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<div class="textblock"><code>#include &quot;<a class="el" href="secp256k1_2src_2util_8h_source.html">util.h</a>&quot;</code><br />
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<p><a href="field__impl_8h_source.html">Go to the source code of this file.</a></p>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:a33b925095ff0c60cd468d5a91d3ec788"><td class="memItemLeft" align="right" valign="top">static <a class="el" href="secp256k1_8h.html#a7ddc487fd46aee88f21cabedb7268b1e">SECP256K1_INLINE</a> int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="field__impl_8h.html#a33b925095ff0c60cd468d5a91d3ec788">secp256k1_fe_equal_var</a> (const <a class="el" href="structsecp256k1__fe.html">secp256k1_fe</a> *a, const <a class="el" href="structsecp256k1__fe.html">secp256k1_fe</a> *b)</td></tr>
<tr class="separator:a33b925095ff0c60cd468d5a91d3ec788"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:adeed9551ce946187f98c5e3d789e9575"><td class="memItemLeft" align="right" valign="top">static int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="field__impl_8h.html#adeed9551ce946187f98c5e3d789e9575">secp256k1_fe_sqrt_var</a> (<a class="el" href="structsecp256k1__fe.html">secp256k1_fe</a> *r, const <a class="el" href="structsecp256k1__fe.html">secp256k1_fe</a> *a)</td></tr>
<tr class="separator:adeed9551ce946187f98c5e3d789e9575"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a3a071aa04ce0d88003b059c0a8ee0c0e"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="field__impl_8h.html#a3a071aa04ce0d88003b059c0a8ee0c0e">secp256k1_fe_inv</a> (<a class="el" href="structsecp256k1__fe.html">secp256k1_fe</a> *r, const <a class="el" href="structsecp256k1__fe.html">secp256k1_fe</a> *a)</td></tr>
<tr class="separator:a3a071aa04ce0d88003b059c0a8ee0c0e"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a0090ecfb39b34a8965cc16ae1feca5aa"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="field__impl_8h.html#a0090ecfb39b34a8965cc16ae1feca5aa">secp256k1_fe_inv_var</a> (<a class="el" href="structsecp256k1__fe.html">secp256k1_fe</a> *r, const <a class="el" href="structsecp256k1__fe.html">secp256k1_fe</a> *a)</td></tr>
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<tr class="memitem:a728a757d8960973603be6f3b2aa13f4e"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="field__impl_8h.html#a728a757d8960973603be6f3b2aa13f4e">secp256k1_fe_inv_all_var</a> (size_t len, <a class="el" href="structsecp256k1__fe.html">secp256k1_fe</a> *r, const <a class="el" href="structsecp256k1__fe.html">secp256k1_fe</a> *a)</td></tr>
<tr class="separator:a728a757d8960973603be6f3b2aa13f4e"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<h2 class="groupheader">Function Documentation</h2>
<a id="a33b925095ff0c60cd468d5a91d3ec788"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a33b925095ff0c60cd468d5a91d3ec788">&#9670;&nbsp;</a></span>secp256k1_fe_equal_var()</h2>
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<td class="memname">static <a class="el" href="secp256k1_8h.html#a7ddc487fd46aee88f21cabedb7268b1e">SECP256K1_INLINE</a> int secp256k1_fe_equal_var </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="structsecp256k1__fe.html">secp256k1_fe</a> *&#160;</td>
<td class="paramname"><em>a</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="structsecp256k1__fe.html">secp256k1_fe</a> *&#160;</td>
<td class="paramname"><em>b</em>&#160;</td>
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<td>)</td>
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<p class="definition">Definition at line <a class="el" href="field__impl_8h_source.html#l00024">24</a> of file <a class="el" href="field__impl_8h_source.html">field_impl.h</a>.</p>
<p class="reference">Referenced by <a class="el" href="field__impl_8h_source.html#l00031">secp256k1_fe_sqrt_var()</a>.</p>
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<a id="a3a071aa04ce0d88003b059c0a8ee0c0e"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a3a071aa04ce0d88003b059c0a8ee0c0e">&#9670;&nbsp;</a></span>secp256k1_fe_inv()</h2>
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<td class="memname">static void secp256k1_fe_inv </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structsecp256k1__fe.html">secp256k1_fe</a> *&#160;</td>
<td class="paramname"><em>r</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="structsecp256k1__fe.html">secp256k1_fe</a> *&#160;</td>
