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  20 <article id="content">
  21 <header>
  22 <h1 class="title">Module <code>szyfrow.hill</code></h1>
  23 </header>
  24 <section id="section-intro">
  25 <details class="source">
  26 <summary>
  27 <span>Expand source code</span>
  28 </summary>
  29 <pre><code class="python">import multiprocessing
  30 import numpy as np
  31 from numpy import matrix
  32 from numpy import linalg
  33 from szyfrow.support.utilities import *
  34 from szyfrow.support.language_models import *
  35 from szyfrow.affine import modular_division_table
  36
  37
  38 def hill_encipher(matrix, message_letters, fillvalue=&#39;a&#39;):
  39     &#34;&#34;&#34;Hill cipher
  40
  41     &gt;&gt;&gt; hill_encipher(np.matrix([[7,8], [11,11]]), &#39;hellothere&#39;)
  42     &#39;drjiqzdrvx&#39;
  43     &gt;&gt;&gt; hill_encipher(np.matrix([[6, 24, 1], [13, 16, 10], [20, 17, 15]]), \
  44         &#39;hello there&#39;)
  45     &#39;tfjflpznvyac&#39;
  46     &#34;&#34;&#34;
  47     n = len(matrix)
  48     sanitised_message = sanitise(message_letters)
  49     if len(sanitised_message) % n != 0:
  50         padding = fillvalue[0] * (n - len(sanitised_message) % n)
  51     else:
  52         padding = &#39;&#39;
  53     message = [pos(c) for c in sanitised_message + padding]
  54     message_chunks = [message[i:i+n] for i in range(0, len(message), n)]
  55     # message_chunks = chunks(message, len(matrix), fillvalue=None)
  56     enciphered_chunks = [((matrix * np.matrix(c).T).T).tolist()[0]
  57             for c in message_chunks]
  58     return cat([unpos(round(l))
  59             for l in sum(enciphered_chunks, [])])
  60
  61 def hill_decipher(matrix, message, fillvalue=&#39;a&#39;):
  62     &#34;&#34;&#34;Hill cipher
  63
  64     &gt;&gt;&gt; hill_decipher(np.matrix([[7,8], [11,11]]), &#39;drjiqzdrvx&#39;)
  65     &#39;hellothere&#39;
  66     &gt;&gt;&gt; hill_decipher(np.matrix([[6, 24, 1], [13, 16, 10], [20, 17, 15]]), \
  67         &#39;tfjflpznvyac&#39;)
  68     &#39;hellothereaa&#39;
  69     &#34;&#34;&#34;
  70     adjoint = linalg.det(matrix)*linalg.inv(matrix)
  71     inverse_determinant = modular_division_table[int(round(linalg.det(matrix))) % 26, 1]
  72     inverse_matrix = (inverse_determinant * adjoint) % 26
  73     return hill_encipher(inverse_matrix, message, fillvalue)
  74
  75 def hill_break(message, matrix_size=2, fitness=Pletters,
  76     number_of_solutions=1, chunksize=500):
  77
  78     all_matrices = [np.matrix(list(m))
  79         for m in itertools.product([list(r)
  80             for r in itertools.product(range(26), repeat=matrix_size)],
  81         repeat=matrix_size)]
  82     valid_matrices = [m for m, d in
  83         zip(all_matrices, (int(round(linalg.det(m))) for m in all_matrices))
  84                   if d != 0
  85                   if d % 2 != 0
  86                   if d % 13 != 0 ]
  87     with multiprocessing.Pool() as pool:
  88         helper_args = [(message, matrix, fitness)
  89                        for matrix in valid_matrices]
  90         # Gotcha: the helper function here needs to be defined at the top level
  91         #   (limitation of Pool.starmap)
  92         breaks = pool.starmap(hill_break_worker, helper_args, chunksize)
  93         if number_of_solutions == 1:
  94             return max(breaks, key=lambda k: k[1])
  95         else:
  96             return sorted(breaks, key=lambda k: k[1], reverse=True)[:number_of_solutions]
  97
  98 def hill_break_worker(message, matrix, fitness):
  99     plaintext = hill_decipher(matrix, message)
 100     fit = fitness(plaintext)
 101     return matrix, fit
 102
 103 if __name__ == &#34;__main__&#34;:
 104     import doctest</code></pre>
 105 </details>
 106 </section>
 107 <section>
 108 </section>
 109 <section>
 110 </section>
 111 <section>
 112 <h2 class="section-title" id="header-functions">Functions</h2>
 113 <dl>
 114 <dt id="szyfrow.hill.cat"><code class="name flex">
 115 <span>def <span class="ident">cat</span></span>(<span>iterable, /)</span>
 116 </code></dt>
 117 <dd>
 118 <div class="desc"><p>Concatenate any number of strings.</p>
 119 <p>The string whose method is called is inserted in between each given string.
