</span> NAMESPACE_END</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> <span class="preprocessor">#if CRYPTOPP_MSC_VERSION</span></div><div class="line"><a name="l00320"></a><span class="lineno"> 320</span> <span class="preprocessor"># pragma warning(pop)</span></div><div class="line"><a name="l00321"></a><span class="lineno"> 321</span> <span class="preprocessor">#endif</span></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> <span class="preprocessor">#endif</span></div><div class="ttc" id="class_modular_arithmetic_html_a042dc36ae961ede73694e4c5dcf7cbbc"><div class="ttname"><a href="class_modular_arithmetic.html#a042dc36ae961ede73694e4c5dcf7cbbc">ModularArithmetic::Double</a></div><div class="ttdeci">const Integer & Double(const Integer &a) const</div><div class="ttdoc">Doubles an element in the ring. </div><div class="ttdef"><b>Definition:</b> <a href="modarith_8h_source.html#l00160">modarith.h:160</a></div></div>
<div class="ttc" id="class_modular_arithmetic_html_a89c5edea6e87341761c35ab03a46bcc0"><div class="ttname"><a href="class_modular_arithmetic.html#a89c5edea6e87341761c35ab03a46bcc0">ModularArithmetic::Equal</a></div><div class="ttdeci">bool Equal(const Integer &a, const Integer &b) const</div><div class="ttdoc">Compare two elements for equality. </div><div class="ttdef"><b>Definition:</b> <a href="modarith_8h_source.html#l00119">modarith.h:119</a></div></div>
<div class="ttc" id="class_modular_arithmetic_html_a7f74883ad789f0db51ed9b45385c14db"><div class="ttname"><a href="class_modular_arithmetic.html#a7f74883ad789f0db51ed9b45385c14db">ModularArithmetic::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="modarith_8h_source.html#l00181">modarith.h:181</a></div></div>
<div class="ttc" id="class_montgomery_representation_html_a5e2e1914f195a03be80c58d62be84f5e"><div class="ttname"><a href="class_montgomery_representation.html#a5e2e1914f195a03be80c58d62be84f5e">MontgomeryRepresentation::IsMontgomeryRepresentation</a></div><div class="ttdeci">bool IsMontgomeryRepresentation() const</div><div class="ttdoc">Retrieves the representation. </div><div class="ttdef"><b>Definition:</b> <a href="modarith_8h_source.html#l00290">modarith.h:290</a></div></div>
<div class="ttc" id="class_modular_arithmetic_html_a584d214676856d1463e14c6407d1cd31"><div class="ttname"><a href="class_modular_arithmetic.html#a584d214676856d1463e14c6407d1cd31">ModularArithmetic::Divide</a></div><div class="ttdeci">const Integer & Divide(const Integer &a, const Integer &b) const</div><div class="ttdoc">Divides elements in the ring. </div><div class="ttdef"><b>Definition:</b> <a href="modarith_8h_source.html#l00202">modarith.h:202</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_abstract_group_html_aa19e1bef00198fb30eb01df3f7076717"><div class="ttname"><a href="class_abstract_group.html#aa19e1bef00198fb30eb01df3f7076717">AbstractGroup::Subtract</a></div><div class="ttdeci">virtual const Element & Subtract(const Element &a, const Element &b) const</div><div class="ttdoc">Subtracts elements in the group. </div><div class="ttdef"><b>Definition:</b> <a href="algebra_8cpp_source.html#l00020">algebra.cpp:20</a></div></div>
<div class="ttc" id="class_abstract_ring_html_a4ba8818fc72fa298cd52fd483bdd6ad4"><div class="ttname"><a href="class_abstract_ring.html#a4ba8818fc72fa298cd52fd483bdd6ad4">AbstractRing::Multiply</a></div><div class="ttdeci">virtual const Element & Multiply(const Element &a, const Element &b) const =0</div><div class="ttdoc">Multiplies elements in the group. </div></div>
<div class="ttc" id="class_integer_html_a2d4d29937f8ef666717530b30f137c37"><div class="ttname"><a href="class_integer.html#a2d4d29937f8ef666717530b30f137c37">Integer::Gcd</a></div><div class="ttdeci">static Integer Gcd(const Integer &a, const Integer &n)</div><div class="ttdoc">Calculate greatest common divisor. </div><div class="ttdef"><b>Definition:</b> <a href="integer_8cpp_source.html#l04381">integer.cpp:4381</a></div></div>
