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<div class="title">ciphers::elliptic_curve_key_exchange Namespace Reference</div> </div>
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<p>namespace <a class="el" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html" title="namespace elliptic_curve_key_exchange">elliptic_curve_key_exchange</a>
<a href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#details">More...</a></p>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="nested-classes"></a>
Classes</h2></td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">struct &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html">Point</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">Definition of struct <a class="el" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html" title="Definition of struct Point.">Point</a>. <a href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html#details">More...</a><br /></td></tr>
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Typedefs</h2></td></tr>
<tr class="memitem:af0a6e3521629c25c2b5d620f26429830"><td class="memItemLeft" align="right" valign="top">typedef struct <a class="el" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html">ciphers::elliptic_curve_key_exchange::Point</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#af0a6e3521629c25c2b5d620f26429830">Point</a></td></tr>
<tr class="memdesc:af0a6e3521629c25c2b5d620f26429830"><td class="mdescLeft">&#160;</td><td class="mdescRight">Definition of struct <a class="el" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html" title="Definition of struct Point.">Point</a>. <a href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#af0a6e3521629c25c2b5d620f26429830">More...</a><br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:ac00616a4e40d3cd5cfb4da87d9ff9af0"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../d1/d83/classuint256__t.html">uint256_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#ac00616a4e40d3cd5cfb4da87d9ff9af0">exp</a> (<a class="el" href="../../d1/d83/classuint256__t.html">uint256_t</a> number, <a class="el" href="../../d1/d83/classuint256__t.html">uint256_t</a> <a class="el" href="../../d7/d35/matrix__exponentiation_8cpp.html#a5769b745458157ef2679949155684f3b">power</a>, const <a class="el" href="../../d1/d83/classuint256__t.html">uint256_t</a> &amp;mod)</td></tr>
<tr class="memdesc:ac00616a4e40d3cd5cfb4da87d9ff9af0"><td class="mdescLeft">&#160;</td><td class="mdescRight">This function calculates number raised to exponent power under modulo mod using <a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/modular_exponentiation.cpp">Modular Exponentiation</a>. <a href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#ac00616a4e40d3cd5cfb4da87d9ff9af0">More...</a><br /></td></tr>
<tr class="separator:ac00616a4e40d3cd5cfb4da87d9ff9af0"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:acc5fe9c2032fb7582c38a20d1fa69bcf"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html">Point</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#acc5fe9c2032fb7582c38a20d1fa69bcf">addition</a> (<a class="el" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html">Point</a> a, <a class="el" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html">Point</a> b, const <a class="el" href="../../d1/d83/classuint256__t.html">uint256_t</a> &amp;curve_a_coeff, <a class="el" href="../../d1/d83/classuint256__t.html">uint256_t</a> mod)</td></tr>
<tr class="memdesc:acc5fe9c2032fb7582c38a20d1fa69bcf"><td class="mdescLeft">&#160;</td><td class="mdescRight">Addition of points. <a href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#acc5fe9c2032fb7582c38a20d1fa69bcf">More...</a><br /></td></tr>
<tr class="separator:acc5fe9c2032fb7582c38a20d1fa69bcf"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a17f3d667241b88115a95282cdd719cb2"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html">Point</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#a17f3d667241b88115a95282cdd719cb2">multiply</a> (const <a class="el" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html">Point</a> &amp;a, const <a class="el" href="../../d1/d83/classuint256__t.html">uint256_t</a> &amp;curve_a_coeff, <a class="el" href="../../d1/d83/classuint256__t.html">uint256_t</a> p, const <a class="el" href="../../d1/d83/classuint256__t.html">uint256_t</a> &amp;mod)</td></tr>
<tr class="memdesc:a17f3d667241b88115a95282cdd719cb2"><td class="mdescLeft">&#160;</td><td class="mdescRight">multiply <a class="el" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html" title="Definition of struct Point.">Point</a> and integer <a href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#a17f3d667241b88115a95282cdd719cb2">More...</a><br /></td></tr>
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</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>namespace <a class="el" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html" title="namespace elliptic_curve_key_exchange">elliptic_curve_key_exchange</a> </p>
