Add ECC docs

2026-02-18 12:36:14 +01:00
parent 16efeaec2d
commit 11041d3180
17 changed files with 1779 additions and 180 deletions
@@ -74,6 +74,8 @@
    </li>
    </ul>
                  </li>
+                  <li class="toctree-l1"><a class="reference internal" href="../ecc/">Elliptic Curve Cryptography</a>
+                  </li>
              </ul>
              <p class="caption"><span class="caption-text">Public Keys</span></p>
              <ul>
@@ -136,7 +138,7 @@



-  <div class="doc doc-children">
+<div class="doc doc-children">



@@ -160,6 +162,7 @@
    <div class="doc doc-contents ">


+
        <p>This simple class represent the Point at the coordinate x and y in a plan</p>


@@ -200,7 +203,6 @@



-
              <details class="quote">
                <summary>Source code in <code>Cryptotools/Groups/point.py</code></summary>
                <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal"> 4</span>
@@ -233,7 +235,7 @@
 <span class="normal">31</span>
 <span class="normal">32</span>
 <span class="normal">33</span>
-<span class="normal">34</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">class</span> <span class="nc">Point</span><span class="p">:</span>
+<span class="normal">34</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">class</span><span class="w"> </span><span class="nc">Point</span><span class="p">:</span>
 <span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">        This simple class represent the Point at the coordinate x and y in a plan</span>

@@ -241,27 +243,27 @@
 <span class="sd">            x (Integer): Position at the x</span>
 <span class="sd">            y (Integer): Position at the y</span>
 <span class="sd">    &quot;&quot;&quot;</span>
-    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
+    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">_x</span> <span class="o">=</span> <span class="n">x</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">_y</span> <span class="o">=</span> <span class="n">y</span>

    <span class="nd">@property</span>
-    <span class="k">def</span> <span class="nf">x</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+    <span class="k">def</span><span class="w"> </span><span class="nf">x</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_x</span>

    <span class="nd">@property</span>
-    <span class="k">def</span> <span class="nf">y</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+    <span class="k">def</span><span class="w"> </span><span class="nf">y</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_y</span>

    <span class="nd">@x</span><span class="o">.</span><span class="n">setter</span>
-    <span class="k">def</span> <span class="nf">x</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
+    <span class="k">def</span><span class="w"> </span><span class="nf">x</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">_x</span> <span class="o">=</span> <span class="n">x</span>

    <span class="nd">@y</span><span class="o">.</span><span class="n">setter</span>
-    <span class="k">def</span> <span class="nf">y</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
+    <span class="k">def</span><span class="w"> </span><span class="nf">y</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">_y</span> <span class="o">=</span> <span class="n">y</span>

-    <span class="k">def</span> <span class="fm">__eq__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
+    <span class="k">def</span><span class="w"> </span><span class="fm">__eq__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
        <span class="nb">print</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_x</span><span class="p">,</span> <span class="n">other</span><span class="o">.</span><span class="n">x</span><span class="p">)</span>
        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_x</span> <span class="o">==</span> <span class="n">other</span><span class="o">.</span><span class="n">x</span> <span class="ow">and</span> <span class="bp">self</span><span class="o">.</span><span class="n">_y</span> <span class="o">==</span> <span class="n">other</span><span class="o">.</span><span class="n">y</span>
 </code></pre></div></td></tr></table></div>
@@ -269,7 +271,7 @@



-  <div class="doc doc-children">
+<div class="doc doc-children">



@@ -286,6 +288,7 @@

    </div>

+
 </div>


@@ -314,7 +317,7 @@



-  <div class="doc doc-children">
+<div class="doc doc-children">



@@ -498,13 +501,13 @@
 <span class="normal">156</span>
 <span class="normal">157</span>
 <span class="normal">158</span>
-<span class="normal">159</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">class</span> <span class="nc">Curve</span><span class="p">:</span>
+<span class="normal">159</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">class</span><span class="w"> </span><span class="nc">Curve</span><span class="p">:</span>
    <span class="c1"># Curve</span>
    <span class="n">WEIERSTRASS</span> <span class="o">=</span> <span class="mi">0</span>
    <span class="n">MONTGOMERY</span> <span class="o">=</span> <span class="mi">1</span>