<div class="ttc" id="class_sec_block_html_af9e98d3f4a7af1156fcf3e6e68f4ae5a"><div class="ttname"><a href="class_sec_block.html#af9e98d3f4a7af1156fcf3e6e68f4ae5a">SecBlock::resize</a></div><div class="ttdeci">void resize(size_type newSize)</div><div class="ttdoc">Change size and preserve contents. </div><div class="ttdef"><b>Definition:</b> <a href="secblock_8h_source.html#l00795">secblock.h:795</a></div></div>
<div class="ttc" id="class_modular_arithmetic_html_ac97e7eea935290b4af9e89591f06f4cf"><div class="ttname"><a href="class_modular_arithmetic.html#ac97e7eea935290b4af9e89591f06f4cf">ModularArithmetic::ConvertOut</a></div><div class="ttdeci">virtual 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="modarith_8h_source.html#l00107">modarith.h:107</a></div></div>
<div class="ttc" id="class_abstract_ring_html_adb4d33ac59a8f8bff1752b75809136e6"><div class="ttname"><a href="class_abstract_ring.html#adb4d33ac59a8f8bff1752b75809136e6">AbstractRing::CascadeExponentiate</a></div><div class="ttdeci">virtual Element CascadeExponentiate(const Element &x, const Integer &e1, const Element &y, const Integer &e2) const</div><div class="ttdoc">TODO. </div><div class="ttdef"><b>Definition:</b> <a href="algebra_8cpp_source.html#l00323">algebra.cpp:323</a></div></div>
<div class="ttc" id="class_sec_block_html"><div class="ttname"><a href="class_sec_block.html">SecBlock< word, AllocatorWithCleanup< word, true > ></a></div></div>
<div class="ttc" id="cryptlib_8h_html"><div class="ttname"><a href="cryptlib_8h.html">cryptlib.h</a></div><div class="ttdoc">Abstract base classes that provide a uniform interface to this library. </div></div>
<div class="ttc" id="class_modular_arithmetic_html_a149c6c7abe3e1729880658db5650e48a"><div class="ttname"><a href="class_modular_arithmetic.html#a149c6c7abe3e1729880658db5650e48a">ModularArithmetic::MultiplicativeInverse</a></div><div class="ttdeci">const Integer & MultiplicativeInverse(const Integer &a) const</div><div class="ttdoc">Calculate the multiplicative inverse of an element in the ring. </div><div class="ttdef"><b>Definition:</b> <a href="modarith_8h_source.html#l00194">modarith.h:194</a></div></div>
<div class="ttc" id="class_abstract_euclidean_domain_html"><div class="ttname"><a href="class_abstract_euclidean_domain.html">AbstractEuclideanDomain</a></div><div class="ttdoc">Abstract Euclidean domain. </div><div class="ttdef"><b>Definition:</b> <a href="algebra_8h_source.html#l00276">algebra.h:276</a></div></div>
<div class="ttc" id="class_modular_arithmetic_html_a5897aea2ee78595979f8f261130c93ee"><div class="ttname"><a href="class_modular_arithmetic.html#a5897aea2ee78595979f8f261130c93ee">ModularArithmetic::MaxElementByteLength</a></div><div class="ttdeci">unsigned int MaxElementByteLength() const</div><div class="ttdoc">Provides the maximum byte size of an element in the ring. </div><div class="ttdef"><b>Definition:</b> <a href="modarith_8h_source.html#l00232">modarith.h:232</a></div></div>
<div class="ttc" id="class_modular_arithmetic_html"><div class="ttname"><a href="class_modular_arithmetic.html">ModularArithmetic</a></div><div class="ttdoc">Ring of congruence classes modulo n. </div><div class="ttdef"><b>Definition:</b> <a href="modarith_8h_source.html#l00038">modarith.h:38</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="class_modular_arithmetic_html_a3c802233b0edf8df4228d65082ff37fa"><div class="ttname"><a href="class_modular_arithmetic.html#a3c802233b0edf8df4228d65082ff37fa">ModularArithmetic::MaxElementBitLength</a></div><div class="ttdeci">unsigned int MaxElementBitLength() const</div><div class="ttdoc">Provides the maximum bit size of an element in the ring. </div><div class="ttdef"><b>Definition:</b> <a href="modarith_8h_source.html#l00227">modarith.h:227</a></div></div>
<div class="ttc" id="algebra_8h_html"><div class="ttname"><a href="algebra_8h.html">algebra.h</a></div><div class="ttdoc">Classes for performing mathematics over different fields. </div></div>