<p>Demonstration of <a href="https://cryptobook.nakov.com/asymmetric-key-ciphers/ecdh-key-exchange">Elliptic Curve Diffie-Hellman</a> key exchange. </p>
</div><h2 class="groupheader">Typedef Documentation</h2>
<a id="af0a6e3521629c25c2b5d620f26429830"></a>
<h2 class="memtitle"><span class="permalink"><a href="#af0a6e3521629c25c2b5d620f26429830">&#9670;&nbsp;</a></span>Point</h2>
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<div class="memproto">
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<td class="memname">typedef struct <a class="el" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html">ciphers::elliptic_curve_key_exchange::Point</a> <a class="el" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html">ciphers::elliptic_curve_key_exchange::Point</a></td>
</tr>
</table>
</div><div class="memdoc">
<p>Definition of struct <a class="el" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html" title="Definition of struct Point.">Point</a>. </p>
<p>Definition of <a class="el" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html" title="Definition of struct Point.">Point</a> in the curve. </p>
</div>
</div>
<h2 class="groupheader">Function Documentation</h2>
<a id="acc5fe9c2032fb7582c38a20d1fa69bcf"></a>
<h2 class="memtitle"><span class="permalink"><a href="#acc5fe9c2032fb7582c38a20d1fa69bcf">&#9670;&nbsp;</a></span>addition()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname"><a class="el" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html">Point</a> ciphers::elliptic_curve_key_exchange::addition </td>
<td>(</td>
<td class="paramtype"><a class="el" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html">Point</a>&#160;</td>
<td class="paramname"><em>a</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html">Point</a>&#160;</td>
<td class="paramname"><em>b</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="../../d1/d83/classuint256__t.html">uint256_t</a> &amp;&#160;</td>
<td class="paramname"><em>curve_a_coeff</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="../../d1/d83/classuint256__t.html">uint256_t</a>&#160;</td>
<td class="paramname"><em>mod</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Addition of points. </p>
<p>Add given point to generate third point. More description can be found <a href="https://en.wikipedia.org/wiki/Elliptic_curve_point_multiplication#Point_addition">here</a>, and <a href="https://en.wikipedia.org/wiki/Elliptic_curve_point_multiplication#Point_doubling">here</a> </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>First point </td></tr>
<tr><td class="paramname">b</td><td>Second point </td></tr>
<tr><td class="paramname">curve_a_coeff</td><td>Coefficient <code>a</code> of the given curve (y^2 = x^3 + ax + b) % mod </td></tr>
<tr><td class="paramname">mod</td><td>Given field </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>the resultant point </dd></dl>
<p>Slope</p>
<p>value zero</p>
<p>slope when the line is tangent to curve. This operation is performed while doubling. Taking derivative of <code>y^2 = x^3 + ax + b</code> =&gt; <code>2y dy = (3 * x^2 + a)dx</code> =&gt; <code>(dy/dx) = (3x^2 + a)/(2y)</code></p>
<p>if y co-ordinate is zero, the slope is infinite, return inf. else calculate the slope (here % mod and store in lambda)</p>
<div class="fragment"><div class="line"><a name="l00111"></a><span class="lineno"> 111</span>&#160; {</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>&#160; <a class="code" href="../../d1/d83/classuint256__t.html">uint256_t</a> lambda(0); <span class="comment">/// Slope</span></div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>&#160; <a class="code" href="../../d1/d83/classuint256__t.html">uint256_t</a> zero(0); <span class="comment">/// value zero</span></div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>&#160; lambda = zero = 0;</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>&#160; <a class="code" href="../../d1/d83/classuint256__t.html">uint256_t</a> inf = ~zero;</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>&#160; <span class="keywordflow">if</span> (a.x != b.x || a.y != b.<a class="code" href="../../d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">y</a>) {</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>&#160; <span class="comment">// Slope being infinite.</span></div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>&#160; <span class="keywordflow">if</span> (b.x == a.x) {</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>&#160; <span class="keywordflow">return</span> {inf, inf};</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>&#160; }</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>&#160; <a class="code" href="../../d1/d83/classuint256__t.html">uint256_t</a> num = (b.