-    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">t</span><span class="p">):</span>
+    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">t</span><span class="p">):</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">_a</span> <span class="o">=</span> <span class="n">a</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">_b</span> <span class="o">=</span> <span class="n">b</span>

@@ -519,7 +522,7 @@
        <span class="bp">self</span><span class="o">.</span><span class="n">_points</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">_pointsSym</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>

-    <span class="k">def</span> <span class="nf">f</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
+    <span class="k">def</span><span class="w"> </span><span class="nf">f</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_type</span> <span class="o">==</span> <span class="n">Curve</span><span class="o">.</span><span class="n">WEIERSTRASS</span><span class="p">:</span>
            <span class="n">y</span> <span class="o">=</span> <span class="nb">pow</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span> <span class="o">+</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_a</span> <span class="o">*</span> <span class="n">x</span><span class="p">)</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">_b</span>
        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_type</span> <span class="o">==</span> <span class="n">Curve</span><span class="o">.</span><span class="n">MONTGOMERY</span><span class="p">:</span>
@@ -528,7 +531,7 @@
            <span class="k">return</span> <span class="n">sqrt</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
        <span class="k">return</span> <span class="kc">None</span>

-    <span class="k">def</span> <span class="nf">generatePoints</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+    <span class="k">def</span><span class="w"> </span><span class="nf">generatePoints</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_xtmp</span><span class="p">:</span>
            <span class="n">y</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">f</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
            <span class="k">if</span> <span class="n">y</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
@@ -547,24 +550,24 @@
            <span class="p">))</span>

    <span class="nd">@property</span>
-    <span class="k">def</span> <span class="nf">x</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+    <span class="k">def</span><span class="w"> </span><span class="nf">x</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_x</span>

    <span class="nd">@property</span>
-    <span class="k">def</span> <span class="nf">y</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+    <span class="k">def</span><span class="w"> </span><span class="nf">y</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_y</span>

    <span class="nd">@property</span>
-    <span class="k">def</span> <span class="nf">yn</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+    <span class="k">def</span><span class="w"> </span><span class="nf">yn</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_yn</span>

-    <span class="k">def</span> <span class="nf">getPoints</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+    <span class="k">def</span><span class="w"> </span><span class="nf">getPoints</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_points</span>

-    <span class="k">def</span> <span class="nf">getPointsSym</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+    <span class="k">def</span><span class="w"> </span><span class="nf">getPointsSym</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_pointsSym</span>

-    <span class="k">def</span> <span class="nf">add</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">P</span><span class="p">,</span> <span class="n">Q</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">Point</span><span class="p">:</span>
+    <span class="k">def</span><span class="w"> </span><span class="nf">add</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">P</span><span class="p">,</span> <span class="n">Q</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">Point</span><span class="p">:</span>
 <span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">            This function operathe addition operation on two points P and Q</span>

@@ -611,7 +614,7 @@
        <span class="n">yr</span> <span class="o">=</span> <span class="p">(</span><span class="n">m</span> <span class="o">*</span> <span class="p">(</span><span class="n">P</span><span class="o">.</span><span class="n">x</span> <span class="o">-</span> <span class="n">xr</span><span class="p">))</span> <span class="o">-</span> <span class="n">P</span><span class="o">.</span><span class="n">y</span>
        <span class="k">return</span> <span class="n">Point</span><span class="p">(</span><span class="n">xr</span><span class="p">,</span> <span class="n">yr</span><span class="p">)</span>

-    <span class="k">def</span> <span class="nf">scalar</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">P</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">Point</span><span class="p">:</span>
+    <span class="k">def</span><span class="w"> </span><span class="nf">scalar</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">P</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">Point</span><span class="p">:</span>
 <span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">            This function compute a Scalar Multiplication of P, n time. This algorithm is also known as Double and Add.</span>

