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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="#details">More...</a></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 id="header-nested-classes" class="groupheader"><a id="nested-classes" name="nested-classes"></a>
Classes</h2></td></tr>
<tr class="memitem:Point" id="r_Point"><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" id="r_af0a6e3521629c25c2b5d620f26429830"><td class="memItemLeft" align="right" valign="top">typedef struct ciphers::elliptic_curve_key_exchange::Point&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#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>. <br /></td></tr>
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<tr class="heading"><td colspan="2"><h2 id="header-func-members" class="groupheader"><a id="func-members" name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:ac00616a4e40d3cd5cfb4da87d9ff9af0" id="r_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="#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="../../df/def/power__for__huge__numbers_8cpp.html#ae249a2af508aa94266023ce8aa81426f">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" target="_blank">Modular Exponentiation</a>. <br /></td></tr>
<tr class="memitem:acc5fe9c2032fb7582c38a20d1fa69bcf" id="r_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="#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. <br /></td></tr>
<tr class="memitem:a17f3d667241b88115a95282cdd719cb2" id="r_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="#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 <br /></td></tr>
</table>
<a name="details" id="details"></a><h2 id="header-details" 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" target="_blank">Elliptic Curve Diffie-Hellman</a> key exchange. </p>
</div><a name="doc-typedef-members" id="doc-typedef-members"></a><h2 id="header-doc-typedef-members" class="groupheader">Typedef Documentation</h2>
<a id="af0a6e3521629c25c2b5d620f26429830" name="af0a6e3521629c25c2b5d620f26429830"></a>
<h2 class="memtitle"><span class="permalink"><a href="#af0a6e3521629c25c2b5d620f26429830">&#9670;&#160;</a></span>Point</h2>
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<td class="memname">typedef struct ciphers::elliptic_curve_key_exchange::Point ciphers::elliptic_curve_key_exchange::Point</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>
<a name="doc-func-members" id="doc-func-members"></a><h2 id="header-doc-func-members" class="groupheader">Function Documentation</h2>
<a id="acc5fe9c2032fb7582c38a20d1fa69bcf" name="acc5fe9c2032fb7582c38a20d1fa69bcf"></a>
<h2 class="memtitle"><span class="permalink"><a href="#acc5fe9c2032fb7582c38a20d1fa69bcf">&#9670;&#160;</a></span>addition()</h2>
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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::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></td> <td class="paramname"><span class="paramname"><em>a</em></span>, </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></td> <td class="paramname"><span class="paramname"><em>b</em></span>, </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;</td> <td class="paramname"><span class="paramname"><em>curve_a_coeff</em></span>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="../../d1/d83/classuint256__t.html">uint256_t</a></td> <td class="paramname"><span class="paramname"><em>mod</em></span>&#160;)</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" target="_blank">here</a>, and <a href="https://en.wikipedia.org/wiki/Elliptic_curve_point_multiplication#Point_doubling" target="_blank">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 <span class="tt">a</span> 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 <span class="tt">y^2 = x^3 + ax + b</span> =&gt; <span class="tt">2y dy = (3 * x^2 + a)dx</span> =&gt; <span class="tt">(dy/dx) = (3x^2 + a)/(2y)</span></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>
<p class="definition">Definition at line <a class="el" href="../../df/d2c/elliptic__curve__key__exchange_8cpp_source.html#l00110">110</a> of file <a class="el" href="../../df/d2c/elliptic__curve__key__exchange_8cpp_source.html">elliptic_curve_key_exchange.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 111</span> {</div>