 120 The result is returned as a new string.</p>
 121 <p>Example: '.'.join(['ab', 'pq', 'rs']) -&gt; 'ab.pq.rs'</p></div>
 122 </dd>
 123 <dt id="szyfrow.hill.hill_break"><code class="name flex">
 124 <span>def <span class="ident">hill_break</span></span>(<span>message, matrix_size=2, fitness=&lt;function Pletters&gt;, number_of_solutions=1, chunksize=500)</span>
 125 </code></dt>
 126 <dd>
 127 <div class="desc"></div>
 128 <details class="source">
 129 <summary>
 130 <span>Expand source code</span>
 131 </summary>
 132 <pre><code class="python">def hill_break(message, matrix_size=2, fitness=Pletters,
 133     number_of_solutions=1, chunksize=500):
 134
 135     all_matrices = [np.matrix(list(m))
 136         for m in itertools.product([list(r)
 137             for r in itertools.product(range(26), repeat=matrix_size)],
 138         repeat=matrix_size)]
 139     valid_matrices = [m for m, d in
 140         zip(all_matrices, (int(round(linalg.det(m))) for m in all_matrices))
 141                   if d != 0
 142                   if d % 2 != 0
 143                   if d % 13 != 0 ]
 144     with multiprocessing.Pool() as pool:
 145         helper_args = [(message, matrix, fitness)
 146                        for matrix in valid_matrices]
 147         # Gotcha: the helper function here needs to be defined at the top level
 148         #   (limitation of Pool.starmap)
 149         breaks = pool.starmap(hill_break_worker, helper_args, chunksize)
 150         if number_of_solutions == 1:
 151             return max(breaks, key=lambda k: k[1])
 152         else:
 153             return sorted(breaks, key=lambda k: k[1], reverse=True)[:number_of_solutions]</code></pre>
 154 </details>
 155 </dd>
 156 <dt id="szyfrow.hill.hill_break_worker"><code class="name flex">
 157 <span>def <span class="ident">hill_break_worker</span></span>(<span>message, matrix, fitness)</span>
 158 </code></dt>
 159 <dd>
 160 <div class="desc"></div>
 161 <details class="source">
 162 <summary>
 163 <span>Expand source code</span>
 164 </summary>
 165 <pre><code class="python">def hill_break_worker(message, matrix, fitness):
 166     plaintext = hill_decipher(matrix, message)
 167     fit = fitness(plaintext)
 168     return matrix, fit</code></pre>
 169 </details>
 170 </dd>
 171 <dt id="szyfrow.hill.hill_decipher"><code class="name flex">
 172 <span>def <span class="ident">hill_decipher</span></span>(<span>matrix, message, fillvalue='a')</span>
 173 </code></dt>
 174 <dd>
 175 <div class="desc"><p>Hill cipher</p>
 176 <pre><code class="language-python-repl">&gt;&gt;&gt; hill_decipher(np.matrix([[7,8], [11,11]]), 'drjiqzdrvx')
 177 'hellothere'
 178 &gt;&gt;&gt; hill_decipher(np.matrix([[6, 24, 1], [13, 16, 10], [20, 17, 15]]),         'tfjflpznvyac')
 179 'hellothereaa'
 180 </code></pre></div>
 181 <details class="source">
 182 <summary>
 183 <span>Expand source code</span>
 184 </summary>
 185 <pre><code class="python">def hill_decipher(matrix, message, fillvalue=&#39;a&#39;):
 186     &#34;&#34;&#34;Hill cipher
 187
 188     &gt;&gt;&gt; hill_decipher(np.matrix([[7,8], [11,11]]), &#39;drjiqzdrvx&#39;)
 189     &#39;hellothere&#39;
 190     &gt;&gt;&gt; hill_decipher(np.matrix([[6, 24, 1], [13, 16, 10], [20, 17, 15]]), \
 191         &#39;tfjflpznvyac&#39;)
 192     &#39;hellothereaa&#39;
 193     &#34;&#34;&#34;
 194     adjoint = linalg.det(matrix)*linalg.inv(matrix)
 195     inverse_determinant = modular_division_table[int(round(linalg.det(matrix))) % 26, 1]
 196     inverse_matrix = (inverse_determinant * adjoint) % 26
 197     return hill_encipher(inverse_matrix, message, fillvalue)          </code></pre>
 198 </details>
 199 </dd>
 200 <dt id="szyfrow.hill.hill_encipher"><code class="name flex">
 201 <span>def <span class="ident">hill_encipher</span></span>(<span>matrix, message_letters, fillvalue='a')</span>
