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 <span id="projectnumber">4.2.1</span>
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<div class="title">rsa.h File Reference<div class="ingroups"><a class="el" href="group__IF__m.html">Integer Factorization Primitives</a> | <a class="el" href="group__IF__rsa__m.html">Integer Factorization Primitives: RSA</a></div></div> </div>
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<p>RSA algorithm.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include "<a class="el" href="rsakp_8h_source.html">beecrypt/rsakp.h</a>"</code><br/>
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Include dependency graph for rsa.h:</div>
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<div class="center"><img src="rsa_8h__incl.png" border="0" usemap="#include_2beecrypt_2rsa_8h" alt=""/></div>
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<area shape="rect" id="node2" href="rsakp_8h.html" title="RSA keypair, headers. " alt="" coords="610,80,728,107"/><area shape="rect" id="node3" href="rsapk_8h.html" title="RSA public key, headers. " alt="" coords="610,155,728,181"/><area shape="rect" id="node4" href="mpbarrett_8h.html" title="Multi-precision integer routines using Barrett modular reduction, headers. " alt="" coords="598,229,740,256"/><area shape="rect" id="node5" href="beecrypt_8h.html" title="BeeCrypt API, headers. " alt="" coords="461,304,597,331"/><area shape="rect" id="node19" href="mpnumber_8h.html" title="Multi-precision numbers, headers. " alt="" coords="595,379,743,405"/><area shape="rect" id="node6" href="api_8h.html" title="BeeCrypt API, portability headers. " alt="" coords="444,528,548,555"/><area shape="rect" id="node18" href="memchunk_8h.html" title="beecrypt/memchunk.h" alt="" coords="421,379,571,405"/><area shape="rect" id="node7" href="gnu_8h.html" title="beecrypt/gnu.h" alt="" coords="442,603,549,629"/><area shape="rect" id="node20" href="mp_8h.html" title="Multi-precision integer routines. " alt="" coords="589,453,693,480"/><area shape="rect" id="node21" href="mpopt_8h.html" title="Multi-precision integer optimization definitions. " alt="" coords="580,528,703,555"/></map>
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<p><a href="rsa_8h_source.html">Go to the source code of this file.</a></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:a56d0efcbcd2a35d462b32760529fc72f"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="rsa_8h.html#a56d0efcbcd2a35d462b32760529fc72f">rsapub</a> (const <a class="el" href="structmpbarrett.html">mpbarrett</a> *n, const <a class="el" href="structmpnumber.html">mpnumber</a> *e, const <a class="el" href="structmpnumber.html">mpnumber</a> *m, <a class="el" href="structmpnumber.html">mpnumber</a> *c)</td></tr>
<tr class="memdesc:a56d0efcbcd2a35d462b32760529fc72f"><td class="mdescLeft"> </td><td class="mdescRight">This function performs a raw RSA public key operation. <a href="#a56d0efcbcd2a35d462b32760529fc72f">More...</a><br/></td></tr>
<tr class="separator:a56d0efcbcd2a35d462b32760529fc72f"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a98805e27f1b3f3d009547408b17c5dac"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="rsa_8h.html#a98805e27f1b3f3d009547408b17c5dac">rsapri</a> (const <a class="el" href="structmpbarrett.html">mpbarrett</a> *n, const <a class="el" href="structmpnumber.html">mpnumber</a> *d, const <a class="el" href="structmpnumber.html">mpnumber</a> *c, <a class="el" href="structmpnumber.html">mpnumber</a> *m)</td></tr>
<tr class="memdesc:a98805e27f1b3f3d009547408b17c5dac"><td class="mdescLeft"> </td><td class="mdescRight">This function performs a raw RSA private key operation. <a href="#a98805e27f1b3f3d009547408b17c5dac">More...</a><br/></td></tr>
<tr class="separator:a98805e27f1b3f3d009547408b17c5dac"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a9b9fc03593383e25bc06d8acab0a276a"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="rsa_8h.html#a9b9fc03593383e25bc06d8acab0a276a">rsapricrt</a> (const <a class="el" href="structmpbarrett.html">mpbarrett</a> *n, const <a class="el" href="structmpbarrett.html">mpbarrett</a> *p, const <a class="el" href="structmpbarrett.html">mpbarrett</a> *q, const <a class="el" href="structmpnumber.html">mpnumber</a> *dp, const <a class="el" href="structmpnumber.html">mpnumber</a> *dq, const <a class="el" href="structmpnumber.html">mpnumber</a> *qi, const <a class="el" href="structmpnumber.html">mpnumber</a> *c, <a class="el" href="structmpnumber.html">mpnumber</a> *m)</td></tr>
