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<div class="textblock"><code>#include "<a class="el" href="scalar_8h_source.html">scalar.h</a>"</code><br />
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<code>#include "<a class="el" href="field_8h_source.html">field.h</a>"</code><br />
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<code>#include "<a class="el" href="group_8h_source.html">group.h</a>"</code><br />
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<code>#include "<a class="el" href="ecmult_8h_source.html">ecmult.h</a>"</code><br />
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<code>#include "<a class="el" href="ecmult__gen_8h_source.html">ecmult_gen.h</a>"</code><br />
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<code>#include "<a class="el" href="ecdsa_8h_source.html">ecdsa.h</a>"</code><br />
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</div>
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<p><a href="ecdsa__impl_8h_source.html">Go to the source code of this file.</a></p>
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<table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
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Functions</h2></td></tr>
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<tr class="memitem:a77ce85411873130e59bc88f17c81b49c"><td class="memItemLeft" align="right" valign="top">static int </td><td class="memItemRight" valign="bottom"><a class="el" href="ecdsa__impl_8h.html#a77ce85411873130e59bc88f17c81b49c">secp256k1_der_read_len</a> (const unsigned char **sigp, const unsigned char *sigend)</td></tr>
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<tr class="separator:a77ce85411873130e59bc88f17c81b49c"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a701c7cf2fd0fa52c2e3301f719f3fe4a"><td class="memItemLeft" align="right" valign="top">static int </td><td class="memItemRight" valign="bottom"><a class="el" href="ecdsa__impl_8h.html#a701c7cf2fd0fa52c2e3301f719f3fe4a">secp256k1_der_parse_integer</a> (<a class="el" href="structsecp256k1__scalar.html">secp256k1_scalar</a> *r, const unsigned char **sig, const unsigned char *sigend)</td></tr>
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<tr class="separator:a701c7cf2fd0fa52c2e3301f719f3fe4a"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:af5f863608f65607ecc117a594448baf1"><td class="memItemLeft" align="right" valign="top">static int </td><td class="memItemRight" valign="bottom"><a class="el" href="ecdsa__impl_8h.html#af5f863608f65607ecc117a594448baf1">secp256k1_ecdsa_sig_parse</a> (<a class="el" href="structsecp256k1__scalar.html">secp256k1_scalar</a> *rr, <a class="el" href="structsecp256k1__scalar.html">secp256k1_scalar</a> *rs, const unsigned char *sig, size_t size)</td></tr>
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<tr class="separator:af5f863608f65607ecc117a594448baf1"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a6c508d97dd87ab97fa01e9abac597a53"><td class="memItemLeft" align="right" valign="top">static int </td><td class="memItemRight" valign="bottom"><a class="el" href="ecdsa__impl_8h.html#a6c508d97dd87ab97fa01e9abac597a53">secp256k1_ecdsa_sig_serialize</a> (unsigned char *sig, size_t *size, const <a class="el" href="structsecp256k1__scalar.html">secp256k1_scalar</a> *ar, const <a class="el" href="structsecp256k1__scalar.html">secp256k1_scalar</a> *as)</td></tr>
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<tr class="separator:a6c508d97dd87ab97fa01e9abac597a53"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a3f5883c08cc865fd9a4ca3f6173b1c26"><td class="memItemLeft" align="right" valign="top">static int </td><td class="memItemRight" valign="bottom"><a class="el" href="ecdsa__impl_8h.html#a3f5883c08cc865fd9a4ca3f6173b1c26">secp256k1_ecdsa_sig_verify</a> (const <a class="el" href="structsecp256k1__ecmult__context.html">secp256k1_ecmult_context</a> *<a class="el" href="tests_8c.html#a06a3e29ada83211a695a49e8f7405842">ctx</a>, const <a class="el" href="structsecp256k1__scalar.html">secp256k1_scalar</a> *sigr, const <a class="el" href="structsecp256k1__scalar.html">secp256k1_scalar</a> *sigs, const <a class="el" href="structsecp256k1__ge.html">secp256k1_ge</a> *pubkey, const <a class="el" href="structsecp256k1__scalar.html">secp256k1_scalar</a> *message)</td></tr>
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<tr class="separator:a3f5883c08cc865fd9a4ca3f6173b1c26"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a3eaa1b23550fa2ccf948e67f2c87a330"><td class="memItemLeft" align="right" valign="top">static int </td><td class="memItemRight" valign="bottom"><a class="el" href="ecdsa__impl_8h.html#a3eaa1b23550fa2ccf948e67f2c87a330">secp256k1_ecdsa_sig_sign</a> (const <a class="el" href="structsecp256k1__ecmult__gen__context.html">secp256k1_ecmult_gen_context</a> *<a class="el" href="tests_8c.html#a06a3e29ada83211a695a49e8f7405842">ctx</a>, <a class="el" href="structsecp256k1__scalar.html">secp256k1_scalar</a> *sigr, <a class="el" href="structsecp256k1__scalar.html">secp256k1_scalar</a> *sigs, const <a class="el" href="structsecp256k1__scalar.html">secp256k1_scalar</a> *seckey, const <a class="el" href="structsecp256k1__scalar.html">secp256k1_scalar</a> *message, const <a class="el" href="structsecp256k1__scalar.html">secp256k1_scalar</a> *nonce, int *recid)</td></tr>