@@ -635,7 +638,7 @@

        <span class="k">return</span> <span class="n">nP</span>

-    <span class="k">def</span> <span class="nf">find_reverse</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">P</span><span class="p">):</span>
+    <span class="k">def</span><span class="w"> </span><span class="nf">find_reverse</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">P</span><span class="p">):</span>
 <span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">            This function return the reverse of the Point P</span>
 <span class="sd">            Args:</span>
@@ -655,7 +658,7 @@



-  <div class="doc doc-children">
+<div class="doc doc-children">



@@ -735,7 +738,7 @@
  </tbody>
 </table>

-            <details class="quote">
+            <details class="mkdocstrings-source">
              <summary>Source code in <code>Cryptotools/Groups/curve.py</code></summary>
              <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal"> 74</span>
 <span class="normal"> 75</span>
@@ -782,7 +785,7 @@
 <span class="normal">116</span>
 <span class="normal">117</span>
 <span class="normal">118</span>
-<span class="normal">119</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">add</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">P</span><span class="p">,</span> <span class="n">Q</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">Point</span><span class="p">:</span>
+<span class="normal">119</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span><span class="w"> </span><span class="nf">add</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">P</span><span class="p">,</span> <span class="n">Q</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">Point</span><span class="p">:</span>
 <span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">        This function operathe addition operation on two points P and Q</span>

@@ -872,7 +875,7 @@ Args:
  </tbody>
 </table>

-            <details class="quote">
+            <details class="mkdocstrings-source">
              <summary>Source code in <code>Cryptotools/Groups/curve.py</code></summary>
              <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">145</span>
 <span class="normal">146</span>
@@ -888,7 +891,7 @@ Args:
 <span class="normal">156</span>
 <span class="normal">157</span>
 <span class="normal">158</span>
-<span class="normal">159</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">find_reverse</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">P</span><span class="p">):</span>
+<span class="normal">159</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span><span class="w"> </span><span class="nf">find_reverse</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">P</span><span class="p">):</span>
 <span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">        This function return the reverse of the Point P</span>
 <span class="sd">        Args:</span>
@@ -978,7 +981,7 @@ Args:
  </tbody>
 </table>

-            <details class="quote">
+            <details class="mkdocstrings-source">
              <summary>Source code in <code>Cryptotools/Groups/curve.py</code></summary>
              <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">121</span>
 <span class="normal">122</span>
@@ -1002,7 +1005,7 @@ Args:
 <span class="normal">140</span>
 <span class="normal">141</span>
 <span class="normal">142</span>
-<span class="normal">143</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">scalar</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">P</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">Point</span><span class="p">:</span>
+<span class="normal">143</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span><span class="w"> </span><span class="nf">scalar</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">P</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">Point</span><span class="p">:</span>
 <span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">        This function compute a Scalar Multiplication of P, n time. This algorithm is also known as Double and Add.</span>

@@ -1037,6 +1040,7 @@ Args:

    </div>

+
 </div>


@@ -1052,7 +1056,7 @@ Args:
          </div><footer>
    <div class="rst-footer-buttons" role="navigation" aria-label="Footer Navigation">
        <a href="../group-theory/" class="btn btn-neutral float-left" title="Group theory"><span class="icon icon-circle-arrow-left"></span> Previous</a>
-        <a href="../rsa/" class="btn btn-neutral float-right" title="RSA">Next <span class="icon icon-circle-arrow-right"></span></a>
+        <a href="../ecc/" class="btn btn-neutral float-right" title="Elliptic Curve Cryptography">Next <span class="icon icon-circle-arrow-right"></span></a>
    </div>

  <hr/>
@@ -1078,7 +1082,7 @@ Args:
      <span><a href="../group-theory/" style="color: #fcfcfc">&laquo; Previous</a></span>
    
    
-      <span><a href="../rsa/" style="color: #fcfcfc">Next &raquo;</a></span>
+      <span><a href="../ecc/" style="color: #fcfcfc">Next &raquo;</a></span>
    
  </span>
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