<div class="line"><span class="lineno"> 112</span> <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> lambda(0); </div>
<div class="line"><span class="lineno"> 113</span> <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> zero(0); </div>
<div class="line"><span class="lineno"> 114</span> lambda = zero = 0;</div>
<div class="line"><span class="lineno"> 115</span> <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> inf = ~zero;</div>
<div class="line"><span class="lineno"> 116</span> <span class="keywordflow">if</span> (a.x != b.x || a.y != b.y) {</div>
<div class="line"><span class="lineno"> 117</span> <span class="comment">// Slope being infinite.</span></div>
<div class="line"><span class="lineno"> 118</span> <span class="keywordflow">if</span> (b.x == a.x) {</div>
<div class="line"><span class="lineno"> 119</span> <span class="keywordflow">return</span> {inf, inf};</div>
<div class="line"><span class="lineno"> 120</span> }</div>
<div class="line"><span class="lineno"> 121</span> <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> num = (b.y - a.y + mod), den = (b.x - a.x + mod);</div>
<div class="line"><span class="lineno"> 122</span> lambda = (num * (<a class="code hl_function" href="#ac00616a4e40d3cd5cfb4da87d9ff9af0">exp</a>(den, mod - 2, mod))) % mod;</div>
<div class="line"><span class="lineno"> 123</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><span class="lineno"> 134</span> <span class="keywordflow">if</span> (!a.y) {</div>
<div class="line"><span class="lineno"> 135</span> <span class="keywordflow">return</span> {inf, inf};</div>
<div class="line"><span class="lineno"> 136</span> }</div>
<div class="line"><span class="lineno"> 137</span> uint256_t axsq = ((a.x * a.x)) % mod;</div>
<div class="line"><span class="lineno"> 138</span> <span class="comment">// Mulitply by 3 adjustment</span></div>
<div class="line"><span class="lineno"> 139</span> axsq += (axsq &lt;&lt; 1);</div>
<div class="line"><span class="lineno"> 140</span> axsq %= mod;</div>
<div class="line"><span class="lineno"> 141</span> <span class="comment">// Mulitply by 2 adjustment</span></div>
<div class="line"><span class="lineno"> 142</span> uint256_t a_2 = (a.y &lt;&lt; 1);</div>
<div class="line"><span class="lineno"> 143</span> lambda =</div>
<div class="line"><span class="lineno"> 144</span> (((axsq + curve_a_coeff) % mod) * <a class="code hl_function" href="#ac00616a4e40d3cd5cfb4da87d9ff9af0">exp</a>(a_2, mod - 2, mod)) % mod;</div>
<div class="line"><span class="lineno"> 145</span> }</div>
<div class="line"><span class="lineno"> 146</span> <a class="code hl_struct" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html">Point</a> c;</div>
<div class="line"><span class="lineno"> 147</span> <span class="comment">// new point: x = ((lambda^2) - x1 - x2)</span></div>
<div class="line"><span class="lineno"> 148</span> <span class="comment">// y = (lambda * (x1 - x)) - y1</span></div>
<div class="line"><span class="lineno"> 149</span> c.x = ((lambda * lambda) % mod + (mod &lt;&lt; 1) - a.x - b.x) % mod;</div>
<div class="line"><span class="lineno"> 150</span> c.<a class="code hl_variable" href="../../d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">y</a> = (((lambda * (a.x + mod - c.x)) % mod) + mod - a.y) % mod;</div>
<div class="line"><span class="lineno"> 151</span> <span class="keywordflow">return</span> c;</div>
<div class="line"><span class="lineno"> 152</span>}</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> <a href="../../da/da3/uint256__t_8hpp_source.html#l00033">uint256_t.hpp:33</a></div></div>
<div class="ttc" id="anamespaceciphers_1_1elliptic__curve__key__exchange_html_ac00616a4e40d3cd5cfb4da87d9ff9af0"><div class="ttname"><a href="#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> <a href="../../df/d2c/elliptic__curve__key__exchange_8cpp_source.html#l00078">elliptic_curve_key_exchange.cpp:78</a></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> <a href="../../d8/d6c/line__segment__intersection_8cpp_source.html#l00014">line_segment_intersection.cpp:14</a></div></div>
