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<div class="title">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></div> </div>
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<p>ElGamal algorithm.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include "<a class="el" href="mpbarrett_8h_source.html">beecrypt/mpbarrett.h</a>"</code><br/>
</div><div class="textblock"><div class="dynheader">
Include dependency graph for elgamal.h:</div>
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<div class="center"><img src="elgamal_8h__incl.png" border="0" usemap="#include_2beecrypt_2elgamal_8h" alt=""/></div>
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<area shape="rect" id="node2" href="mpbarrett_8h.html" title="Multi-precision integer routines using Barrett modular reduction, headers. " alt="" coords="598,80,740,107"/><area shape="rect" id="node3" href="beecrypt_8h.html" title="BeeCrypt API, headers. " alt="" coords="461,155,597,181"/><area shape="rect" id="node17" href="mpnumber_8h.html" title="Multi-precision numbers, headers. " alt="" coords="595,229,743,256"/><area shape="rect" id="node4" href="api_8h.html" title="BeeCrypt API, portability headers. " alt="" coords="444,379,548,405"/><area shape="rect" id="node16" href="memchunk_8h.html" title="beecrypt/memchunk.h" alt="" coords="421,229,571,256"/><area shape="rect" id="node5" href="gnu_8h.html" title="beecrypt/gnu.h" alt="" coords="442,453,549,480"/><area shape="rect" id="node18" href="mp_8h.html" title="Multi-precision integer routines. " alt="" coords="589,304,693,331"/><area shape="rect" id="node19" href="mpopt_8h.html" title="Multi-precision integer optimization definitions. " alt="" coords="580,379,703,405"/></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 class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:a71210da412fefa0f230a7f988eb83c31"><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 class="memdesc:a71210da412fefa0f230a7f988eb83c31"><td class="mdescLeft"> </td><td class="mdescRight">This function performs raw ElGamal signing, variant 1. <a href="#a71210da412fefa0f230a7f988eb83c31">More...</a><br/></td></tr>
<tr class="separator:a71210da412fefa0f230a7f988eb83c31"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ab5a4857d59add82a522e0c08c83298f8"><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 class="memdesc:ab5a4857d59add82a522e0c08c83298f8"><td class="mdescLeft"> </td><td class="mdescRight">This function performs raw ElGamal signing, variant 3. <a href="#ab5a4857d59add82a522e0c08c83298f8">More...</a><br/></td></tr>
<tr class="separator:ab5a4857d59add82a522e0c08c83298f8"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ab91d86edb1453350a8e4023e694474ec"><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 class="memdesc:ab91d86edb1453350a8e4023e694474ec"><td class="mdescLeft"> </td><td class="mdescRight">This function performs raw ElGamal verification, variant 1. <a href="#ab91d86edb1453350a8e4023e694474ec">More...</a><br/></td></tr>
<tr class="separator:ab91d86edb1453350a8e4023e694474ec"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aaa1c3bb1ca269e9b40ee8a561a3f78f6"><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 class="memdesc:aaa1c3bb1ca269e9b40ee8a561a3f78f6"><td class="mdescLeft"> </td><td class="mdescRight">This function performs raw ElGamal verification, variant 3. <a href="#aaa1c3bb1ca269e9b40ee8a561a3f78f6">More...</a><br/></td></tr>
<tr class="separator:aaa1c3bb1ca269e9b40ee8a561a3f78f6"><td class="memSeparator" colspan="2"> </td></tr>
</table>
<a name="details" id="details"></a><h2 class="groupheader">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="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="a71210da412fefa0f230a7f988eb83c31"></a>
<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 class="params"><dt>Parameters</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 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="ab91d86edb1453350a8e4023e694474ec"></a>
<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 class="params"><dt>Parameters</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 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>
</div>
<a class="anchor" id="ab5a4857d59add82a522e0c08c83298f8"></a>
<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 class="params"><dt>Parameters</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 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="aaa1c3bb1ca269e9b40ee8a561a3f78f6"></a>
<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 class="params"><dt>Parameters</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 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>
</div>
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