<td class="paramname"><em>a</em>&#160;</td>
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<td>)</td>
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<p>The binary representation of (p - 2) has 5 blocks of 1s, with lengths in { 1, 2, 22, 223 }. Use an addition chain to calculate 2^n - 1 for each block: [1], [2], 3, 6, 9, 11, [22], 44, 88, 176, 220, [223]</p>
<p class="definition">Definition at line <a class="el" href="field__impl_8h_source.html#l00129">129</a> of file <a class="el" href="field__impl_8h_source.html">field_impl.h</a>.</p>
<p class="reference">Referenced by <a class="el" href="field__impl_8h_source.html#l00219">secp256k1_fe_inv_var()</a>.</p>
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<a id="a728a757d8960973603be6f3b2aa13f4e"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a728a757d8960973603be6f3b2aa13f4e">&#9670;&nbsp;</a></span>secp256k1_fe_inv_all_var()</h2>
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<td class="memname">static void secp256k1_fe_inv_all_var </td>
<td>(</td>
<td class="paramtype">size_t&#160;</td>
<td class="paramname"><em>len</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structsecp256k1__fe.html">secp256k1_fe</a> *&#160;</td>
<td class="paramname"><em>r</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="structsecp256k1__fe.html">secp256k1_fe</a> *&#160;</td>
<td class="paramname"><em>a</em>&#160;</td>
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<td>)</td>
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<p class="definition">Definition at line <a class="el" href="field__impl_8h_source.html#l00256">256</a> of file <a class="el" href="field__impl_8h_source.html">field_impl.h</a>.</p>
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<a id="a0090ecfb39b34a8965cc16ae1feca5aa"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a0090ecfb39b34a8965cc16ae1feca5aa">&#9670;&nbsp;</a></span>secp256k1_fe_inv_var()</h2>
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<td class="memname">static void secp256k1_fe_inv_var </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structsecp256k1__fe.html">secp256k1_fe</a> *&#160;</td>
<td class="paramname"><em>r</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="structsecp256k1__fe.html">secp256k1_fe</a> *&#160;</td>
<td class="paramname"><em>a</em>&#160;</td>
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<td>)</td>
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<p class="definition">Definition at line <a class="el" href="field__impl_8h_source.html#l00219">219</a> of file <a class="el" href="field__impl_8h_source.html">field_impl.h</a>.</p>
<p class="reference">Referenced by <a class="el" href="field__impl_8h_source.html#l00256">secp256k1_fe_inv_all_var()</a>.</p>
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<a id="adeed9551ce946187f98c5e3d789e9575"></a>
<h2 class="memtitle"><span class="permalink"><a href="#adeed9551ce946187f98c5e3d789e9575">&#9670;&nbsp;</a></span>secp256k1_fe_sqrt_var()</h2>
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<td class="memname">static int secp256k1_fe_sqrt_var </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structsecp256k1__fe.html">secp256k1_fe</a> *&#160;</td>
<td class="paramname"><em>r</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="structsecp256k1__fe.html">secp256k1_fe</a> *&#160;</td>
<td class="paramname"><em>a</em>&#160;</td>
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<td>)</td>
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<p>Given that p is congruent to 3 mod 4, we can compute the square root of a mod p as the (p+1)/4'th power of a.</p>
<p>As (p+1)/4 is an even number, it will have the same result for a and for (-a). Only one of these two numbers actually has a square root however, so we test at the end by squaring and comparing to the input. Also because (p+1)/4 is an even number, the computed square root is itself always a square (a ** ((p+1)/4) is the square of a ** ((p+1)/8)).</p>
<p>The binary representation of (p + 1)/4 has 3 blocks of 1s, with lengths in { 2, 22, 223 }. Use an addition chain to calculate 2^n - 1 for each block: 1, [2], 3, 6, 9, 11, [22], 44, 88, 176, 220, [223]</p>
<p class="definition">Definition at line <a class="el" href="field__impl_8h_source.html#l00031">31</a> of file <a class="el" href="field__impl_8h_source.html">field_impl.h</a>.</p>
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