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<tr class="separator:a3eaa1b23550fa2ccf948e67f2c87a330"><td class="memSeparator" colspan="2"> </td></tr>
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</table><table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="var-members"></a>
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Variables</h2></td></tr>
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<tr class="memitem:a46b45ada7a9487fc9ecda46927094f74"><td class="memItemLeft" align="right" valign="top">static const <a class="el" href="structsecp256k1__fe.html">secp256k1_fe</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="ecdsa__impl_8h.html#a46b45ada7a9487fc9ecda46927094f74">secp256k1_ecdsa_const_order_as_fe</a></td></tr>
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<tr class="separator:a46b45ada7a9487fc9ecda46927094f74"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a2f1a533c601e3dfa234d2f860670d137"><td class="memItemLeft" align="right" valign="top">static const <a class="el" href="structsecp256k1__fe.html">secp256k1_fe</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="ecdsa__impl_8h.html#a2f1a533c601e3dfa234d2f860670d137">secp256k1_ecdsa_const_p_minus_order</a></td></tr>
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<tr class="separator:a2f1a533c601e3dfa234d2f860670d137"><td class="memSeparator" colspan="2"> </td></tr>
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</table>
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<h2 class="groupheader">Function Documentation</h2>
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<a id="a701c7cf2fd0fa52c2e3301f719f3fe4a"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a701c7cf2fd0fa52c2e3301f719f3fe4a">◆ </a></span>secp256k1_der_parse_integer()</h2>
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<td class="memname">static int secp256k1_der_parse_integer </td>
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<td>(</td>
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<td class="paramtype"><a class="el" href="structsecp256k1__scalar.html">secp256k1_scalar</a> * </td>
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<td class="paramname"><em>r</em>, </td>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">const unsigned char ** </td>
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<td class="paramname"><em>sig</em>, </td>
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<td class="paramkey"></td>
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<td class="paramtype">const unsigned char * </td>
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<td class="paramname"><em>sigend</em> </td>
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<p class="definition">Definition at line <a class="el" href="ecdsa__impl_8h_source.html#l00101">101</a> of file <a class="el" href="ecdsa__impl_8h_source.html">ecdsa_impl.h</a>.</p>
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<p class="reference">Referenced by <a class="el" href="ecdsa__impl_8h_source.html#l00147">secp256k1_ecdsa_sig_parse()</a>.</p>
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<a id="a77ce85411873130e59bc88f17c81b49c"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a77ce85411873130e59bc88f17c81b49c">◆ </a></span>secp256k1_der_read_len()</h2>
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<td class="memname">static int secp256k1_der_read_len </td>
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<td>(</td>
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<td class="paramtype">const unsigned char ** </td>
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<td class="paramname"><em>sigp</em>, </td>
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<td class="paramkey"></td>
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<td class="paramtype">const unsigned char * </td>
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<td class="paramname"><em>sigend</em> </td>
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<span class="mlabels"><span class="mlabel">static</span></span> </td>
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<p class="definition">Definition at line <a class="el" href="ecdsa__impl_8h_source.html#l00049">49</a> of file <a class="el" href="ecdsa__impl_8h_source.html">ecdsa_impl.h</a>.</p>
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<p class="reference">Referenced by <a class="el" href="ecdsa__impl_8h_source.html#l00101">secp256k1_der_parse_integer()</a>, and <a class="el" href="ecdsa__impl_8h_source.html#l00147">secp256k1_ecdsa_sig_parse()</a>.</p>
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<a id="af5f863608f65607ecc117a594448baf1"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#af5f863608f65607ecc117a594448baf1">◆ </a></span>secp256k1_ecdsa_sig_parse()</h2>
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<td class="memname">static int secp256k1_ecdsa_sig_parse </td>
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<td>(</td>
