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<p>CryptoTools provides several utils function wich can be used for cryptography purposes</p>
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<div class="doc doc-object doc-module">
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<div class="doc doc-object doc-function">
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<h2 id="Cryptotools.Utils.utils.bin_expo" class="doc doc-heading">
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<code class="highlight language-python"><span class="n">bin_expo</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">e</span><span class="p">)</span></code>
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</h2>
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<div class="doc doc-contents ">
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<p>This function perform an binary exponentiation, also known as Exponentiation squaring.
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A binary exponentiation is the process for computing an integer power of a number, such as a ** n.
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For doing that, the first step is to convert the exponent into a binary representation
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And for each 1 bit, we compute the exponent.</p>
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<table class="field-list">
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<colgroup>
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<col class="field-name" />
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<col class="field-body" />
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</colgroup>
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<tbody valign="top">
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<tr class="field">
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<th class="field-name">Parameters:</th>
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<td class="field-body">
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<ul class="first simple">
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<li>
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<b><code>n</code></b>
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(<code><span title="Integer">Integer</span></code>)
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–
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<div class="doc-md-description">
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<p>it's the base</p>
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</div>
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</li>
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<li>
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<b><code>e</code></b>
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(<code><span title="Integer">Integer</span></code>)
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–
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<div class="doc-md-description">
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<p>it's the exponent</p>
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</div>
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</li>
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</ul>
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<th class="field-name">Returns:</th>
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<td class="field-body">
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<ul class="first simple">
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<li>
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<code><span title="int">int</span></code>
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–
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<div class="doc-md-description">
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<p>Return the result of the exponentation of n ** e</p>
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</div>
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</li>
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</ul>
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</td>
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</tr>
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</tbody>
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</table>
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<details class="quote">
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<summary>Source code in <code>Cryptotools/Utils/utils.py</code></summary>
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<div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">35</span>
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<span class="normal">62</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">bin_expo</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">e</span><span class="p">)</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
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<span class="w"> </span><span class="sd">"""</span>
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<span class="sd"> This function perform an binary exponentiation, also known as Exponentiation squaring.</span>
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<span class="sd"> A binary exponentiation is the process for computing an integer power of a number, such as a ** n.</span>
|
||||
<span class="sd"> For doing that, the first step is to convert the exponent into a binary representation</span>
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<span class="sd"> And for each 1 bit, we compute the exponent.</span>
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<span class="sd"> Args:</span>
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<span class="sd"> n (Integer): it's the base</span>
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<span class="sd"> e (Integer): it's the exponent</span>
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<span class="sd"> Returns:</span>
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<span class="sd"> Return the result of the exponentation of n ** e</span>
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<span class="sd"> """</span>
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<span class="n">binary</span> <span class="o">=</span> <span class="nb">bin</span><span class="p">(</span><span class="n">e</span><span class="p">)[</span><span class="mi">2</span><span class="p">:]</span> <span class="c1"># Remove the prefix 0b</span>
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<span class="n">r</span> <span class="o">=</span> <span class="mi">1</span>
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<span class="n">exp</span> <span class="o">=</span> <span class="mi">1</span>
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<span class="c1"># We need to reverse, and to start from the right to left</span>
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<span class="c1"># Otherwise, we do on left to the right</span>
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<span class="c1"># It's dirty, maybe we can find another way to do that</span>
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<span class="k">for</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">binary</span><span class="p">[::</span><span class="o">-</span><span class="mi">1</span><span class="p">]:</span>
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<span class="k">if</span> <span class="n">b</span> <span class="o">==</span> <span class="s1">'1'</span><span class="p">:</span>
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<span class="n">r</span> <span class="o">*=</span> <span class="n">n</span> <span class="o">**</span> <span class="n">exp</span>
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<span class="nb">print</span><span class="p">(</span><span class="n">n</span> <span class="o">**</span> <span class="n">exp</span><span class="p">,</span> <span class="n">exp</span><span class="p">)</span>