<tr class="memdesc:a9b9fc03593383e25bc06d8acab0a276a"><td class="mdescLeft"> </td><td class="mdescRight">This function performs a raw RSA private key operation, with application of the Chinese Remainder Theorem. <a href="#a9b9fc03593383e25bc06d8acab0a276a">More...</a><br/></td></tr>
<tr class="separator:a9b9fc03593383e25bc06d8acab0a276a"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aca849ebe0d68770764957907baf891b0"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="rsa_8h.html#aca849ebe0d68770764957907baf891b0">rsavrfy</a> (const <a class="el" href="structmpbarrett.html">mpbarrett</a> *n, const <a class="el" href="structmpnumber.html">mpnumber</a> *e, const <a class="el" href="structmpnumber.html">mpnumber</a> *m, const <a class="el" href="structmpnumber.html">mpnumber</a> *c)</td></tr>
<tr class="memdesc:aca849ebe0d68770764957907baf891b0"><td class="mdescLeft"> </td><td class="mdescRight">This function performs a raw RSA verification. <a href="#aca849ebe0d68770764957907baf891b0">More...</a><br/></td></tr>
<tr class="separator:aca849ebe0d68770764957907baf891b0"><td class="memSeparator" colspan="2"> </td></tr>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>RSA algorithm. </p>
<dl class="section author"><dt>Author</dt><dd>Bob Deblier <a href="#" onclick="location.href='mai'+'lto:'+'bob'+'.d'+'ebl'+'ie'+'r@t'+'el'+'ene'+'t.'+'be'; return false;">bob.d<span style="display: none;">.nosp@m.</span>ebli<span style="display: none;">.nosp@m.</span>er@te<span style="display: none;">.nosp@m.</span>lene<span style="display: none;">.nosp@m.</span>t.be</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a class="anchor" id="a98805e27f1b3f3d009547408b17c5dac"></a>
<div class="memitem">
<div class="memproto">
<table class="memname">
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<td class="memname">int rsapri </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="structmpbarrett.html">mpbarrett</a> * </td>
<td class="paramname"><em>n</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="structmpnumber.html">mpnumber</a> * </td>
<td class="paramname"><em>d</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="structmpnumber.html">mpnumber</a> * </td>
<td class="paramname"><em>c</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structmpnumber.html">mpnumber</a> * </td>
<td class="paramname"><em>m</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>This function performs a raw RSA private key operation. </p>
<p>This function can be used for decryption and signing.</p>
<p>It performs the operation: </p>
<ul>
<li><img class="formulaInl" alt="$m=c^{d}\ \textrm{mod}\ n$" src="form_32.png"/></li>
</ul>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">n</td><td>The modulus. </td></tr>
<tr><td class="paramname">d</td><td>The private exponent. </td></tr>
<tr><td class="paramname">c</td><td>The ciphertext. </td></tr>
<tr><td class="paramname">m</td><td>The message. </td></tr>
</table>
</dd>
</dl>
<dl class="retval"><dt>Return values</dt><dd>
<table class="retval">
<tr><td class="paramname">0</td><td>on success. </td></tr>
<tr><td class="paramname">-1</td><td>on failure. </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a class="anchor" id="a9b9fc03593383e25bc06d8acab0a276a"></a>
<div class="memitem">
<div class="memproto">
<table class="memname">
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<td class="memname">int rsapricrt </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="structmpbarrett.html">mpbarrett</a> * </td>
<td class="paramname"><em>n</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="structmpbarrett.html">mpbarrett</a> * </td>
<td class="paramname"><em>p</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="structmpbarrett.html">mpbarrett</a> * </td>
<td class="paramname"><em>q</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="structmpnumber.html">mpnumber</a> * </td>
<td class="paramname"><em>dp</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="structmpnumber.html">mpnumber</a> * </td>
<td class="paramname"><em>dq</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="structmpnumber.html">mpnumber</a> * </td>
<td class="paramname"><em>qi</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="structmpnumber.html">mpnumber</a> * </td>
<td class="paramname"><em>c</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structmpnumber.html">mpnumber</a> * </td>