<a class="code" href="../../d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">y</a> - a.y + mod), den = (b.x - a.x + mod);</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>&#160; lambda = (num * (<a class="code" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#ac00616a4e40d3cd5cfb4da87d9ff9af0">exp</a>(den, mod - 2, mod))) % mod;</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>&#160; } <span class="keywordflow">else</span> {<span class="comment"></span></div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>&#160;<span class="comment"> /**</span></div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>&#160;<span class="comment"> * slope when the line is tangent to curve. This operation is performed</span></div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>&#160;<span class="comment"> * while doubling. Taking derivative of `y^2 = x^3 + ax + b`</span></div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>&#160;<span class="comment"> * =&gt; `2y dy = (3 * x^2 + a)dx`</span></div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>&#160;<span class="comment"> * =&gt; `(dy/dx) = (3x^2 + a)/(2y)`</span></div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>&#160;<span class="comment"> */</span><span class="comment"></span></div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>&#160;<span class="comment"> /**</span></div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>&#160;<span class="comment"> * if y co-ordinate is zero, the slope is infinite, return inf.</span></div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>&#160;<span class="comment"> * else calculate the slope (here % mod and store in lambda)</span></div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>&#160; <span class="keywordflow">if</span> (!a.y) {</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>&#160; <span class="keywordflow">return</span> {inf, inf};</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>&#160; }</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>&#160; <a class="code" href="../../d1/d83/classuint256__t.html">uint256_t</a> axsq = ((a.x * a.x)) % mod;</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>&#160; <span class="comment">// Mulitply by 3 adjustment</span></div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>&#160; axsq += (axsq &lt;&lt; 1);</div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>&#160; axsq %= mod;</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>&#160; <span class="comment">// Mulitply by 2 adjustment</span></div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>&#160; <a class="code" href="../../d1/d83/classuint256__t.html">uint256_t</a> a_2 = (a.y &lt;&lt; 1);</div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>&#160; lambda =</div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>&#160; (((axsq + curve_a_coeff) % mod) * <a class="code" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#ac00616a4e40d3cd5cfb4da87d9ff9af0">exp</a>(a_2, mod - 2, mod)) % mod;</div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>&#160; }</div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>&#160; <a class="code" href="../../d8/dc8/struct_point.html">Point</a> c;</div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>&#160; <span class="comment">// new point: x = ((lambda^2) - x1 - x2)</span></div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>&#160; <span class="comment">// y = (lambda * (x1 - x)) - y1</span></div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>&#160; c.x = ((lambda * lambda) % mod + (mod &lt;&lt; 1) - a.x - b.x) % mod;</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>&#160; c.<a class="code" href="../../d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">y</a> = (((lambda * (a.x + mod - c.x)) % mod) + mod - a.y) % mod;</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>&#160; <span class="keywordflow">return</span> c;</div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>&#160;}</div>
<div class="ttc" id="aclassuint256__t_html"><div class="ttname"><a href="../../d1/d83/classuint256__t.html">uint256_t</a></div><div class="ttdoc">class for 256-bit unsigned integer</div><div class="ttdef"><b>Definition:</b> uint256_t.hpp:33</div></div>
<div class="ttc" id="anamespaceciphers_1_1elliptic__curve__key__exchange_html_ac00616a4e40d3cd5cfb4da87d9ff9af0"><div class="ttname"><a href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#ac00616a4e40d3cd5cfb4da87d9ff9af0">ciphers::elliptic_curve_key_exchange::exp</a></div><div class="ttdeci">uint256_t exp(uint256_t number, uint256_t power, const uint256_t &amp;mod)</div><div class="ttdoc">This function calculates number raised to exponent power under modulo mod using Modular Exponentiatio...</div><div class="ttdef"><b>Definition:</b> elliptic_curve_key_exchange.cpp:78</div></div>
<div class="ttc" id="astruct_point_html"><div class="ttname"><a href="../../d8/dc8/struct_point.html">Point</a></div><div class="ttdef"><b>Definition:</b> line_segment_intersection.cpp:12</div></div>