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<span class="n">exp</span> <span class="o">*=</span> <span class="mi">2</span>
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<span class="k">return</span> <span class="n">r</span>
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</code></pre></div></td></tr></table></div>
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</details>
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</div>
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</div>
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<div class="doc doc-object doc-function">
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<h2 id="Cryptotools.Utils.utils.egcd" class="doc doc-heading">
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<code class="highlight language-python"><span class="n">egcd</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span></code>
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</h2>
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<div class="doc doc-contents ">
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<p>This function compute the Extended Euclidean algorithm
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https://user.eng.umd.edu/~danadach/Cryptography_20/ExtEuclAlg.pdf
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https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm</p>
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<table class="field-list">
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<colgroup>
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<col class="field-name" />
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<col class="field-body" />
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</colgroup>
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<tbody valign="top">
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<tr class="field">
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<th class="field-name">Parameters:</th>
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<td class="field-body">
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||||
<ul class="first simple">
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<li>
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<b><code>a</code></b>
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(<code><span title="Integer">Integer</span></code>)
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–
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<div class="doc-md-description">
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<p>the number a</p>
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</div>
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</li>
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<li>
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<b><code>b</code></b>
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(<code><span title="Integer">Integer</span></code>)
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–
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<div class="doc-md-description">
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<p>the number b</p>
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</div>
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</li>
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</ul>
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</td>
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</tr>
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</tbody>
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</table>
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||||
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<details class="quote">
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||||
<summary>Source code in <code>Cryptotools/Utils/utils.py</code></summary>
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<div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">18</span>
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<span class="normal">19</span>
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<span class="normal">20</span>
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<span class="normal">33</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">egcd</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
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<span class="w"> </span><span class="sd">"""</span>
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<span class="sd"> This function compute the Extended Euclidean algorithm</span>
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<span class="sd"> https://user.eng.umd.edu/~danadach/Cryptography_20/ExtEuclAlg.pdf</span>
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||||
<span class="sd"> https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm</span>
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<span class="sd"> Args:</span>
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||||
<span class="sd"> a (Integer): the number a</span>
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<span class="sd"> b (Integer): the number b</span>
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<span class="sd"> """</span>
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<span class="k">if</span> <span class="n">a</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
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<span class="k">return</span> <span class="n">b</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span>
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<span class="n">gcd</span><span class="p">,</span> <span class="n">x1</span><span class="p">,</span> <span class="n">y1</span> <span class="o">=</span> <span class="n">egcd</span><span class="p">(</span><span class="n">b</span> <span class="o">%</span> <span class="n">a</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span>
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<span class="n">x</span> <span class="o">=</span> <span class="n">y1</span> <span class="o">-</span> <span class="p">(</span><span class="n">b</span> <span class="o">//</span> <span class="n">a</span><span class="p">)</span> <span class="o">*</span> <span class="n">x1</span>
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<span class="n">y</span> <span class="o">=</span> <span class="n">x1</span>
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<span class="k">return</span> <span class="n">gcd</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span>
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</code></pre></div></td></tr></table></div>
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</details>
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</div>
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</div>
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<div class="doc doc-object doc-function">
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<h2 id="Cryptotools.Utils.utils.exponent_squaring" class="doc doc-heading">
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<code class="highlight language-python"><span class="n">exponent_squaring</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">e</span><span class="p">)</span></code>
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</h2>
|
||||
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||||
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<div class="doc doc-contents ">
|
||||
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||||
<p>This function perform an exponentiation squaring, which compute an integer power of a number based on the following algorithm:
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||||
n ** e = {
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||||
1 # if n is 0
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||||
