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<a href="#func-members">Functions</a> </div>
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<h1>include/beecrypt/elgamal.h File Reference<div class="ingroups"><a class="el" href="group__DL__m.html">Discrete Logarithm Primitives</a> | <a class="el" href="group__DL__elgamal__m.html">Discrete Logarithm Primitives: ElGamal</a></div></h1> </div>
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<p>ElGamal algorithm.
<a href="#_details">More...</a></p>
<div class="textblock"><code>#include "beecrypt/mpbarrett.h"</code><br/>
</div><div class="textblock"><div class="dynheader">
Include dependency graph for elgamal.h:</div>
<div class="dyncontent">
<div class="center"><img src="elgamal_8h__incl.png" border="0" usemap="#include_2beecrypt_2elgamal_8h" alt=""/></div>
<map name="include_2beecrypt_2elgamal_8h" id="include_2beecrypt_2elgamal_8h">
</map>
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<p><a href="elgamal_8h_source.html">Go to the source code of this file.</a></p>
<table class="memberdecls">
<tr><td colspan="2"><h2><a name="func-members"></a>
Functions</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="elgamal_8h.html#a71210da412fefa0f230a7f988eb83c31">elgv1sign</a> (const <a class="el" href="structmpbarrett.html">mpbarrett</a> *p, const <a class="el" href="structmpbarrett.html">mpbarrett</a> *n, const <a class="el" href="structmpnumber.html">mpnumber</a> *g, <a class="el" href="structrandomGeneratorContext.html">randomGeneratorContext</a> *, const <a class="el" href="structmpnumber.html">mpnumber</a> *hm, const <a class="el" href="structmpnumber.html">mpnumber</a> *x, <a class="el" href="structmpnumber.html">mpnumber</a> *r, <a class="el" href="structmpnumber.html">mpnumber</a> *s)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">This function performs raw ElGamal signing, variant 1. <a href="#a71210da412fefa0f230a7f988eb83c31"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="elgamal_8h.html#ab5a4857d59add82a522e0c08c83298f8">elgv3sign</a> (const <a class="el" href="structmpbarrett.html">mpbarrett</a> *p, const <a class="el" href="structmpbarrett.html">mpbarrett</a> *n, const <a class="el" href="structmpnumber.html">mpnumber</a> *g, <a class="el" href="structrandomGeneratorContext.html">randomGeneratorContext</a> *, const <a class="el" href="structmpnumber.html">mpnumber</a> *hm, const <a class="el" href="structmpnumber.html">mpnumber</a> *x, <a class="el" href="structmpnumber.html">mpnumber</a> *r, <a class="el" href="structmpnumber.html">mpnumber</a> *s)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">This function performs raw ElGamal signing, variant 3. <a href="#ab5a4857d59add82a522e0c08c83298f8"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="elgamal_8h.html#ab91d86edb1453350a8e4023e694474ec">elgv1vrfy</a> (const <a class="el" href="structmpbarrett.html">mpbarrett</a> *p, const <a class="el" href="structmpbarrett.html">mpbarrett</a> *n, const <a class="el" href="structmpnumber.html">mpnumber</a> *g, const <a class="el" href="structmpnumber.html">mpnumber</a> *hm, const <a class="el" href="structmpnumber.html">mpnumber</a> *y, const <a class="el" href="structmpnumber.html">mpnumber</a> *r, const <a class="el" href="structmpnumber.html">mpnumber</a> *s)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">This function performs raw ElGamal verification, variant 1. <a href="#ab91d86edb1453350a8e4023e694474ec"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="elgamal_8h.html#aaa1c3bb1ca269e9b40ee8a561a3f78f6">elgv3vrfy</a> (const <a class="el" href="structmpbarrett.html">mpbarrett</a> *p, const <a class="el" href="structmpbarrett.html">mpbarrett</a> *n, const <a class="el" href="structmpnumber.html">mpnumber</a> *g, const <a class="el" href="structmpnumber.html">mpnumber</a> *hm, const <a class="el" href="structmpnumber.html">mpnumber</a> *y, const <a class="el" href="structmpnumber.html">mpnumber</a> *r, const <a class="el" href="structmpnumber.html">mpnumber</a> *s)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">This function performs raw ElGamal verification, variant 3. <a href="#aaa1c3bb1ca269e9b40ee8a561a3f78f6"></a><br/></td></tr>
</table>