<td class="paramname"><em>m</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>This function performs a raw RSA private key operation, with application of the Chinese Remainder Theorem. </p>
<p>It performs the operation: </p>
<ul>
<li><img class="formulaInl" alt="$j_1=c^{dp}\ \textrm{mod}\ p$" src="form_33.png"/> </li>
<li><img class="formulaInl" alt="$j_2=c^{dq}\ \textrm{mod}\ q$" src="form_34.png"/> </li>
<li><img class="formulaInl" alt="$h=qi \cdot (j_1-j_2)\ \textrm{mod}\ p$" src="form_35.png"/> </li>
<li><img class="formulaInl" alt="$m=j_2+hq$" src="form_36.png"/></li>
</ul>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">n</td><td>The modulus. </td></tr>
<tr><td class="paramname">p</td><td>The first prime factor. </td></tr>
<tr><td class="paramname">q</td><td>The second prime factor. </td></tr>
<tr><td class="paramname">dp</td><td>The private exponent d mod (p-1). </td></tr>
<tr><td class="paramname">dq</td><td>The private exponent d (q-1). </td></tr>
<tr><td class="paramname">qi</td><td>The inverse of q mod p. </td></tr>
<tr><td class="paramname">c</td><td>The ciphertext. </td></tr>
<tr><td class="paramname">m</td><td>The message. </td></tr>
</table>
</dd>
</dl>
<dl class="retval"><dt>Return values</dt><dd>
<table class="retval">
<tr><td class="paramname">0</td><td>on success. </td></tr>
<tr><td class="paramname">-1</td><td>on failure. </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a class="anchor" id="a56d0efcbcd2a35d462b32760529fc72f"></a>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">int rsapub </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="structmpbarrett.html">mpbarrett</a> * </td>
<td class="paramname"><em>n</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="structmpnumber.html">mpnumber</a> * </td>
<td class="paramname"><em>e</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="structmpnumber.html">mpnumber</a> * </td>
<td class="paramname"><em>m</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structmpnumber.html">mpnumber</a> * </td>
<td class="paramname"><em>c</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>This function performs a raw RSA public key operation. </p>
<p>This function can be used for encryption and verifying.</p>
<p>It performs the following operation: </p>
<ul>
<li><img class="formulaInl" alt="$c=m^{e}\ \textrm{mod}\ n$" src="form_31.png"/></li>
</ul>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">n</td><td>The RSA modulus. </td></tr>
<tr><td class="paramname">e</td><td>The RSA public exponent. </td></tr>
<tr><td class="paramname">m</td><td>The message. </td></tr>
<tr><td class="paramname">c</td><td>The ciphertext. </td></tr>
</table>
</dd>
</dl>
<dl class="retval"><dt>Return values</dt><dd>
<table class="retval">
<tr><td class="paramname">0</td><td>on success. </td></tr>
<tr><td class="paramname">-1</td><td>on failure. </td></tr>
</table>
</dd>
</dl>
</div>
</div>
<a class="anchor" id="aca849ebe0d68770764957907baf891b0"></a>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">int rsavrfy </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="structmpbarrett.html">mpbarrett</a> * </td>
<td class="paramname"><em>n</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="structmpnumber.html">mpnumber</a> * </td>
<td class="paramname"><em>e</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="structmpnumber.html">mpnumber</a> * </td>
<td class="paramname"><em>m</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="structmpnumber.html">mpnumber</a> * </td>
<td class="paramname"><em>c</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>This function performs a raw RSA verification. </p>
<p>It verifies if ciphertext <em>c</em> was encrypted from cleartext <em>m</em> with the private key matching the given public key <em></em>(n, e).</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">n</td><td>The modulus. </td></tr>
<tr><td class="paramname">e</td><td>The public exponent. </td></tr>
<tr><td class="paramname">m</td><td>The cleartext message. </td></tr>
<tr><td class="paramname">c</td><td>The ciphertext message. </td></tr>
</table>
</dd>
</dl>
<dl class="retval"><dt>Return values</dt><dd>
<table class="retval">
<tr><td class="paramname">1</td><td>on success. </td></tr>
<tr><td class="paramname">0</td><td>on failure. </td></tr>
</table>
</dd>
</dl>
</div>
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