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<p>ECP group structure.
<a href="structecp__group.html#details">More...</a></p>
<p><code>#include <<a class="el" href="ecp_8h_source.html">ecp.h</a>></code></p>
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Data Fields</h2></td></tr>
<tr class="memitem:a8f7b8f453c94152dcb7227639511f323"><td class="memItemLeft" align="right" valign="top"><a class="el" href="ecp_8h.html#a751fce96f17826537221248b4ed5cbd2">ecp_group_id</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="structecp__group.html#a8f7b8f453c94152dcb7227639511f323">id</a></td></tr>
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<tr class="memitem:adb738e2c6df3c75c4b30b2b1c3e61256"><td class="memItemLeft" align="right" valign="top"><a class="el" href="structecp__point.html">ecp_point</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="structecp__group.html#adb738e2c6df3c75c4b30b2b1c3e61256">G</a></td></tr>
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<tr class="memitem:a6b424e0dbad7d3c900375a2ff0154b95"><td class="memItemLeft" align="right" valign="top"><a class="el" href="structmpi.html">mpi</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="structecp__group.html#a6b424e0dbad7d3c900375a2ff0154b95">N</a></td></tr>
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<tr class="memitem:a3a813481e3d2548e372bab92c50f4d48"><td class="memItemLeft" align="right" valign="top">size_t </td><td class="memItemRight" valign="bottom"><a class="el" href="structecp__group.html#a3a813481e3d2548e372bab92c50f4d48">pbits</a></td></tr>
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<tr class="memitem:a372ef0b2cbf3232760e108e5b97c8a3e"><td class="memItemLeft" align="right" valign="top">size_t </td><td class="memItemRight" valign="bottom"><a class="el" href="structecp__group.html#a372ef0b2cbf3232760e108e5b97c8a3e">nbits</a></td></tr>
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<tr class="memitem:af88943414b51c063db7077e833a3f293"><td class="memItemLeft" align="right" valign="top">unsigned int </td><td class="memItemRight" valign="bottom"><a class="el" href="structecp__group.html#af88943414b51c063db7077e833a3f293">h</a></td></tr>
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<tr class="memitem:afcdbaba12db0549629c81baeba2fd738"><td class="memItemLeft" align="right" valign="top">int(* </td><td class="memItemRight" valign="bottom"><a class="el" href="structecp__group.html#afcdbaba12db0549629c81baeba2fd738">modp</a> )(<a class="el" href="structmpi.html">mpi</a> *)</td></tr>
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<tr class="memitem:a1b5b1955d1f8c3f5d275e1b70fa2ef6b"><td class="memItemLeft" align="right" valign="top">int(* </td><td class="memItemRight" valign="bottom"><a class="el" href="structecp__group.html#a1b5b1955d1f8c3f5d275e1b70fa2ef6b">t_pre</a> )(<a class="el" href="structecp__point.html">ecp_point</a> *, void *)</td></tr>
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<tr class="memitem:a725515d364696ab58c49cab20a27bbc5"><td class="memItemLeft" align="right" valign="top">int(* </td><td class="memItemRight" valign="bottom"><a class="el" href="structecp__group.html#a725515d364696ab58c49cab20a27bbc5">t_post</a> )(<a class="el" href="structecp__point.html">ecp_point</a> *, void *)</td></tr>
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<tr class="memitem:aeb5e272208e1568f6f806d4ab14b782f"><td class="memItemLeft" align="right" valign="top">void * </td><td class="memItemRight" valign="bottom"><a class="el" href="structecp__group.html#aeb5e272208e1568f6f806d4ab14b782f">t_data</a></td></tr>
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<tr class="memitem:a14f55dfcfab4b1807f499bde186dff1d"><td class="memItemLeft" align="right" valign="top"><a class="el" href="structecp__point.html">ecp_point</a> * </td><td class="memItemRight" valign="bottom"><a class="el" href="structecp__group.html#a14f55dfcfab4b1807f499bde186dff1d">T</a></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>ECP group structure. </p>
<p>We consider two types of curves equations:</p>
<ol type="1">
<li>Short Weierstrass y^2 = x^3 + A x + B mod P (SEC1 + RFC 4492)</li>
<li>Montgomery, y^2 = x^3 + A x^2 + x mod P (M255 + draft) In both cases, a generator G for a prime-order subgroup is fixed. In the short weierstrass, this subgroup is actually the whole curve, and its cardinal is denoted by N.</li>
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<p>In the case of Short Weierstrass curves, our code requires that N is an odd prime. (Use odd in <a class="el" href="ecp_8h.html#a337b0e41153f458872f7f73bad93711c" title="Multiplication by an integer: R = m * P (Not thread-safe to use same group in multiple threads) ...">ecp_mul()</a> and prime in <a class="el" href="ecdsa_8h.html#a5a5858bde5c49005fefbe74883fc9a9d" title="Compute ECDSA signature of a previously hashed message. ">ecdsa_sign()</a> for blinding.)</p>