<hr/><a name="_details"></a><h2>Detailed Description</h2>
<div class="textblock"><p>ElGamal algorithm. </p>
<p>For more information on this algorithm, see: "Handbook of Applied Cryptography", 11.5.2: "The ElGamal signature scheme", p. 454-459</p>
<p>Two of the signature variants in Note 11.70 are implemented.</p>
<dl class="todo"><dt><b><a class="el" href="todo.html#_todo000002">Todo:</a></b></dt><dd>Implement ElGamal encryption and decryption.</dd></dl>
<dl class="todo"><dt><b><a class="el" href="todo.html#_todo000003">Todo:</a></b></dt><dd>Explore the possibility of using simultaneous multiple exponentiation, as described in HAC, 14.87 (iii).</dd></dl>
<dl class="author"><dt><b>Author:</b></dt><dd>Bob Deblier <<a href="mailto:bob.deblier@telenet.be">bob.deblier@telenet.be</a>> </dd></dl>
</div><hr/><h2>Function Documentation</h2>
<a class="anchor" id="a71210da412fefa0f230a7f988eb83c31"></a><!-- doxytag: member="elgamal.h::elgv1sign" ref="a71210da412fefa0f230a7f988eb83c31" args="(const mpbarrett *p, const mpbarrett *n, const mpnumber *g, randomGeneratorContext *, const mpnumber *hm, const mpnumber *x, mpnumber *r, mpnumber *s)" -->
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">int elgv1sign </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>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>g</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structrandomGeneratorContext.html">randomGeneratorContext</a> * </td>
<td class="paramname"><em>rgc</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>hm</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>x</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>r</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>s</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>This function performs raw ElGamal signing, variant 1. </p>
<p>Signing equations:</p>
<ul>
<li><img class="formulaInl" alt="$r=g^{k}\ \textrm{mod}\ p$" src="form_21.png"/> </li>
<li><img class="formulaInl" alt="$s=k^{-1}(h(m)-xr)\ \textrm{mod}\ (p-1)$" src="form_22.png"/></li>
</ul>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">p</td><td>The prime. </td></tr>
<tr><td class="paramname">n</td><td>The reducer mod (p-1). </td></tr>
<tr><td class="paramname">g</td><td>The generator. </td></tr>
<tr><td class="paramname">rgc</td><td>The pseudo-random generat </td></tr>
<tr><td class="paramname">hm</td><td>The hash to be signed. </td></tr>
<tr><td class="paramname">x</td><td>The private key value. </td></tr>
<tr><td class="paramname">r</td><td>The signature's <em>r</em> value. </td></tr>
<tr><td class="paramname">s</td><td>The signature's <em>s</em> value. </td></tr>
</table>
</dd>
</dl>
<dl><dt><b>Return values:</b></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="ab91d86edb1453350a8e4023e694474ec"></a><!-- doxytag: member="elgamal.h::elgv1vrfy" ref="ab91d86edb1453350a8e4023e694474ec" args="(const mpbarrett *p, const mpbarrett *n, const mpnumber *g, const mpnumber *hm, const mpnumber *y, const mpnumber *r, const mpnumber *s)" -->
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">int elgv1vrfy </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>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>g</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>hm</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>y</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>r</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>s</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>This function performs raw ElGamal verification, variant 1. </p>
<p>Verifying equations:</p>
<ul>
<li>Check <img class="formulaInl" alt="$0<r<p$" src="form_23.png"/> and <img class="formulaInl" alt="$0<s<(p-1)$" src="form_24.png"/> </li>
<li><img class="formulaInl" alt="$v_1=y^{r}r^{s}\ \textrm{mod}\ p$" src="form_25.png"/> </li>
<li><img class="formulaInl" alt="$v_2=g^{h(m)}\ \textrm{mod}\ p$" src="form_26.png"/> </li>
<li>Check <img class="formulaInl" alt="$v_1=v_2$" src="form_27.png"/></li>
</ul>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">p</td><td>The prime. </td></tr>
<tr><td class="paramname">n</td><td>The reducer mod (p-1). </td></tr>
<tr><td class="paramname">g</td><td>The generator. </td></tr>
<tr><td class="paramname">hm</td><td>The hash to be signed. </td></tr>