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<td class="paramtype"><a class="el" href="structsecp256k1__scalar.html">secp256k1_scalar</a> * </td>
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<td class="paramname"><em>rr</em>, </td>
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<td class="paramkey"></td>
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<td class="paramtype"><a class="el" href="structsecp256k1__scalar.html">secp256k1_scalar</a> * </td>
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<td class="paramname"><em>rs</em>, </td>
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<td class="paramname"><em>sig</em>, </td>
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<td class="paramtype">size_t </td>
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<p class="definition">Definition at line <a class="el" href="ecdsa__impl_8h_source.html#l00147">147</a> of file <a class="el" href="ecdsa__impl_8h_source.html">ecdsa_impl.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a6c508d97dd87ab97fa01e9abac597a53">◆ </a></span>secp256k1_ecdsa_sig_serialize()</h2>
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<td class="memname">static int secp256k1_ecdsa_sig_serialize </td>
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<td>(</td>
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<td class="paramtype">unsigned char * </td>
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<td class="paramname"><em>sig</em>, </td>
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<td class="paramname"><em>ar</em>, </td>
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<td class="paramname"><em>as</em> </td>
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<p class="definition">Definition at line <a class="el" href="ecdsa__impl_8h_source.html#l00179">179</a> of file <a class="el" href="ecdsa__impl_8h_source.html">ecdsa_impl.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a3eaa1b23550fa2ccf948e67f2c87a330">◆ </a></span>secp256k1_ecdsa_sig_sign()</h2>
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<td>(</td>
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<td class="paramtype">const <a class="el" href="structsecp256k1__ecmult__gen__context.html">secp256k1_ecmult_gen_context</a> * </td>
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<td class="paramname"><em>ctx</em>, </td>
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<td class="paramtype"><a class="el" href="structsecp256k1__scalar.html">secp256k1_scalar</a> * </td>
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<td class="paramname"><em>sigr</em>, </td>
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<td class="paramtype"><a class="el" href="structsecp256k1__scalar.html">secp256k1_scalar</a> * </td>
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<td class="paramname"><em>sigs</em>, </td>
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<td class="paramtype">const <a class="el" href="structsecp256k1__scalar.html">secp256k1_scalar</a> * </td>
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<td class="paramname"><em>seckey</em>, </td>
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<td class="paramtype">const <a class="el" href="structsecp256k1__scalar.html">secp256k1_scalar</a> * </td>
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<td class="paramname"><em>message</em>, </td>
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<td class="paramtype">const <a class="el" href="structsecp256k1__scalar.html">secp256k1_scalar</a> * </td>
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<p class="definition">Definition at line <a class="el" href="ecdsa__impl_8h_source.html#l00257">257</a> of file <a class="el" href="ecdsa__impl_8h_source.html">ecdsa_impl.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a3f5883c08cc865fd9a4ca3f6173b1c26">◆ </a></span>secp256k1_ecdsa_sig_verify()</h2>
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<td>(</td>
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<td class="paramtype">const <a class="el" href="structsecp256k1__ecmult__context.html">secp256k1_ecmult_context</a> * </td>
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<td class="paramtype">const <a class="el" href="structsecp256k1__scalar.html">secp256k1_scalar</a> * </td>
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<td class="paramtype">const <a class="el" href="structsecp256k1__ge.html">secp256k1_ge</a> * </td>
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<td class="paramname"><em>pubkey</em>, </td>
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<p>We now have the recomputed R point in pr, and its claimed x coordinate (modulo n) in xr. Naively, we would extract the x coordinate from pr (requiring a inversion modulo p), compute the remainder modulo n, and compare it to xr. However: </p><pre class="fragment"> xr == X(pr) mod n