<p>In the case of Montgomery curves, we don't store A but (A + 2) / 4 which is the quantity actually used in the formulas. Also, nbits is not the size of N but the required size for private keys.</p>
<p>If modp is NULL, reduction modulo P is done using a generic algorithm. Otherwise, it must point to a function that takes an mpi in the range 0..2^(2*pbits)-1 and transforms it in-place in an integer of little more than pbits, so that the integer may be efficiently brought in the 0..P-1 range by a few additions or substractions. It must return 0 on success and non-zero on failure. </p>
<p>Definition at line <a class="el" href="ecp_8h_source.html#l00136">136</a> of file <a class="el" href="ecp_8h_source.html">ecp.h</a>.</p>
</div><h2 class="groupheader">Field Documentation</h2>
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<li>A in the equation, or 2. (A + 2) / 4 </li>
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<p>Definition at line <a class="el" href="ecp_8h_source.html#l00140">140</a> of file <a class="el" href="ecp_8h_source.html">ecp.h</a>.</p>
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<li>B in the equation, or 2. unused </li>
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<p>Definition at line <a class="el" href="ecp_8h_source.html#l00141">141</a> of file <a class="el" href="ecp_8h_source.html">ecp.h</a>.</p>
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<p>generator of the (sub)group used </p>
<p>Definition at line <a class="el" href="ecp_8h_source.html#l00142">142</a> of file <a class="el" href="ecp_8h_source.html">ecp.h</a>.</p>
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<p>internal: 1 if the constants are static </p>
<p>Definition at line <a class="el" href="ecp_8h_source.html#l00146">146</a> of file <a class="el" href="ecp_8h_source.html">ecp.h</a>.</p>
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<p>internal group identifier </p>
<p>Definition at line <a class="el" href="ecp_8h_source.html#l00138">138</a> of file <a class="el" href="ecp_8h_source.html">ecp.h</a>.</p>
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<p>function for fast reduction mod P </p>
<p>Definition at line <a class="el" href="ecp_8h_source.html#l00147">147</a> of file <a class="el" href="ecp_8h_source.html">ecp.h</a>.</p>
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<li>the order of G, or 2. unused </li>
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<p>Definition at line <a class="el" href="ecp_8h_source.html#l00143">143</a> of file <a class="el" href="ecp_8h_source.html">ecp.h</a>.</p>
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<p>number of bits in 1. P, or 2. private keys </p>
<p>Definition at line <a class="el" href="ecp_8h_source.html#l00145">145</a> of file <a class="el" href="ecp_8h_source.html">ecp.h</a>.</p>
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<p>prime modulus of the base field </p>
<p>Definition at line <a class="el" href="ecp_8h_source.html#l00139">139</a> of file <a class="el" href="ecp_8h_source.html">ecp.h</a>.</p>
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<p>number of bits in P </p>
<p>Definition at line <a class="el" href="ecp_8h_source.html#l00144">144</a> of file <a class="el" href="ecp_8h_source.html">ecp.h</a>.</p>
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<p>pre-computed points for ecp_mul_comb() </p>
<p>Definition at line <a class="el" href="ecp_8h_source.html#l00151">151</a> of file <a class="el" href="ecp_8h_source.html">ecp.h</a>.</p>
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<p>unused </p>
<p>Definition at line <a class="el" href="ecp_8h_source.html#l00150">150</a> of file <a class="el" href="ecp_8h_source.html">ecp.h</a>.</p>
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<p>unused </p>
<p>Definition at line <a class="el" href="ecp_8h_source.html#l00149">149</a> of file <a class="el" href="ecp_8h_source.html">ecp.h</a>.</p>
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<p>unused </p>
<p>Definition at line <a class="el" href="ecp_8h_source.html#l00148">148</a> of file <a class="el" href="ecp_8h_source.html">ecp.h</a>.</p>
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<p>number for pre-computed points </p>
<p>Definition at line <a class="el" href="ecp_8h_source.html#l00152">152</a> of file <a class="el" href="ecp_8h_source.html">ecp.h</a>.</p>
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<hr/>The documentation for this struct was generated from the following file:<ul>
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