<div class="ttc" id="astruct_point_html_a2e1b5fb2b2a83571f5c0bc0f66a73cf7"><div class="ttname"><a href="../../d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">Point::y</a></div><div class="ttdeci">int y</div><div class="ttdoc">Point respect to x coordinate.</div><div class="ttdef"><b>Definition:</b> line_segment_intersection.cpp:14</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#ac00616a4e40d3cd5cfb4da87d9ff9af0">&#9670;&nbsp;</a></span>exp()</h2>
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<td class="memname"><a class="el" href="../../d1/d83/classuint256__t.html">uint256_t</a> ciphers::elliptic_curve_key_exchange::exp </td>
<td>(</td>
<td class="paramtype"><a class="el" href="../../d1/d83/classuint256__t.html">uint256_t</a>&#160;</td>
<td class="paramname"><em>number</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="../../d1/d83/classuint256__t.html">uint256_t</a>&#160;</td>
<td class="paramname"><em>power</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="../../d1/d83/classuint256__t.html">uint256_t</a> &amp;&#160;</td>
<td class="paramname"><em>mod</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
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<p>This function calculates number raised to exponent power under modulo mod using <a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/modular_exponentiation.cpp">Modular Exponentiation</a>. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">number</td><td>integer base </td></tr>
<tr><td class="paramname">power</td><td>unsigned integer exponent </td></tr>
<tr><td class="paramname">mod</td><td>integer modulo </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>number raised to power modulo mod </dd></dl>
<div class="fragment"><div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; {</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; <span class="keywordflow">if</span> (!power) {</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../d1/d83/classuint256__t.html">uint256_t</a>(1);</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; }</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; <a class="code" href="../../d1/d83/classuint256__t.html">uint256_t</a> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>(1);</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160; number = number % mod;</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; <span class="keywordflow">while</span> (power) {</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; <span class="keywordflow">if</span> ((power &amp; 1)) {</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = (<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> * number) % mod;</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160; }</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160; <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#a7cf5feaf168b88e74544da59ed830311">power</a> &gt;&gt;= 1;</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160; <span class="keywordflow">if</span> (power) {</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>&#160; number = (number * number) % mod;</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160; }</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160; }</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160; <span class="keywordflow">return</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>;</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160;}</div>
<div class="ttc" id="afibonacci__sum_8cpp_html_a7cf5feaf168b88e74544da59ed830311"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#a7cf5feaf168b88e74544da59ed830311">math::fibonacci_sum::power</a></div><div class="ttdeci">math::fibonacci_sum::matrix power(math::fibonacci_sum::matrix T, uint64_t ex)</div><div class="ttdef"><b>Definition:</b> fibonacci_sum.cpp:57</div></div>
<div class="ttc" id="amatrix__exponentiation_8cpp_html_ad8389ed58fd0ec66df248014775ad1fa"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a></div><div class="ttdeci">ll ans(ll n)</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:91</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a17f3d667241b88115a95282cdd719cb2">&#9670;&nbsp;</a></span>multiply()</h2>
<div class="memitem">
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<td class="memname"><a class="el" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html">Point</a> ciphers::elliptic_curve_key_exchange::multiply </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html">Point</a> &amp;&#160;</td>
<td class="paramname"><em>a</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="../../d1/d83/classuint256__t.html">uint256_t</a> &amp;&#160;</td>
<td class="paramname"><em>curve_a_coeff</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="../../d1/d83/classuint256__t.html">uint256_t</a>&#160;</td>
<td class="paramname"><em>p</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="../../d1/d83/classuint256__t.html">uint256_t</a> &amp;&#160;</td>
<td class="paramname"><em>mod</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
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<p>multiply <a class="el" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html" title="Definition of struct Point.">Point</a> and integer </p>
