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  22 <header>
  23 <h1 class="title">Module <code>szyfrow.affine</code></h1>
  24 </header>
  25 <section id="section-intro">
  26 <p>Enciphering and deciphering using the <a href="https://en.wikipedia.org/wiki/Affine_cipher">affine cipher</a>.
  27 Also attempts to break messages that use an affine cipher.</p>
  28 <p>The affine cipher operates one letter at a time. It converts each letter to a
  29 number, then enciphers that number using a multiplier and a number. The result
  30 is taken mod 26 and converted back into a letter.</p>
  31 <p>For a multiplier <em>m</em> and adder <em>a</em>, a letter converted to number <em>x</em> is
  32 enciphered as <em>E(x)</em> = (<em>m</em> <em>x</em> + <em>a</em>) mod 26. Deciphering uses the modular
  33 inverse of <em>m</em>, <em>m</em>⁻¹, so that <em>D(x)</em> = <em>m</em>⁻¹ (<em>x</em> - <em>a</em>) mod 26.</p>
  34 <p>If <code>one_based</code> is <code>True</code>, the conversion between letters and numbers maps
  35 'a' → 1, 'b' → 2, … 'z'→ 26 and the <code>mod</code> function is adjusted to keep
  36 numbers in this range during enciphering and deciphering. If <code>one_based</code> is
  37 <code>False</code>, the conversion maps 'a' → 0, 'b' → 1, … 'z'→ 25 and <code>mod</code> behaves
  38 normally.</p>
  39 <details class="source">
  40 <summary>
  41 <span>Expand source code</span>
  42 </summary>
  43 <pre><code class="python">&#34;&#34;&#34;Enciphering and deciphering using the [affine cipher](https://en.wikipedia.org/wiki/Affine_cipher).
  44 Also attempts to break messages that use an affine cipher.
  45
  46 The affine cipher operates one letter at a time. It converts each letter to a
  47 number, then enciphers that number using a multiplier and a number. The result
  48 is taken mod 26 and converted back into a letter.
  49
  50 For a multiplier _m_ and adder _a_, a letter converted to number _x_ is
  51 enciphered as _E(x)_ = (_m_ _x_ + _a_) mod 26. Deciphering uses the modular
  52 inverse of _m_, _m_⁻¹, so that _D(x)_ = _m_⁻¹ (_x_ - _a_) mod 26.
  53
  54 If `one_based` is `True`, the conversion between letters and numbers maps
  55 &#39;a&#39; → 1, &#39;b&#39; → 2, … &#39;z&#39;→ 26 and the `mod` function is adjusted to keep
  56 numbers in this range during enciphering and deciphering. If `one_based` is
  57 `False`, the conversion maps &#39;a&#39; → 0, &#39;b&#39; → 1, … &#39;z&#39;→ 25 and `mod` behaves
  58 normally.
  59 &#34;&#34;&#34;
  60
  61 from szyfrow.support.utilities import *
  62 from szyfrow.support.language_models import *
  63
  64 modular_division_table = {
  65     (multiplier, (multiplier * plaintext) % 26): plaintext
  66     for plaintext in range(26)
  67     for multiplier in range(26)
  68     }
  69
  70
  71 def affine_encipher_letter(accented_letter, multiplier=1, adder=0, one_based=True):
  72     &#34;&#34;&#34;Encipher a letter, given a multiplier and adder.
  73
  74     Accented version of latin letters (such as é and ö) are converted to their
  75     non-accented versions before encryption.
