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<div id="projectbrief">Isogeny-based post-quantum Diffie-Hellman protocol.</div>
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<div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="preprocessor">#ifndef _ARITHMETIC_H_</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="preprocessor">#define _ARITHMETIC_H_</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span> </div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="preprocessor">#include &quot;string.h&quot;</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="preprocessor">#include &quot;stdbool.h&quot;</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span> </div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="preprocessor">#include &quot;<a class="code" href="memory_8h.html">memory.h</a>&quot;</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="preprocessor">#include &quot;models.h&quot;</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="preprocessor">#include &quot;auxiliary.h&quot;</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="preprocessor">#include &quot;pretty_print.h&quot;</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span> </div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="preprocessor">#include &lt;gmp.h&gt;</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span><span class="preprocessor">#include &lt;flint/fmpz.h&gt;</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="preprocessor">#include &lt;flint/fq.h&gt;</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span> </div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="preprocessor">#include &quot;../Polynomials/roots.h&quot;</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span> </div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="comment">/*********************************************</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="comment"> Base field embbeding</span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="comment">*********************************************/</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="keywordtype">void</span> MG_curve_update_field(<a class="code hl_struct" href="struct_m_g__curve__t.html">MG_curve_t</a> *, <a class="code hl_struct" href="struct_m_g__curve__t.html">MG_curve_t</a> *, <span class="keyword">const</span> fq_ctx_t *);</div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="keywordtype">void</span> MG_curve_update_field_(<a class="code hl_struct" href="struct_m_g__curve__t.html">MG_curve_t</a> *, <span class="keyword">const</span> fq_ctx_t *);</div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> </div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="comment">/*********************************************</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="comment"> Elliptic curves</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="comment">*********************************************/</span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="keywordtype">void</span> SW_j_invariant(fq_t *, <a class="code hl_struct" href="struct_s_w__curve__t.html">SW_curve_t</a> *);</div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="keywordtype">void</span> MG_j_invariant(fq_t *, <a class="code hl_struct" href="struct_m_g__curve__t.html">MG_curve_t</a> *);</div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="keywordtype">void</span> TN_j_invariant(fq_t *, <a class="code hl_struct" href="struct_t_n__curve__t.html">TN_curve_t</a> *);</div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> </div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span><span class="comment">/*********************************************</span></div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="comment"> Points on elliptic curves</span></div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="comment">*********************************************/</span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="keywordtype">void</span> SW_point_isinfinity(<span class="keywordtype">bool</span> *, <a class="code hl_struct" href="struct_s_w__point__t.html">SW_point_t</a> *);</div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span><span class="keywordtype">void</span> MG_point_isinfinity(<span class="keywordtype">bool</span> *, <a class="code hl_struct" href="struct_m_g__point__t.html">MG_point_t</a> *);</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span><span class="keywordtype">bool</span> MG_point_isinfinity_(<a class="code hl_struct" href="struct_m_g__point__t.html">MG_point_t</a> *);</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span><span class="keywordtype">int</span> SW_point_isvalid(<span class="keywordtype">bool</span> *, <a class="code hl_struct" href="struct_s_w__point__t.html">SW_point_t</a> *);</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="keywordtype">int</span> MG_point_isvalid(<span class="keywordtype">bool</span> *, <a class="code hl_struct" href="struct_m_g__point__t.html">MG_point_t</a> *);</div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="keywordtype">void</span> MG_point_isinfty(<span class="keywordtype">bool</span> *, <a class="code hl_struct" href="struct_m_g__point__t.html">MG_point_t</a> *);</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="keywordtype">void</span> MG_point_normalize(<a class="code hl_struct" href="struct_m_g__point__t.html">MG_point_t</a> *);</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> </div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="comment">/*********************************************</span></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span><span class="comment"> Random torsion point generation</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span><span class="comment">*********************************************/</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span><span class="keywordtype">void</span> SW_point_rand_ninfty(<a class="code hl_struct" href="struct_s_w__point__t.html">SW_point_t</a> *);</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span><span class="keywordtype">void</span> MG_point_rand_ninfty(<a class="code hl_struct" href="struct_m_g__point__t.html">MG_point_t</a> *, flint_rand_t);</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span><span class="keywordtype">void</span> MG_point_rand_ninfty_nsquare(<a class="code hl_struct" href="struct_m_g__point__t.html">MG_point_t</a> *, flint_rand_t);</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> </div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span><span class="comment">/*********************************************</span></div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span><span class="comment"> Montgomery curve arithmetic</span></div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span><span