<div class="ttc" id="astructciphers_1_1elliptic__curve__key__exchange_1_1_point_html"><div class="ttname"><a href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html">ciphers::elliptic_curve_key_exchange::Point</a></div><div class="ttdoc">Definition of struct Point.</div><div class="ttdef"><b>Definition</b> <a href="../../df/d2c/elliptic__curve__key__exchange_8cpp_source.html#l00046">elliptic_curve_key_exchange.cpp:46</a></div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#ac00616a4e40d3cd5cfb4da87d9ff9af0">&#9670;&#160;</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></td> <td class="paramname"><span class="paramname"><em>number</em></span>, </td>
</tr>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="../../d1/d83/classuint256__t.html">uint256_t</a></td> <td class="paramname"><span class="paramname"><em>power</em></span>, </td>
</tr>
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<td class="paramkey"></td>
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<td class="paramtype">const <a class="el" href="../../d1/d83/classuint256__t.html">uint256_t</a> &amp;</td> <td class="paramname"><span class="paramname"><em>mod</em></span>&#160;)</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" target="_blank">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>
<p class="definition">Definition at line <a class="el" href="../../df/d2c/elliptic__curve__key__exchange_8cpp_source.html#l00078">78</a> of file <a class="el" href="../../df/d2c/elliptic__curve__key__exchange_8cpp_source.html">elliptic_curve_key_exchange.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 78</span> {</div>
<div class="line"><span class="lineno"> 79</span> <span class="keywordflow">if</span> (!<a class="code hl_function" href="../../df/def/power__for__huge__numbers_8cpp.html#ae249a2af508aa94266023ce8aa81426f">power</a>) {</div>
<div class="line"><span class="lineno"> 80</span> <span class="keywordflow">return</span> <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a>(1);</div>
<div class="line"><span class="lineno"> 81</span> }</div>
<div class="line"><span class="lineno"> 82</span> <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> ans(1);</div>
<div class="line"><span class="lineno"> 83</span> number = number % mod;</div>
<div class="line"><span class="lineno"> 84</span> <span class="keywordflow">while</span> (<a class="code hl_function" href="../../df/def/power__for__huge__numbers_8cpp.html#ae249a2af508aa94266023ce8aa81426f">power</a>) {</div>
<div class="line"><span class="lineno"> 85</span> <span class="keywordflow">if</span> ((<a class="code hl_function" href="../../df/def/power__for__huge__numbers_8cpp.html#ae249a2af508aa94266023ce8aa81426f">power</a> &amp; 1)) {</div>
<div class="line"><span class="lineno"> 86</span> ans = (ans * number) % mod;</div>
<div class="line"><span class="lineno"> 87</span> }</div>
<div class="line"><span class="lineno"> 88</span> <a class="code hl_function" href="../../df/def/power__for__huge__numbers_8cpp.html#ae249a2af508aa94266023ce8aa81426f">power</a> &gt;&gt;= 1;</div>
<div class="line"><span class="lineno"> 89</span> <span class="keywordflow">if</span> (<a class="code hl_function" href="../../df/def/power__for__huge__numbers_8cpp.html#ae249a2af508aa94266023ce8aa81426f">power</a>) {</div>
<div class="line"><span class="lineno"> 90</span> number = (number * number) % mod;</div>
<div class="line"><span class="lineno"> 91</span> }</div>
<div class="line"><span class="lineno"> 92</span> }</div>
<div class="line"><span class="lineno"> 93</span> <span class="keywordflow">return</span> ans;</div>
<div class="line"><span class="lineno"> 94</span>}</div>
<div class="ttc" id="apower__for__huge__numbers_8cpp_html_ae249a2af508aa94266023ce8aa81426f"><div class="ttname"><a href="../../df/def/power__for__huge__numbers_8cpp.html#ae249a2af508aa94266023ce8aa81426f">power</a></div><div class="ttdeci">void power(int x, int n)</div><div class="ttdef"><b>Definition</b> <a href="../../df/def/power__for__huge__numbers_8cpp_source.html#l00056">power_for_huge_numbers.cpp:56</a></div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a17f3d667241b88115a95282cdd719cb2">&#9670;&#160;</a></span>multiply()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