  76
  77     &gt;&gt;&gt; cat(affine_encipher_letter(l, 3, 5, True) \
  78             for l in string.ascii_letters)
  79     &#39;hknqtwzcfiloruxadgjmpsvybeHKNQTWZCFILORUXADGJMPSVYBE&#39;
  80     &gt;&gt;&gt; cat(affine_encipher_letter(l, 3, 5, False) \
  81             for l in string.ascii_letters)
  82     &#39;filoruxadgjmpsvybehknqtwzcFILORUXADGJMPSVYBEHKNQTWZC&#39;
  83     &#34;&#34;&#34;
  84     letter = unaccent(accented_letter)
  85     if letter in string.ascii_letters:
  86         letter_number = pos(letter)
  87         if one_based: letter_number += 1
  88         cipher_number = (letter_number * multiplier + adder) % 26
  89         if one_based: cipher_number -= 1
  90         if letter in string.ascii_uppercase:
  91             return unpos(cipher_number).upper()
  92         else:
  93             return unpos(cipher_number)
  94     else:
  95         return letter
  96
  97 def affine_decipher_letter(letter, multiplier=1, adder=0, one_based=True):
  98     &#34;&#34;&#34;Encipher a letter, given a multiplier and adder
  99
 100     &gt;&gt;&gt; cat(affine_decipher_letter(l, 3, 5, True) \
 101             for l in &#39;hknqtwzcfiloruxadgjmpsvybeHKNQTWZCFILORUXADGJMPSVYBE&#39;)
 102     &#39;abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ&#39;
 103     &gt;&gt;&gt; cat(affine_decipher_letter(l, 3, 5, False) \
 104             for l in &#39;filoruxadgjmpsvybehknqtwzcFILORUXADGJMPSVYBEHKNQTWZC&#39;)
 105     &#39;abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ&#39;
 106     &#34;&#34;&#34;
 107     if letter in string.ascii_letters:
 108         cipher_number = pos(letter)
 109         if one_based: cipher_number += 1
 110         plaintext_number = (
 111             modular_division_table[multiplier, (cipher_number - adder) % 26]
 112             )
 113         if one_based: plaintext_number -= 1
 114         if letter in string.ascii_uppercase:
 115             return unpos(plaintext_number).upper()
 116         else:
 117             return unpos(plaintext_number)
 118     else:
 119         return letter
 120
 121 def affine_encipher(message, multiplier=1, adder=0, one_based=True):
 122     &#34;&#34;&#34;Encipher a message
 123
 124     &gt;&gt;&gt; affine_encipher(&#39;hours passed during which jerico tried every &#39; \
 125            &#39;trick he could think of&#39;, 15, 22, True)
 126     &#39;lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg jfaoe ls omytd jlaxe mh&#39;
 127     &#34;&#34;&#34;
 128     enciphered = [affine_encipher_letter(l, multiplier, adder, one_based)
 129                   for l in message]
 130     return cat(enciphered)
 131
 132 def affine_decipher(message, multiplier=1, adder=0, one_based=True):
 133     &#34;&#34;&#34;Decipher a message
 134
 135     &gt;&gt;&gt; affine_decipher(&#39;lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg &#39; \
 136            &#39;jfaoe ls omytd jlaxe mh&#39;, 15, 22, True)
 137     &#39;hours passed during which jerico tried every trick he could think of&#39;
 138     &#34;&#34;&#34;
 139     enciphered = [affine_decipher_letter(l, multiplier, adder, one_based)
 140                   for l in message]
 141     return cat(enciphered)
 142
 143
 144
 145 def affine_break(message, fitness=Pletters):
 146     &#34;&#34;&#34;Breaks an affine cipher using frequency analysis.
 147
 148     It tries all possible combinations of multiplier, adder, and one_based,
 149     scores the fitness of the text decipherd with each combination, and returns
 150     the key that produces the most fit deciphered text.
 151
 152     &gt;&gt;&gt; affine_break(&#39;lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg jfaoe ls &#39; \
 153           &#39;omytd jlaxe mh jm bfmibj umis hfsul axubafkjamx. ls kffkxwsd jls &#39; \
 154           &#39;ofgbjmwfkiu olfmxmtmwaokttg jlsx ls kffkxwsd jlsi zg tsxwjl. jlsx &#39; \
 155           &#39;ls umfjsd jlsi zg hfsqysxog. ls dmmdtsd mx jls bats mh bkbsf. ls &#39; \
 156           &#39;bfmctsd kfmyxd jls lyj, mztanamyu xmc jm clm cku tmmeaxw kj lai &#39; \
 157           &#39;kxd clm ckuxj.&#39;) # doctest: +ELLIPSIS
 158     ((15, 22, True), -340.601181913...)