(n ** (e / 2)) ** 2 # if n is even
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((n ** (e - 1 / 2)) ** 2) * n # if n is odd
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}</p>
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<table class="field-list">
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<colgroup>
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<col class="field-name" />
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<col class="field-body" />
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</colgroup>
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<tbody valign="top">
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||||
<tr class="field">
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<th class="field-name">Parameters:</th>
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||||
<td class="field-body">
|
||||
<ul class="first simple">
|
||||
<li>
|
||||
<b><code>n</code></b>
|
||||
(<code><span title="Integer">Integer</span></code>)
|
||||
–
|
||||
<div class="doc-md-description">
|
||||
<p>n is the base of n ** e</p>
|
||||
</div>
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||||
</li>
|
||||
<li>
|
||||
<b><code>e</code></b>
|
||||
(<code><span title="Integer">Integer</span></code>)
|
||||
–
|
||||
<div class="doc-md-description">
|
||||
<p>e is the exponent</p>
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</div>
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</li>
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||||
</ul>
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</td>
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</tr>
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||||
</tbody>
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||||
</table>
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||||
|
||||
<details class="quote">
|
||||
<summary>Source code in <code>Cryptotools/Utils/utils.py</code></summary>
|
||||
<div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">64</span>
|
||||
<span class="normal">65</span>
|
||||
<span class="normal">66</span>
|
||||
<span class="normal">67</span>
|
||||
<span class="normal">68</span>
|
||||
<span class="normal">69</span>
|
||||
<span class="normal">70</span>
|
||||
<span class="normal">71</span>
|
||||
<span class="normal">72</span>
|
||||
<span class="normal">73</span>
|
||||
<span class="normal">74</span>
|
||||
<span class="normal">75</span>
|
||||
<span class="normal">76</span>
|
||||
<span class="normal">77</span>
|
||||
<span class="normal">78</span>
|
||||
<span class="normal">79</span>
|
||||
<span class="normal">80</span>
|
||||
<span class="normal">81</span>
|
||||
<span class="normal">82</span>
|
||||
<span class="normal">83</span>
|
||||
<span class="normal">84</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">exponent_squaring</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">e</span><span class="p">):</span>
|
||||
<span class="w"> </span><span class="sd">"""</span>
|
||||
<span class="sd"> This function perform an exponentiation squaring, which compute an integer power of a number based on the following algorithm:</span>
|
||||
<span class="sd"> n ** e = {</span>
|
||||
<span class="sd"> 1 # if n is 0</span>
|
||||
<span class="sd"> (n ** (e / 2)) ** 2 # if n is even</span>
|
||||
<span class="sd"> ((n ** (e - 1 / 2)) ** 2) * n # if n is odd</span>
|
||||
<span class="sd"> }</span>
|
||||
|
||||
<span class="sd"> Args:</span>
|
||||
<span class="sd"> n (Integer): n is the base of n ** e</span>
|
||||
<span class="sd"> e (Integer): e is the exponent</span>
|
||||
<span class="sd"> """</span>
|
||||
<span class="k">if</span> <span class="n">e</span> <span class="o"><</span> <span class="mi">0</span><span class="p">:</span>
|
||||
<span class="k">return</span> <span class="n">exponent_squaring</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="n">n</span><span class="p">,</span> <span class="o">-</span><span class="n">e</span><span class="p">)</span>
|
||||
<span class="k">elif</span> <span class="n">e</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
|
||||
<span class="k">return</span> <span class="mi">1</span>
|
||||
<span class="k">elif</span> <span class="n">e</span> <span class="o">%</span> <span class="mi">2</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span> <span class="c1"># n is odd</span>
|
||||
<span class="k">return</span> <span class="n">exponent_squaring</span><span class="p">(</span><span class="n">n</span> <span class="o">*</span> <span class="n">n</span><span class="p">,</span> <span class="p">(</span><span class="n">e</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">n</span>
|
||||
<span class="k">elif</span> <span class="n">e</span> <span class="o">%</span> <span class="mi">2</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span> <span class="c1"># n is even</span>
|
||||
<span class="k">return</span> <span class="n">exponent_squaring</span><span class="p">(</span><span class="n">n</span> <span class="o">*</span> <span class="n">n</span><span class="p">,</span> <span class="n">e</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span>
|
||||
</code></pre></div></td></tr></table></div>
|
||||
</details>
|
||||
</div>
|
||||
|
||||
</div>
|
||||
|
||||
<div class="doc doc-object doc-function">
|
||||
|
||||
|
||||
<h2 id="Cryptotools.Utils.utils.gcd" class="doc doc-heading">
|
||||
<code class="highlight language-python"><span class="n">gcd</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span></code>
|
||||
|
||||
</h2>
|
||||
|
||||
|
||||
<div class="doc doc-contents ">
|
||||
|
||||
<p>This function calculate the GCD (Greatest Common Divisor of the number a of b
|
||||
Args:
|
||||
a (Integer): the number a
|
||||
b (integer): the number b</p>
|
||||
|
||||
|
||||
<details class="return" open>
|
||||
<summary>Return</summary>
|
||||
<p>the GCD</p>
|
||||
</details>
|
||||
|
||||
<details class="quote">
|
||||
<summary>Source code in <code>Cryptotools/Utils/utils.py</code></summary>
|
||||
<div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal"> 3</span>
|
||||
<span class="normal"> 4</span>
|
||||
<span class="normal"> 5</span>
|
||||
<span class="normal"> 6</span>
|
||||
<span class="normal"> 7</span>
|
||||
<span class="normal"> 8</span>
|
||||
<span class="normal"> 9</span>
|
||||
<span class="normal">10</span>
|
||||
<span class="normal">11</span>
|
||||
<span class="normal">12</span>
|
||||
<span class="normal">13</span>
|
||||
<span class="normal">14</span>
|
||||
<span class="normal">15</span>
|
||||
<span class="normal">16</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">def</span> <span class="nf">gcd</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="w"> </span><span class="sd">"""</span>
|
||||
<span class="sd"> This function calculate the GCD (Greatest Common Divisor of the number a of b</span>
|
||||
<span class="sd"> Args:</span>
|
||||
<span class="sd"> a (Integer): the number a</span>
|
||||
<span class="sd"> b (integer): the number b</span>
|
||||
|
||||
<span class="sd"> Return:</span>
|
||||
<span class="sd"> the GCD </span>
|
||||
<span class="sd"> """</span>
|
||||
|
||||
<span class="k">if</span> <span class="n">b</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
|
||||
<span class="k">return</span> <span class="n">a</span>
|
||||
<span class="k">return</span> <span class="n">gcd</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">a</span><span class="o">%</span><span class="n">b</span><span class="p">)</span>
|
||||
</code></pre></div></td></tr></table></div>
|
||||
</details>
|
||||
</div>
|
||||
|
||||
</div>
|
||||
|
||||
|
||||
|
||||
</div>
|
||||
|
||||
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|
||||
|
||||
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|
||||
|
||||
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||||
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||||
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