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<p>ECP group structure.
<a href="structmbedtls__ecp__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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Collaboration diagram for mbedtls_ecp_group:</div>
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Data Fields</h2></td></tr>
<tr class="memitem:a3e572cd2e40e1c23fc9a7a6aef7122d6"><td class="memItemLeft" align="right" valign="top"><a class="el" href="ecp_8h.html#af79e530ea8f8416480f805baa20b1a2d">mbedtls_ecp_group_id</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="structmbedtls__ecp__group.html#a3e572cd2e40e1c23fc9a7a6aef7122d6">id</a></td></tr>
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<tr class="memitem:a7e0aca0789ca8f5c38d3a0c98b2f9809"><td class="memItemLeft" align="right" valign="top"><a class="el" href="structmbedtls__ecp__point.html">mbedtls_ecp_point</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="structmbedtls__ecp__group.html#a7e0aca0789ca8f5c38d3a0c98b2f9809">G</a></td></tr>
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<tr class="memitem:a7104724a939b7eef2ae3627db410e1e8"><td class="memItemLeft" align="right" valign="top"><a class="el" href="structmbedtls__mpi.html">mbedtls_mpi</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="structmbedtls__ecp__group.html#a7104724a939b7eef2ae3627db410e1e8">N</a></td></tr>
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<tr class="memitem:a039ad9e51dc52e46a422e74051b2b837"><td class="memItemLeft" align="right" valign="top">size_t </td><td class="memItemRight" valign="bottom"><a class="el" href="structmbedtls__ecp__group.html#a039ad9e51dc52e46a422e74051b2b837">pbits</a></td></tr>
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<tr class="memitem:aee5ef1a30d9a5e34810c7a9a7120a10b"><td class="memItemLeft" align="right" valign="top">size_t </td><td class="memItemRight" valign="bottom"><a class="el" href="structmbedtls__ecp__group.html#aee5ef1a30d9a5e34810c7a9a7120a10b">nbits</a></td></tr>
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<tr class="memitem:a3cc458ace9f663e7827a6c3556e75e64"><td class="memItemLeft" align="right" valign="top">unsigned int </td><td class="memItemRight" valign="bottom"><a class="el" href="structmbedtls__ecp__group.html#a3cc458ace9f663e7827a6c3556e75e64">h</a></td></tr>
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<tr class="memitem:ad828ec2b9dcccb7664744fa5b69f561f"><td class="memItemLeft" align="right" valign="top">int(* </td><td class="memItemRight" valign="bottom"><a class="el" href="structmbedtls__ecp__group.html#ad828ec2b9dcccb7664744fa5b69f561f">modp</a> )(<a class="el" href="structmbedtls__mpi.html">mbedtls_mpi</a> *)</td></tr>
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<tr class="memitem:a2a4fbe0909b4feb994eaac95e1281cc6"><td class="memItemLeft" align="right" valign="top">int(* </td><td class="memItemRight" valign="bottom"><a class="el" href="structmbedtls__ecp__group.html#a2a4fbe0909b4feb994eaac95e1281cc6">t_pre</a> )(<a class="el" href="structmbedtls__ecp__point.html">mbedtls_ecp_point</a> *, void *)</td></tr>
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<tr class="memitem:aa67390761ba1d1f8b724d1550e451908"><td class="memItemLeft" align="right" valign="top">int(* </td><td class="memItemRight" valign="bottom"><a class="el" href="structmbedtls__ecp__group.html#aa67390761ba1d1f8b724d1550e451908">t_post</a> )(<a class="el" href="structmbedtls__ecp__point.html">mbedtls_ecp_point</a> *, void *)</td></tr>
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<tr class="memitem:a7400fa2acba24d9b8a7a107d9fcde36f"><td class="memItemLeft" align="right" valign="top">void * </td><td class="memItemRight" valign="bottom"><a class="el" href="structmbedtls__ecp__group.html#a7400fa2acba24d9b8a7a107d9fcde36f">t_data</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 (Curve25519 + 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#a4d005045c302e100c78bdc587e8f0e6a" title="Multiplication by an integer: R = m * P (Not thread-safe to use same group in multiple threads) ...">mbedtls_ecp_mul()</a> and prime in <a class="el" href="ecdsa_8h.html#af10f6fda2169862871d0ac07555c8641" title="This function computes the ECDSA signature of a previously-hashed message. ">mbedtls_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 <a class="el" href="structmbedtls__mpi.html" title="MPI structure. ">mbedtls_mpi</a> 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 class="definition">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>
</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 class="definition">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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<li>B in the equation, or 2. unused </li>
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<p class="definition">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>generator of the (sub)group used </p>
<p class="definition">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: 1 if the constants are static </p>
<p class="definition">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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<td class="memname"><a class="el" href="ecp_8h.html#af79e530ea8f8416480f805baa20b1a2d">mbedtls_ecp_group_id</a> mbedtls_ecp_group::id</td>
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<p>internal group identifier </p>
<p class="definition">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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<td class="memname">int(* mbedtls_ecp_group::modp) (<a class="el" href="structmbedtls__mpi.html">mbedtls_mpi</a> *)</td>
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<p>function for fast reduction mod P </p>
<p class="definition">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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<li>the order of G, or 2. unused </li>
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<p class="definition">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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<p>number of bits in 1. P, or 2. private keys </p>
<p class="definition">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>prime modulus of the base field </p>
<p class="definition">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 P </p>
<p class="definition">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>pre-computed points for ecp_mul_comb() </p>
<p class="definition">Definition at line <a class="el" href="ecp_8h_source.html#l00155">155</a> of file <a class="el" href="ecp_8h_source.html">ecp.h</a>.</p>
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<p>unused </p>
<p class="definition">Definition at line <a class="el" href="ecp_8h_source.html#l00154">154</a> of file <a class="el" href="ecp_8h_source.html">ecp.h</a>.</p>
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<p>unused </p>
<p class="definition">Definition at line <a class="el" href="ecp_8h_source.html#l00153">153</a> of file <a class="el" href="ecp_8h_source.html">ecp.h</a>.</p>
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<p>unused </p>
<p class="definition">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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<h2 class="memtitle"><span class="permalink"><a href="#a4b9a1bf79d2023dbc3807dc7e12059af">◆ </a></span>T_size</h2>
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<td class="memname">size_t mbedtls_ecp_group::T_size</td>
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<p>number for pre-computed points </p>
<p class="definition">Definition at line <a class="el" href="ecp_8h_source.html#l00156">156</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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