<p>Multiply <a class="el" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html" title="Definition of struct Point.">Point</a> by a scalar factor (here it is a private key p). The multiplication is called as <a href="https://en.wikipedia.org/wiki/Elliptic_curve_point_multiplication#Double-and-add">double and add method</a> </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td><a class="el" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html" title="Definition of struct Point.">Point</a> to multiply </td></tr>
<tr><td class="paramname">curve_a_coeff</td><td>Coefficient of given curve (y^2 = x^3 + ax + b) % mod </td></tr>
<tr><td class="paramname">p</td><td>The scalar value </td></tr>
<tr><td class="paramname">mod</td><td>Given field </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>the resultant point </dd></dl>
<div class="fragment"><div class="line"><a name="l00166"></a><span class="lineno"> 166</span>&#160; {</div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>&#160; <a class="code" href="../../d8/dc8/struct_point.html">Point</a> <a class="code" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = a;</div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>&#160; <a class="code" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>.x %= mod;</div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>&#160; <a class="code" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>.y %= mod;</div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>&#160; <a class="code" href="../../d1/d83/classuint256__t.html">uint256_t</a> inf{};</div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>&#160; inf = ~<a class="code" href="../../d1/d83/classuint256__t.html">uint256_t</a>(0);</div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>&#160; <a class="code" href="../../d8/dc8/struct_point.html">Point</a> Q = {inf, inf};</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>&#160; <span class="keywordflow">while</span> (p) {</div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>&#160; <span class="keywordflow">if</span> ((p &amp; 1)) {</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>&#160; <span class="keywordflow">if</span> (Q.x == inf &amp;&amp; Q.<a class="code" href="../../d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">y</a> == inf) {</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>&#160; Q.x = <a class="code" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>.x;</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>&#160; Q.<a class="code" href="../../d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">y</a> = <a class="code" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>.y;</div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>&#160; } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>&#160; Q = <a class="code" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#acc5fe9c2032fb7582c38a20d1fa69bcf">addition</a>(Q, N, curve_a_coeff, mod);</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>&#160; }</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>&#160; }</div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>&#160; p &gt;&gt;= 1;</div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>&#160; <span class="keywordflow">if</span> (p) {</div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>&#160; <a class="code" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = <a class="code" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#acc5fe9c2032fb7582c38a20d1fa69bcf">addition</a>(N, N, curve_a_coeff, mod);</div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>&#160; }</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>&#160; }</div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>&#160; <span class="keywordflow">return</span> Q;</div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>&#160;}</div>
<div class="ttc" id="adata__structures_2sparse__table_8cpp_html_a10f3ffb3f6f7e1b83d556b9c8de89a5d"><div class="ttname"><a href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">data_structures::sparse_table::N</a></div><div class="ttdeci">constexpr uint32_t N</div><div class="ttdoc">A struct to represent sparse table for min() as their invariant function, for the given array A....</div><div class="ttdef"><b>Definition:</b> sparse_table.cpp:47</div></div>
<div class="ttc" id="anamespaceciphers_1_1elliptic__curve__key__exchange_html_acc5fe9c2032fb7582c38a20d1fa69bcf"><div class="ttname"><a href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#acc5fe9c2032fb7582c38a20d1fa69bcf">ciphers::elliptic_curve_key_exchange::addition</a></div><div class="ttdeci">Point addition(Point a, Point b, const uint256_t &amp;curve_a_coeff, uint256_t mod)</div><div class="ttdoc">Addition of points.</div><div class="ttdef"><b>Definition:</b> elliptic_curve_key_exchange.cpp:110</div></div>
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