 159     &#34;&#34;&#34;
 160     sanitised_message = sanitise(message)
 161     best_multiplier = 0
 162     best_adder = 0
 163     best_one_based = True
 164     best_fit = float(&#34;-inf&#34;)
 165     for one_based in [True, False]:
 166         for multiplier in [x for x in range(1, 26, 2) if x != 13]:
 167             for adder in range(26):
 168                 plaintext = affine_decipher(sanitised_message,
 169                                             multiplier, adder, one_based)
 170                 fit = fitness(plaintext)
 171                 if fit &gt; best_fit:
 172                     best_fit = fit
 173                     best_multiplier = multiplier
 174                     best_adder = adder
 175                     best_one_based = one_based
 176
 177     return (best_multiplier, best_adder, best_one_based), best_fit</code></pre>
 178 </details>
 179 </section>
 180 <section>
 181 </section>
 182 <section>
 183 </section>
 184 <section>
 185 <h2 class="section-title" id="header-functions">Functions</h2>
 186 <dl>
 187 <dt id="szyfrow.affine.affine_break"><code class="name flex">
 188 <span>def <span class="ident">affine_break</span></span>(<span>message, fitness=&lt;function Pletters&gt;)</span>
 189 </code></dt>
 190 <dd>
 191 <div class="desc"><p>Breaks an affine cipher using frequency analysis.</p>
 192 <p>It tries all possible combinations of multiplier, adder, and one_based,
 193 scores the fitness of the text decipherd with each combination, and returns
 194 the key that produces the most fit deciphered text.</p>
 195 <pre><code class="language-python-repl">&gt;&gt;&gt; affine_break('lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg jfaoe ls '           'omytd jlaxe mh jm bfmibj umis hfsul axubafkjamx. ls kffkxwsd jls '           'ofgbjmwfkiu olfmxmtmwaokttg jlsx ls kffkxwsd jlsi zg tsxwjl. jlsx '           'ls umfjsd jlsi zg hfsqysxog. ls dmmdtsd mx jls bats mh bkbsf. ls '           'bfmctsd kfmyxd jls lyj, mztanamyu xmc jm clm cku tmmeaxw kj lai '           'kxd clm ckuxj.') # doctest: +ELLIPSIS
 196 ((15, 22, True), -340.601181913...)
 197 </code></pre></div>
 198 <details class="source">
 199 <summary>
 200 <span>Expand source code</span>
 201 </summary>
 202 <pre><code class="python">def affine_break(message, fitness=Pletters):
 203     &#34;&#34;&#34;Breaks an affine cipher using frequency analysis.
 204
 205     It tries all possible combinations of multiplier, adder, and one_based,
 206     scores the fitness of the text decipherd with each combination, and returns
 207     the key that produces the most fit deciphered text.
 208
 209     &gt;&gt;&gt; affine_break(&#39;lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg jfaoe ls &#39; \
 210           &#39;omytd jlaxe mh jm bfmibj umis hfsul axubafkjamx. ls kffkxwsd jls &#39; \
 211           &#39;ofgbjmwfkiu olfmxmtmwaokttg jlsx ls kffkxwsd jlsi zg tsxwjl. jlsx &#39; \
 212           &#39;ls umfjsd jlsi zg hfsqysxog. ls dmmdtsd mx jls bats mh bkbsf. ls &#39; \
 213           &#39;bfmctsd kfmyxd jls lyj, mztanamyu xmc jm clm cku tmmeaxw kj lai &#39; \
 214           &#39;kxd clm ckuxj.&#39;) # doctest: +ELLIPSIS
 215     ((15, 22, True), -340.601181913...)