<div class="ttc" id="class_buffered_transformation_html"><div class="ttname"><a href="class_buffered_transformation.html">BufferedTransformation</a></div><div class="ttdoc">Interface for buffered transformations. </div><div class="ttdef"><b>Definition:</b> <a href="cryptlib_8h_source.html#l01545">cryptlib.h:1545</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="class_abstract_ring_html"><div class="ttname"><a href="class_abstract_ring.html">AbstractRing< Integer ></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="class_modular_arithmetic_html_abd2425e1caf5af1a290b424cadb1517c"><div class="ttname"><a href="class_modular_arithmetic.html#abd2425e1caf5af1a290b424cadb1517c">ModularArithmetic::Identity</a></div><div class="ttdeci">const Integer & Identity() const</div><div class="ttdoc">Provides the Identity element. </div><div class="ttdef"><b>Definition:</b> <a href="modarith_8h_source.html#l00124">modarith.h:124</a></div></div>
<div class="ttc" id="class_integer_html_aea313b73beda59a8c4ee2de11d637412"><div class="ttname"><a href="class_integer.html#aea313b73beda59a8c4ee2de11d637412">Integer::IsUnit</a></div><div class="ttdeci">bool IsUnit() const</div><div class="ttdoc">Determine if 1 or -1. </div><div class="ttdef"><b>Definition:</b> <a href="integer_8cpp_source.html#l04352">integer.cpp:4352</a></div></div>
<div class="ttc" id="secblock_8h_html"><div class="ttname"><a href="secblock_8h.html">secblock.h</a></div><div class="ttdoc">Classes and functions for secure memory allocations. </div></div>
<div class="ttc" id="class_montgomery_representation_html_a4591893e6fb0e05f4d2585cddcc15201"><div class="ttname"><a href="class_montgomery_representation.html#a4591893e6fb0e05f4d2585cddcc15201">MontgomeryRepresentation::Clone</a></div><div class="ttdeci">virtual ModularArithmetic * Clone() const</div><div class="ttdoc">Clone a MontgomeryRepresentation. </div><div class="ttdef"><b>Definition:</b> <a href="modarith_8h_source.html#l00288">modarith.h:288</a></div></div>
<div class="ttc" id="class_modular_arithmetic_html_a0ebc62368fdab13aae9521778beeea4c"><div class="ttname"><a href="class_modular_arithmetic.html#a0ebc62368fdab13aae9521778beeea4c">ModularArithmetic::operator==</a></div><div class="ttdeci">bool operator==(const ModularArithmetic &rhs) const</div><div class="ttdoc">Compares two ModularArithmetic for equality. </div><div class="ttdef"><b>Definition:</b> <a href="modarith_8h_source.html#l00253">modarith.h:253</a></div></div>
<div class="ttc" id="class_modular_arithmetic_html_a3b88a85b11eb1a826d26d01bdaafbf0a"><div class="ttname"><a href="class_modular_arithmetic.html#a3b88a85b11eb1a826d26d01bdaafbf0a">ModularArithmetic::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="modarith_8h_source.html#l00174">modarith.h:174</a></div></div>
<div class="ttc" id="class_abstract_ring_html_aba109f4e7932d77a8251c1ec20627571"><div class="ttname"><a href="class_abstract_ring.html#aba109f4e7932d77a8251c1ec20627571">AbstractRing::MultiplicativeInverse</a></div><div class="ttdeci">virtual const Element & MultiplicativeInverse(const Element &a) const =0</div><div class="ttdoc">Calculate the multiplicative inverse of an element in the group. </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="class_modular_arithmetic_html_a71a51e5b665bf7fb89af2ccba19f0043"><div class="ttname"><a href="class_modular_arithmetic.html#a71a51e5b665bf7fb89af2ccba19f0043">ModularArithmetic::GetModulus</a></div><div class="ttdeci">const Integer & GetModulus() const</div><div class="ttdoc">Retrieves the modulus. </div><div class="ttdef"><b>Definition:</b> <a href="modarith_8h_source.html#l00083">modarith.h:83</a></div></div>
<div class="ttc" id="class_montgomery_representation_html_aebab2112b22e0af65d4d0048166ca432"><div class="ttname"><a href="class_montgomery_representation.html#aebab2112b22e0af65d4d0048166ca432">MontgomeryRepresentation::MultiplicativeIdentity</a></div><div class="ttdeci">const Integer & MultiplicativeIdentity() const</div><div class="ttdoc">Retrieves the multiplicative identity. </div><div class="ttdef"><b>Definition:</b> <a href="modarith_8h_source.html#l00297">modarith.h:297</a></div></div>