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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;</td> <td class="paramname"><span class="paramname"><em>a</em></span>, </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;</td> <td class="paramname"><span class="paramname"><em>curve_a_coeff</em></span>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="../../d1/d83/classuint256__t.html">uint256_t</a></td> <td class="paramname"><span class="paramname"><em>p</em></span>, </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;</td> <td class="paramname"><span class="paramname"><em>mod</em></span>&#160;)</td>
</tr>
</table>
</div><div class="memdoc">
<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" target="_blank">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>
<p class="definition">Definition at line <a class="el" href="../../df/d2c/elliptic__curve__key__exchange_8cpp_source.html#l00165">165</a> of file <a class="el" href="../../df/d2c/elliptic__curve__key__exchange_8cpp_source.html">elliptic_curve_key_exchange.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 166</span> {</div>
<div class="line"><span class="lineno"> 167</span> <a class="code hl_struct" href="../../d6/d45/structciphers_1_1elliptic__curve__key__exchange_1_1_point.html">Point</a> N = a;</div>
<div class="line"><span class="lineno"> 168</span> N.x %= mod;</div>
<div class="line"><span class="lineno"> 169</span> N.y %= mod;</div>
<div class="line"><span class="lineno"> 170</span> <a class="code hl_class" href="../../d1/d83/classuint256__t.html">uint256_t</a> inf{};</div>
<div class="line"><span class="lineno"> 171</span> inf = <a class="code hl_class" href="../../d1/d83/classuint256__t.html">~uint256_t</a>(0);</div>
<div class="line"><span class="lineno"> 172</span> <a class="code hl_struct" href="../../d8/dc8/struct_point.html">Point</a> Q = {inf, inf};</div>
<div class="line"><span class="lineno"> 173</span> <span class="keywordflow">while</span> (p) {</div>
<div class="line"><span class="lineno"> 174</span> <span class="keywordflow">if</span> ((p &amp; 1)) {</div>
<div class="line"><span class="lineno"> 175</span> <span class="keywordflow">if</span> (Q.x == inf &amp;&amp; Q.<a class="code hl_variable" href="../../d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">y</a> == inf) {</div>
<div class="line"><span class="lineno"> 176</span> Q.x = N.x;</div>
<div class="line"><span class="lineno"> 177</span> Q.<a class="code hl_variable" href="../../d8/dc8/struct_point.html#a2e1b5fb2b2a83571f5c0bc0f66a73cf7">y</a> = N.y;</div>
<div class="line"><span class="lineno"> 178</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><span class="lineno"> 179</span> Q = <a class="code hl_function" href="#acc5fe9c2032fb7582c38a20d1fa69bcf">addition</a>(Q, N, curve_a_coeff, mod);</div>
<div class="line"><span class="lineno"> 180</span> }</div>
<div class="line"><span class="lineno"> 181</span> }</div>
<div class="line"><span class="lineno"> 182</span> p &gt;&gt;= 1;</div>
<div class="line"><span class="lineno"> 183</span> <span class="keywordflow">if</span> (p) {</div>
<div class="line"><span class="lineno"> 184</span> <a class="code hl_variable" href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = <a class="code hl_function" href="#acc5fe9c2032fb7582c38a20d1fa69bcf">addition</a>(N, N, curve_a_coeff, mod);</div>
<div class="line"><span class="lineno"> 185</span> }</div>
<div class="line"><span class="lineno"> 186</span> }</div>
<div class="line"><span class="lineno"> 187</span> <span class="keywordflow">return</span> Q;</div>
<div class="line"><span class="lineno"> 188</span>}</div>
<div class="ttc" id="anamespaceciphers_1_1elliptic__curve__key__exchange_html_acc5fe9c2032fb7582c38a20d1fa69bcf"><div class="ttname"><a href="#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> <a href="../../df/d2c/elliptic__curve__key__exchange_8cpp_source.html#l00110">elliptic_curve_key_exchange.cpp:110</a></div></div>
<div class="ttc" id="asparse__table_8cpp_html_a10f3ffb3f6f7e1b83d556b9c8de89a5d"><div class="ttname"><a href="../../d8/dab/sparse__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> <a href="../../d8/dab/sparse__table_8cpp_source.html#l00048">sparse_table.cpp:48</a></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> <a href="../../d8/d6c/line__segment__intersection_8cpp_source.html#l00012">line_segment_intersection.cpp:12</a></div></div>
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