 216     &#34;&#34;&#34;
 217     sanitised_message = sanitise(message)
 218     best_multiplier = 0
 219     best_adder = 0
 220     best_one_based = True
 221     best_fit = float(&#34;-inf&#34;)
 222     for one_based in [True, False]:
 223         for multiplier in [x for x in range(1, 26, 2) if x != 13]:
 224             for adder in range(26):
 225                 plaintext = affine_decipher(sanitised_message,
 226                                             multiplier, adder, one_based)
 227                 fit = fitness(plaintext)
 228                 if fit &gt; best_fit:
 229                     best_fit = fit
 230                     best_multiplier = multiplier
 231                     best_adder = adder
 232                     best_one_based = one_based
 233
 234     return (best_multiplier, best_adder, best_one_based), best_fit</code></pre>
 235 </details>
 236 </dd>
 237 <dt id="szyfrow.affine.affine_decipher"><code class="name flex">
 238 <span>def <span class="ident">affine_decipher</span></span>(<span>message, multiplier=1, adder=0, one_based=True)</span>
 239 </code></dt>
 240 <dd>
 241 <div class="desc"><p>Decipher a message</p>
 242 <pre><code class="language-python-repl">&gt;&gt;&gt; affine_decipher('lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg '            'jfaoe ls omytd jlaxe mh', 15, 22, True)
 243 'hours passed during which jerico tried every trick he could think of'
 244 </code></pre></div>
 245 <details class="source">
 246 <summary>
 247 <span>Expand source code</span>
 248 </summary>
 249 <pre><code class="python">def affine_decipher(message, multiplier=1, adder=0, one_based=True):
 250     &#34;&#34;&#34;Decipher a message
 251
 252     &gt;&gt;&gt; affine_decipher(&#39;lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg &#39; \
 253            &#39;jfaoe ls omytd jlaxe mh&#39;, 15, 22, True)
 254     &#39;hours passed during which jerico tried every trick he could think of&#39;
 255     &#34;&#34;&#34;
 256     enciphered = [affine_decipher_letter(l, multiplier, adder, one_based)
 257                   for l in message]
 258     return cat(enciphered)</code></pre>
 259 </details>
 260 </dd>
 261 <dt id="szyfrow.affine.affine_decipher_letter"><code class="name flex">
 262 <span>def <span class="ident">affine_decipher_letter</span></span>(<span>letter, multiplier=1, adder=0, one_based=True)</span>
 263 </code></dt>
 264 <dd>
 265 <div class="desc"><p>Encipher a letter, given a multiplier and adder</p>
 266 <pre><code class="language-python-repl">&gt;&gt;&gt; cat(affine_decipher_letter(l, 3, 5, True)             for l in 'hknqtwzcfiloruxadgjmpsvybeHKNQTWZCFILORUXADGJMPSVYBE')
 267 'abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ'
 268 &gt;&gt;&gt; cat(affine_decipher_letter(l, 3, 5, False)             for l in 'filoruxadgjmpsvybehknqtwzcFILORUXADGJMPSVYBEHKNQTWZC')
 269 'abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ'
 270 </code></pre></div>
 271 <details class="source">
 272 <summary>
 273 <span>Expand source code</span>
 274 </summary>
 275 <pre><code class="python">def affine_decipher_letter(letter, multiplier=1, adder=0, one_based=True):
 276     &#34;&#34;&#34;Encipher a letter, given a multiplier and adder
 277
 278     &gt;&gt;&gt; cat(affine_decipher_letter(l, 3, 5, True) \
 279             for l in &#39;hknqtwzcfiloruxadgjmpsvybeHKNQTWZCFILORUXADGJMPSVYBE&#39;)