<div class="ttc" id="class_abstract_group_html_ab22563bc0dcb544399d7e22b3589e165"><div class="ttname"><a href="class_abstract_group.html#ab22563bc0dcb544399d7e22b3589e165">AbstractGroup::Inverse</a></div><div class="ttdeci">virtual const Element & Inverse(const Element &a) const =0</div><div class="ttdoc">Inverts the element in the group. </div></div>
<div class="ttc" id="class_modular_arithmetic_html_a1cdfc924e8d11f9620bd826535aabb62"><div class="ttname"><a href="class_modular_arithmetic.html#a1cdfc924e8d11f9620bd826535aabb62">ModularArithmetic::ModularArithmetic</a></div><div class="ttdeci">ModularArithmetic(const Integer &modulus=Integer::One())</div><div class="ttdoc">Construct a ModularArithmetic. </div><div class="ttdef"><b>Definition:</b> <a href="modarith_8h_source.html#l00049">modarith.h:49</a></div></div>
<div class="ttc" id="class_abstract_group_html"><div class="ttname"><a href="class_abstract_group.html">AbstractGroup< Integer ></a></div></div>
<div class="ttc" id="class_modular_arithmetic_html_afc5cb8d95e05c9f8975b1b940218d07c"><div class="ttname"><a href="class_modular_arithmetic.html#afc5cb8d95e05c9f8975b1b940218d07c">ModularArithmetic::ConvertIn</a></div><div class="ttdeci">virtual 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#l00099">modarith.h:99</a></div></div>
<div class="ttc" id="class_modular_arithmetic_html_a2ea01ae9e84d5392a8781b99d5cba83f"><div class="ttname"><a href="class_modular_arithmetic.html#a2ea01ae9e84d5392a8781b99d5cba83f">ModularArithmetic::Clone</a></div><div class="ttdeci">virtual ModularArithmetic * Clone() const</div><div class="ttdoc">Clone a ModularArithmetic. </div><div class="ttdef"><b>Definition:</b> <a href="modarith_8h_source.html#l00065">modarith.h:65</a></div></div>
<div class="ttc" id="class_abstract_group_html_ab03cc0a23f23c6aa1c003e11f9abb8c5"><div class="ttname"><a href="class_abstract_group.html#ab03cc0a23f23c6aa1c003e11f9abb8c5">AbstractGroup::Accumulate</a></div><div class="ttdeci">virtual Element & Accumulate(Element &a, const Element &b) const</div><div class="ttdoc">TODO. </div><div class="ttdef"><b>Definition:</b> <a href="algebra_8cpp_source.html#l00027">algebra.cpp:27</a></div></div>
<div class="ttc" id="class_modular_arithmetic_html_a2d7a07fd3831386eb9315c4e1f5fcf25"><div class="ttname"><a href="class_modular_arithmetic.html#a2d7a07fd3831386eb9315c4e1f5fcf25">ModularArithmetic::SetModulus</a></div><div class="ttdeci">void SetModulus(const Integer &newModulus)</div><div class="ttdoc">Sets the modulus. </div><div class="ttdef"><b>Definition:</b> <a href="modarith_8h_source.html#l00087">modarith.h:87</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_modular_arithmetic_html_a6abf94f5924223c316c04752ba39795a"><div class="ttname"><a href="class_modular_arithmetic.html#a6abf94f5924223c316c04752ba39795a">ModularArithmetic::RandomElement</a></div><div class="ttdeci">Element RandomElement(RandomNumberGenerator &rng, const RandomizationParameter &ignore_for_now=0) const</div><div class="ttdoc">Provides a random element in the ring. </div><div class="ttdef"><b>Definition:</b> <a href="modarith_8h_source.html#l00242">modarith.h:242</a></div></div>
<div class="ttc" id="class_montgomery_representation_html_a63d9f4e3b09f34349fcc87059d86a77a"><div class="ttname"><a href="class_montgomery_representation.html#a63d9f4e3b09f34349fcc87059d86a77a">MontgomeryRepresentation::CascadeExponentiate</a></div><div class="ttdeci">Integer CascadeExponentiate(const Integer &x, const Integer &e1, const Integer &y, const Integer &e2) const</div><div class="ttdoc">TODO. </div><div class="ttdef"><b>Definition:</b> <a href="modarith_8h_source.html#l00306">modarith.h:306</a></div></div>