<tr><td class="paramname">y</td><td>The public key value. </td></tr>
<tr><td class="paramname">r</td><td>The signature's <em>r</em> value. </td></tr>
<tr><td class="paramname">s</td><td>The signature's <em>s</em> value. </td></tr>
</table>
</dd>
</dl>
<dl><dt><b>Return values:</b></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>
</div>
<a class="anchor" id="ab5a4857d59add82a522e0c08c83298f8"></a><!-- doxytag: member="elgamal.h::elgv3sign" ref="ab5a4857d59add82a522e0c08c83298f8" args="(const mpbarrett *p, const mpbarrett *n, const mpnumber *g, randomGeneratorContext *, const mpnumber *hm, const mpnumber *x, mpnumber *r, mpnumber *s)" -->
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">int elgv3sign </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>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>g</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structrandomGeneratorContext.html">randomGeneratorContext</a> * </td>
<td class="paramname"><em>rgc</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>hm</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>x</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>r</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>s</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>This function performs raw ElGamal signing, variant 3. </p>
<p>Signing equations:</p>
<ul>
<li><img class="formulaInl" alt="$r=g^{k}\ \textrm{mod}\ p$" src="form_21.png"/> </li>
<li><img class="formulaInl" alt="$s=xr+kh(m)\ \textrm{mod}\ (p-1)$" src="form_28.png"/></li>
</ul>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">p</td><td>The prime. </td></tr>
<tr><td class="paramname">n</td><td>The reducer mod (p-1). </td></tr>
<tr><td class="paramname">g</td><td>The generator. </td></tr>
<tr><td class="paramname">rgc</td><td>The pseudo-random generat </td></tr>
<tr><td class="paramname">hm</td><td>The hash to be signed. </td></tr>
<tr><td class="paramname">x</td><td>The private key value. </td></tr>
<tr><td class="paramname">r</td><td>The signature's <em>r</em> value. </td></tr>
<tr><td class="paramname">s</td><td>The signature's <em>s</em> value. </td></tr>
</table>
</dd>
</dl>
<dl><dt><b>Return values:</b></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="aaa1c3bb1ca269e9b40ee8a561a3f78f6"></a><!-- doxytag: member="elgamal.h::elgv3vrfy" ref="aaa1c3bb1ca269e9b40ee8a561a3f78f6" args="(const mpbarrett *p, const mpbarrett *n, const mpnumber *g, const mpnumber *hm, const mpnumber *y, const mpnumber *r, const mpnumber *s)" -->
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">int elgv3vrfy </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>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>g</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>hm</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>y</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>r</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>s</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>This function performs raw ElGamal verification, variant 3. </p>
<p>Verifying equations:</p>
<ul>
<li>Check <img class="formulaInl" alt="$0<r<p$" src="form_23.png"/> and <img class="formulaInl" alt="$0<s<(p-1)$" src="form_24.png"/> </li>
<li><img class="formulaInl" alt="$v_1=g^{s}\ \textrm{mod}\ p$" src="form_29.png"/> </li>
<li><img class="formulaInl" alt="$v_2=y^{r}r^{h(m)}\ \textrm{mod}\ p$" src="form_30.png"/> </li>
<li>Check <img class="formulaInl" alt="$v_1=v_2$" src="form_27.png"/></li>
</ul>
<dl><dt><b>Parameters:</b></dt><dd>
<table class="params">
<tr><td class="paramname">p</td><td>The prime. </td></tr>
<tr><td class="paramname">n</td><td>The reducer mod (p-1). </td></tr>
<tr><td class="paramname">g</td><td>The generator. </td></tr>
<tr><td class="paramname">hm</td><td>The hash to be signed. </td></tr>
<tr><td class="paramname">y</td><td>The public key value. </td></tr>
<tr><td class="paramname">r</td><td>The signature's <em>r</em> value. </td></tr>
<tr><td class="paramname">s</td><td>The signature's <em>s</em> value. </td></tr>
</table>
</dd>
</dl>
<dl><dt><b>Return values:</b></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>
</div>
</div>
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