 280     &#39;abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ&#39;
 281     &gt;&gt;&gt; cat(affine_decipher_letter(l, 3, 5, False) \
 282             for l in &#39;filoruxadgjmpsvybehknqtwzcFILORUXADGJMPSVYBEHKNQTWZC&#39;)
 283     &#39;abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ&#39;
 284     &#34;&#34;&#34;
 285     if letter in string.ascii_letters:
 286         cipher_number = pos(letter)
 287         if one_based: cipher_number += 1
 288         plaintext_number = (
 289             modular_division_table[multiplier, (cipher_number - adder) % 26]
 290             )
 291         if one_based: plaintext_number -= 1
 292         if letter in string.ascii_uppercase:
 293             return unpos(plaintext_number).upper()
 294         else:
 295             return unpos(plaintext_number)
 296     else:
 297         return letter</code></pre>
 298 </details>
 299 </dd>
 300 <dt id="szyfrow.affine.affine_encipher"><code class="name flex">
 301 <span>def <span class="ident">affine_encipher</span></span>(<span>message, multiplier=1, adder=0, one_based=True)</span>
 302 </code></dt>
 303 <dd>
 304 <div class="desc"><p>Encipher a message</p>
 305 <pre><code class="language-python-repl">&gt;&gt;&gt; affine_encipher('hours passed during which jerico tried every '            'trick he could think of', 15, 22, True)
 306 'lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg jfaoe ls omytd jlaxe mh'
 307 </code></pre></div>
 308 <details class="source">
 309 <summary>
 310 <span>Expand source code</span>
 311 </summary>
 312 <pre><code class="python">def affine_encipher(message, multiplier=1, adder=0, one_based=True):
 313     &#34;&#34;&#34;Encipher a message
 314
 315     &gt;&gt;&gt; affine_encipher(&#39;hours passed during which jerico tried every &#39; \
 316            &#39;trick he could think of&#39;, 15, 22, True)
 317     &#39;lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg jfaoe ls omytd jlaxe mh&#39;
 318     &#34;&#34;&#34;
 319     enciphered = [affine_encipher_letter(l, multiplier, adder, one_based)
 320                   for l in message]
 321     return cat(enciphered)</code></pre>
 322 </details>
 323 </dd>
 324 <dt id="szyfrow.affine.affine_encipher_letter"><code class="name flex">
 325 <span>def <span class="ident">affine_encipher_letter</span></span>(<span>accented_letter, multiplier=1, adder=0, one_based=True)</span>
 326 </code></dt>
 327 <dd>
 328 <div class="desc"><p>Encipher a letter, given a multiplier and adder.</p>
 329 <p>Accented version of latin letters (such as é and ö) are converted to their
 330 non-accented versions before encryption.</p>
 331 <pre><code class="language-python-repl">&gt;&gt;&gt; cat(affine_encipher_letter(l, 3, 5, True)             for l in string.ascii_letters)
 332 'hknqtwzcfiloruxadgjmpsvybeHKNQTWZCFILORUXADGJMPSVYBE'
 333 &gt;&gt;&gt; cat(affine_encipher_letter(l, 3, 5, False)             for l in string.ascii_letters)
 334 'filoruxadgjmpsvybehknqtwzcFILORUXADGJMPSVYBEHKNQTWZC'
 335 </code></pre></div>
 336 <details class="source">
 337 <summary>
 338 <span>Expand source code</span>
 339 </summary>
 340 <pre><code class="python">def affine_encipher_letter(accented_letter, multiplier=1, adder=0, one_based=True):
 341     &#34;&#34;&#34;Encipher a letter, given a multiplier and adder.
 342
 343     Accented version of latin letters (such as é and ö) are converted to their
 344     non-accented versions before encryption.