<div class="ttc" id="class_abstract_group_html_aa813430d9e4244de24c487d090eb5797"><div class="ttname"><a href="class_abstract_group.html#aa813430d9e4244de24c487d090eb5797">AbstractGroup::Add</a></div><div class="ttdeci">virtual const Element & Add(const Element &a, const Element &b) const =0</div><div class="ttdoc">Adds elements in the group. </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="class_abstract_group_html_a40f7de55eddc193e07a7c3b5acad781a"><div class="ttname"><a href="class_abstract_group.html#a40f7de55eddc193e07a7c3b5acad781a">AbstractGroup::Reduce</a></div><div class="ttdeci">virtual Element & Reduce(Element &a, const Element &b) const</div><div class="ttdoc">Reduces an element in the congruence class. </div><div class="ttdef"><b>Definition:</b> <a href="algebra_8cpp_source.html#l00032">algebra.cpp:32</a></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="class_modular_arithmetic_html_a7a7bf808b07baa755ed9ce9f300ce743"><div class="ttname"><a href="class_modular_arithmetic.html#a7a7bf808b07baa755ed9ce9f300ce743">ModularArithmetic::ModularArithmetic</a></div><div class="ttdeci">ModularArithmetic(const ModularArithmetic &ma)</div><div class="ttdoc">Copy construct a ModularArithmetic. </div><div class="ttdef"><b>Definition:</b> <a href="modarith_8h_source.html#l00054">modarith.h:54</a></div></div>
<div class="ttc" id="class_modular_arithmetic_html_af942a7ca057b363cb7a4c74f15a9530e"><div class="ttname"><a href="class_modular_arithmetic.html#af942a7ca057b363cb7a4c74f15a9530e">ModularArithmetic::MultiplicativeIdentity</a></div><div class="ttdeci">const Integer & MultiplicativeIdentity() const</div><div class="ttdoc">Retrieves the multiplicative identity. </div><div class="ttdef"><b>Definition:</b> <a href="modarith_8h_source.html#l00166">modarith.h:166</a></div></div>
<div class="ttc" id="class_montgomery_representation_html_a1b03500e21a63d27be5c137877b69d43"><div class="ttname"><a href="class_montgomery_representation.html#a1b03500e21a63d27be5c137877b69d43">MontgomeryRepresentation::SimultaneousExponentiate</a></div><div class="ttdeci">void SimultaneousExponentiate(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const</div><div class="ttdoc">Exponentiates a base to multiple exponents in the ring. </div><div class="ttdef"><b>Definition:</b> <a href="modarith_8h_source.html#l00309">modarith.h:309</a></div></div>
<div class="ttc" id="class_abstract_ring_html_a63530b69e7bfa78e5ee7b072cc798f0a"><div class="ttname"><a href="class_abstract_ring.html#a63530b69e7bfa78e5ee7b072cc798f0a">AbstractRing::SimultaneousExponentiate</a></div><div class="ttdeci">virtual void SimultaneousExponentiate(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const</div><div class="ttdoc">Exponentiates a base to multiple exponents in the Ring. </div><div class="ttdef"><b>Definition:</b> <a href="algebra_8cpp_source.html#l00334">algebra.cpp:334</a></div></div>
<div class="ttc" id="class_modular_arithmetic_html_a7a93adfe41f5545dcfaf3ee9f2b49bc3"><div class="ttname"><a href="class_modular_arithmetic.html#a7a93adfe41f5545dcfaf3ee9f2b49bc3">ModularArithmetic::IsMontgomeryRepresentation</a></div><div class="ttdeci">virtual bool IsMontgomeryRepresentation() const</div><div class="ttdoc">Retrieves the representation. </div><div class="ttdef"><b>Definition:</b> <a href="modarith_8h_source.html#l00092">modarith.h:92</a></div></div>
<div class="ttc" id="class_modular_arithmetic_html_a0d8edd3e4ff60627b92e93ebd00cdfb3"><div class="ttname"><a href="class_modular_arithmetic.html#a0d8edd3e4ff60627b92e93ebd00cdfb3">ModularArithmetic::IsUnit</a></div><div class="ttdeci">bool IsUnit(const Integer &a) const</div><div class="ttdoc">Determines whether an element is a unit in the ring. </div><div class="ttdef"><b>Definition:</b> <a href="modarith_8h_source.html#l00187">modarith.h:187</a></div></div>
</div><!-- fragment --></div><!-- contents -->
<!-- start footer part -->
<hr class="footer"/><address class="footer"><small>
Generated on Sun Sep 16 2018 07:57:57 for Crypto++ by  <a href="http://www.doxygen.org/index.html">
<img class="footer" src="doxygen.png" alt="doxygen"/>
</a> 1.8.14
</small></address>
</body>
</html>
distrib
>
Mageia
>
7
>
armv7hl
>
media
>
core-release
>
by-pkgid
>
0a67b807a02637f2cae68649d519a89d
>
files
>
2442