 202 </code></dt>
 203 <dd>
 204 <div class="desc"><p>Hill cipher</p>
 205 <pre><code class="language-python-repl">&gt;&gt;&gt; hill_encipher(np.matrix([[7,8], [11,11]]), 'hellothere')
 206 'drjiqzdrvx'
 207 &gt;&gt;&gt; hill_encipher(np.matrix([[6, 24, 1], [13, 16, 10], [20, 17, 15]]),         'hello there')
 208 'tfjflpznvyac'
 209 </code></pre></div>
 210 <details class="source">
 211 <summary>
 212 <span>Expand source code</span>
 213 </summary>
 214 <pre><code class="python">def hill_encipher(matrix, message_letters, fillvalue=&#39;a&#39;):
 215     &#34;&#34;&#34;Hill cipher
 216
 217     &gt;&gt;&gt; hill_encipher(np.matrix([[7,8], [11,11]]), &#39;hellothere&#39;)
 218     &#39;drjiqzdrvx&#39;
 219     &gt;&gt;&gt; hill_encipher(np.matrix([[6, 24, 1], [13, 16, 10], [20, 17, 15]]), \
 220         &#39;hello there&#39;)
 221     &#39;tfjflpznvyac&#39;
 222     &#34;&#34;&#34;
 223     n = len(matrix)
 224     sanitised_message = sanitise(message_letters)
 225     if len(sanitised_message) % n != 0:
 226         padding = fillvalue[0] * (n - len(sanitised_message) % n)
 227     else:
 228         padding = &#39;&#39;
 229     message = [pos(c) for c in sanitised_message + padding]
 230     message_chunks = [message[i:i+n] for i in range(0, len(message), n)]
 231     # message_chunks = chunks(message, len(matrix), fillvalue=None)
 232     enciphered_chunks = [((matrix * np.matrix(c).T).T).tolist()[0]
 233             for c in message_chunks]
 234     return cat([unpos(round(l))
 235             for l in sum(enciphered_chunks, [])])</code></pre>
 236 </details>
 237 </dd>
 238 <dt id="szyfrow.hill.lcat"><code class="name flex">
 239 <span>def <span class="ident">lcat</span></span>(<span>iterable, /)</span>
 240 </code></dt>
 241 <dd>
 242 <div class="desc"><p>Concatenate any number of strings.</p>
 243 <p>The string whose method is called is inserted in between each given string.
 244 The result is returned as a new string.</p>
 245 <p>Example: '.'.join(['ab', 'pq', 'rs']) -&gt; 'ab.pq.rs'</p></div>
 246 </dd>
 247 <dt id="szyfrow.hill.wcat"><code class="name flex">
 248 <span>def <span class="ident">wcat</span></span>(<span>iterable, /)</span>
 249 </code></dt>
 250 <dd>
 251 <div class="desc"><p>Concatenate any number of strings.</p>
 252 <p>The string whose method is called is inserted in between each given string.
 253 The result is returned as a new string.</p>
 254 <p>Example: '.'.join(['ab', 'pq', 'rs']) -&gt; 'ab.pq.rs'</p></div>
 255 </dd>
 256 </dl>
 257 </section>
 258 <section>
 259 </section>
 260 </article>
 261 <nav id="sidebar">
 262 <h1>Index</h1>
 263 <div class="toc">
 264 <ul></ul>
 265 </div>
 266 <ul id="index">
 267 <li><h3>Super-module</h3>
 268 <ul>
 269 <li><code><a title="szyfrow" href="index.html">szyfrow</a></code></li>
 270 </ul>
 271 </li>
 272 <li><h3><a href="#header-functions">Functions</a></h3>
 273 <ul class="two-column">
 274 <li><code><a title="szyfrow.hill.cat" href="#szyfrow.hill.cat">cat</a></code></li>
 275 <li><code><a title="szyfrow.hill.hill_break" href="#szyfrow.hill.hill_break">hill_break</a></code></li>
 276 <li><code><a title="szyfrow.hill.hill_break_worker" href="#szyfrow.hill.hill_break_worker">hill_break_worker</a></code></li>
 277 <li><code><a title="szyfrow.hill.hill_decipher" href="#szyfrow.hill.hill_decipher">hill_decipher</a></code></li>
 278 <li><code><a title="szyfrow.hill.hill_encipher" href="#szyfrow.hill.hill_encipher">hill_encipher</a></code></li>
 279 <li><code><a title="szyfrow.hill.lcat" href="#szyfrow.hill.lcat">lcat</a></code></li>
 280 <li><code><a title="szyfrow.hill.wcat" href="#szyfrow.hill.wcat">wcat</a></code></li>
 281 </ul>
 282 </li>
 283 </ul>
 284 </nav>
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