class="comment">*********************************************/</span></div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span><span class="keywordtype">int</span> MG_curve_normalize(<a class="code hl_struct" href="struct_m_g__curve__t.html">MG_curve_t</a> *);</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span><span class="keywordtype">int</span> MG_rec_y(fq_t, <a class="code hl_struct" href="struct_m_g__point__t.html">MG_point_t</a> *);</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span><span class="keywordtype">void</span> MG_xADD(<a class="code hl_struct" href="struct_m_g__point__t.html">MG_point_t</a> *, <a class="code hl_struct" href="struct_m_g__point__t.html">MG_point_t</a>, <a class="code hl_struct" href="struct_m_g__point__t.html">MG_point_t</a>, <a class="code hl_struct" href="struct_m_g__point__t.html">MG_point_t</a>);</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span><span class="keywordtype">void</span> MG_xDBL(<a class="code hl_struct" href="struct_m_g__point__t.html">MG_point_t</a> *, <a class="code hl_struct" href="struct_m_g__point__t.html">MG_point_t</a>);</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span><span class="keywordtype">void</span> MG_xDBL_const(<a class="code hl_struct" href="struct_m_g__point__t.html">MG_point_t</a> *, <a class="code hl_struct" href="struct_m_g__point__t.html">MG_point_t</a> ,<span class="keyword">const</span> fq_t);</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> </div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span><span class="comment">/*********************************************</span></div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span><span class="comment"> Montgomery ladder</span></div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span><span class="comment">*********************************************/</span></div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span><span class="keywordtype">void</span> MG_ladder_rec(<a class="code hl_struct" href="struct_m_g__point__t.html">MG_point_t</a> *, <a class="code hl_struct" href="struct_m_g__point__t.html">MG_point_t</a> *, fmpz_t, <a class="code hl_struct" href="struct_m_g__point__t.html">MG_point_t</a>, <span class="keyword">const</span> fq_ctx_t *);</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span><span class="keywordtype">void</span> MG_ladder(<a class="code hl_struct" href="struct_m_g__point__t.html">MG_point_t</a> *x0, fmpz_t k, <a class="code hl_struct" href="struct_m_g__point__t.html">MG_point_t</a> P);</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span><span class="keywordtype">void</span> MG_ladder_iter(<a class="code hl_struct" href="struct_m_g__point__t.html">MG_point_t</a> *, <a class="code hl_struct" href="struct_m_g__point__t.html">MG_point_t</a> *, fmpz_t, <a class="code hl_struct" href="struct_m_g__point__t.html">MG_point_t</a>, fq_ctx_t *);</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span><span class="keywordtype">void</span> MG_ladder_iter_(<a class="code hl_struct" href="struct_m_g__point__t.html">MG_point_t</a> *, fmpz_t, <a class="code hl_struct" href="struct_m_g__point__t.html">MG_point_t</a> *);</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> </div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span><span class="comment">/*********************************************</span></div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span><span class="comment"> Torsion</span></div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span><span class="comment">*********************************************/</span></div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span><span class="keywordtype">void</span> MG_curve_trace(fmpz_t);</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span><span class="keywordtype">void</span> MG_curve_card_base(fmpz_t, <a class="code hl_struct" href="struct_m_g__curve__t.html">MG_curve_t</a> *);</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span><span class="keywordtype">void</span> MG_curve_card_ext(fmpz_t, <a class="code hl_struct" href="struct_m_g__curve__t.html">MG_curve_t</a> *, fmpz_t r);</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span><span class="keywordtype">int</span> MG_curve_rand_torsion(<a class="code hl_struct" href="struct_m_g__point__t.html">MG_point_t</a> *, fmpz_t, fmpz_t);</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span><span class="keywordtype">int</span> MG_curve_rand_torsion_(<a class="code hl_struct" href="struct_m_g__point__t.html">MG_point_t</a> *, fmpz_t, fmpz_t);</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> </div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span><span class="comment">/*********************************************</span></div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span><span class="comment"> Tate normal curve and Montgomery conversion</span></div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span><span class="comment">*********************************************/</span></div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span><span class="keywordtype">void</span> MG_get_TN(<a class="code hl_struct" href="struct_t_n__curve__t.html">TN_curve_t</a> *, <a class="code hl_struct" href="struct_m_g__curve__t.html">MG_curve_t</a> *, <a class="code hl_struct" href="struct_m_g__point__t.html">MG_point_t</a> *, fmpz_t);</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span><span class="keywordtype">int</span> TN_get_MG(<a class="code hl_struct" href="struct_m_g__curve__t.html">MG_curve_t</a> *, <a class="code hl_struct" href="struct_t_n__curve__t.html">TN_curve_t</a> *);</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> </div>
<div class="ttc" id="amemory_8h_html"><div class="ttname"><a href="memory_8h.html">memory.h</a></div></div>
<div class="ttc" id="astruct_m_g__curve__t_html"><div class="ttname"><a href="struct_m_g__curve__t.html">MG_curve_t</a></div><div class="ttdef"><b>Definition:</b> models.h:34</div></div>
<div class="ttc" id="astruct_m_g__point__t_html"><div class="ttname"><a href="struct_m_g__point__t.html">MG_point_t</a></div><div class="ttdef"><b>Definition:</b> models.h:43</div></div>
<div class="ttc" id="astruct_s_w__curve__t_html"><div class="ttname"><a href="struct_s_w__curve__t.html">SW_curve_t</a></div><div class="ttdef"><b>Definition:</b> models.h:16</div></div>
<div class="ttc" id="astruct_s_w__point__t_html"><div class="ttname"><a href="struct_s_w__point__t.html">SW_point_t</a></div><div class="ttdef"><b>Definition:</b> models.h:25</div></div>
<div class="ttc" id="astruct_t_n__curve__t_html"><div class="ttname"><a href="struct_t_n__curve__t.html">TN_curve_t</a></div><div class="ttdef"><b>Definition:</b> models.h:52</div></div>
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