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</pre><p> <=> exists h. (xr + h * n < p && xr + h * n == <a class="el" href="net_8cpp.html#a826edd40636cbaa44266b97c8c6a4fa3">X(pr)</a>) [Since 2 * n > p, h can only be 0 or 1] <=> (xr == <a class="el" href="net_8cpp.html#a826edd40636cbaa44266b97c8c6a4fa3">X(pr)</a>) || (xr + n < p && xr + n == <a class="el" href="net_8cpp.html#a826edd40636cbaa44266b97c8c6a4fa3">X(pr)</a>) [In Jacobian coordinates, <a class="el" href="net_8cpp.html#a826edd40636cbaa44266b97c8c6a4fa3">X(pr)</a> is pr.x / pr.z^2 mod p] <=> (xr == pr.x / pr.z^2 mod p) || (xr + n < p && xr + n == pr.x / pr.z^2 mod p) [Multiplying both sides of the equations by pr.z^2 mod p] <=> (xr * pr.z^2 mod p == pr.x) || (xr + n < p && (xr + n) * pr.z^2 mod p == pr.x)</p>
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<p>Thus, we can avoid the inversion, but we have to check both cases separately. secp256k1_gej_eq_x implements the (xr * pr.z^2 mod p == pr.x) test.</p>
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<p class="definition">Definition at line <a class="el" href="ecdsa__impl_8h_source.html#l00203">203</a> of file <a class="el" href="ecdsa__impl_8h_source.html">ecdsa_impl.h</a>.</p>
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<h2 class="groupheader">Variable Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a46b45ada7a9487fc9ecda46927094f74">◆ </a></span>secp256k1_ecdsa_const_order_as_fe</h2>
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<td class="memname">const <a class="el" href="structsecp256k1__fe.html">secp256k1_fe</a> secp256k1_ecdsa_const_order_as_fe</td>
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<b>Initial value:</b><div class="fragment"><div class="line">= <a class="code" href="field__10x26_8h.html#a8c00ba3d97ea0d9b0d461463e890de15">SECP256K1_FE_CONST</a>(</div><div class="line"> 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL,</div><div class="line"> 0xBAAEDCE6UL, 0xAF48A03BUL, 0xBFD25E8CUL, 0xD0364141UL</div><div class="line">)</div><div class="ttc" id="field__10x26_8h_html_a8c00ba3d97ea0d9b0d461463e890de15"><div class="ttname"><a href="field__10x26_8h.html#a8c00ba3d97ea0d9b0d461463e890de15">SECP256K1_FE_CONST</a></div><div class="ttdeci">#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0)</div><div class="ttdef"><b>Definition:</b> <a href="field__10x26_8h_source.html#l00038">field_10x26.h:38</a></div></div>
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</div><!-- fragment --><p>Group order for secp256k1 defined as 'n' in "Standards for Efficient Cryptography" (SEC2) 2.7.1 sage: for t in xrange(1023, -1, -1): .. p = 2**256 - 2**32 - t .. if p.is_prime(): .. print 'x'p .. break 'fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f' sage: a = 0 sage: b = 7 sage: F = FiniteField (p) sage: 'x' % (EllipticCurve ([F (a), F (b)]).order()) 'fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141' </p>
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<p class="definition">Definition at line <a class="el" href="ecdsa__impl_8h_source.html#l00031">31</a> of file <a class="el" href="ecdsa__impl_8h_source.html">ecdsa_impl.h</a>.</p>
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<p class="reference">Referenced by <a class="el" href="recovery_2main__impl_8h_source.html#l00087">secp256k1_ecdsa_sig_recover()</a>, and <a class="el" href="ecdsa__impl_8h_source.html#l00203">secp256k1_ecdsa_sig_verify()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a2f1a533c601e3dfa234d2f860670d137">◆ </a></span>secp256k1_ecdsa_const_p_minus_order</h2>
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<td class="memname">const <a class="el" href="structsecp256k1__fe.html">secp256k1_fe</a> secp256k1_ecdsa_const_p_minus_order</td>
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<b>Initial value:</b><div class="fragment"><div class="line">= <a class="code" href="field__10x26_8h.html#a8c00ba3d97ea0d9b0d461463e890de15">SECP256K1_FE_CONST</a>(</div><div class="line"> 0, 0, 0, 1, 0x45512319UL, 0x50B75FC4UL, 0x402DA172UL, 0x2FC9BAEEUL</div><div class="line">)</div><div class="ttc" id="field__10x26_8h_html_a8c00ba3d97ea0d9b0d461463e890de15"><div class="ttname"><a href="field__10x26_8h.html#a8c00ba3d97ea0d9b0d461463e890de15">SECP256K1_FE_CONST</a></div><div class="ttdeci">#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0)</div><div class="ttdef"><b>Definition:</b> <a href="field__10x26_8h_source.html#l00038">field_10x26.h:38</a></div></div>
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</div><!-- fragment --><p>Difference between field and order, values 'p' and 'n' values defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. sage: p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F sage: a = 0 sage: b = 7 sage: F = FiniteField (p) sage: 'x' % (p - EllipticCurve ([F (a), F (b)]).order()) '14551231950b75fc4402da1722fc9baee' </p>
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<p class="definition">Definition at line <a class="el" href="ecdsa__impl_8h_source.html#l00045">45</a> of file <a class="el" href="ecdsa__impl_8h_source.html">ecdsa_impl.h</a>.</p>
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<p class="reference">Referenced by <a class="el" href="recovery_2main__impl_8h_source.html#l00087">secp256k1_ecdsa_sig_recover()</a>, and <a class="el" href="ecdsa__impl_8h_source.html#l00203">secp256k1_ecdsa_sig_verify()</a>.</p>
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