 345
 346     &gt;&gt;&gt; cat(affine_encipher_letter(l, 3, 5, True) \
 347             for l in string.ascii_letters)
 348     &#39;hknqtwzcfiloruxadgjmpsvybeHKNQTWZCFILORUXADGJMPSVYBE&#39;
 349     &gt;&gt;&gt; cat(affine_encipher_letter(l, 3, 5, False) \
 350             for l in string.ascii_letters)
 351     &#39;filoruxadgjmpsvybehknqtwzcFILORUXADGJMPSVYBEHKNQTWZC&#39;
 352     &#34;&#34;&#34;
 353     letter = unaccent(accented_letter)
 354     if letter in string.ascii_letters:
 355         letter_number = pos(letter)
 356         if one_based: letter_number += 1
 357         cipher_number = (letter_number * multiplier + adder) % 26
 358         if one_based: cipher_number -= 1
 359         if letter in string.ascii_uppercase:
 360             return unpos(cipher_number).upper()
 361         else:
 362             return unpos(cipher_number)
 363     else:
 364         return letter</code></pre>
 365 </details>
 366 </dd>
 367 <dt id="szyfrow.affine.cat"><code class="name flex">
 368 <span>def <span class="ident">cat</span></span>(<span>iterable, /)</span>
 369 </code></dt>
 370 <dd>
 371 <div class="desc"><p>Concatenate any number of strings.</p>
 372 <p>The string whose method is called is inserted in between each given string.
 373 The result is returned as a new string.</p>
 374 <p>Example: '.'.join(['ab', 'pq', 'rs']) -&gt; 'ab.pq.rs'</p></div>
 375 </dd>
 376 <dt id="szyfrow.affine.lcat"><code class="name flex">
 377 <span>def <span class="ident">lcat</span></span>(<span>iterable, /)</span>
 378 </code></dt>
 379 <dd>
 380 <div class="desc"><p>Concatenate any number of strings.</p>
 381 <p>The string whose method is called is inserted in between each given string.
 382 The result is returned as a new string.</p>
 383 <p>Example: '.'.join(['ab', 'pq', 'rs']) -&gt; 'ab.pq.rs'</p></div>
 384 </dd>
 385 <dt id="szyfrow.affine.wcat"><code class="name flex">
 386 <span>def <span class="ident">wcat</span></span>(<span>iterable, /)</span>
 387 </code></dt>
 388 <dd>
 389 <div class="desc"><p>Concatenate any number of strings.</p>
 390 <p>The string whose method is called is inserted in between each given string.
 391 The result is returned as a new string.</p>
 392 <p>Example: '.'.join(['ab', 'pq', 'rs']) -&gt; 'ab.pq.rs'</p></div>
 393 </dd>
 394 </dl>
 395 </section>
 396 <section>
 397 </section>
 398 </article>
 399 <nav id="sidebar">
 400 <h1>Index</h1>
 401 <div class="toc">
 402 <ul></ul>
 403 </div>
 404 <ul id="index">
 405 <li><h3>Super-module</h3>
 406 <ul>
 407 <li><code><a title="szyfrow" href="index.html">szyfrow</a></code></li>
 408 </ul>
 409 </li>
 410 <li><h3><a href="#header-functions">Functions</a></h3>
 411 <ul class="">
 412 <li><code><a title="szyfrow.affine.affine_break" href="#szyfrow.affine.affine_break">affine_break</a></code></li>
 413 <li><code><a title="szyfrow.affine.affine_decipher" href="#szyfrow.affine.affine_decipher">affine_decipher</a></code></li>
 414 <li><code><a title="szyfrow.affine.affine_decipher_letter" href="#szyfrow.affine.affine_decipher_letter">affine_decipher_letter</a></code></li>
 415 <li><code><a title="szyfrow.affine.affine_encipher" href="#szyfrow.affine.affine_encipher">affine_encipher</a></code></li>
 416 <li><code><a title="szyfrow.affine.affine_encipher_letter" href="#szyfrow.affine.affine_encipher_letter">affine_encipher_letter</a></code></li>
 417 <li><code><a title="szyfrow.affine.cat" href="#szyfrow.affine.cat">cat</a></code></li>
 418 <li><code><a title="szyfrow.affine.lcat" href="#szyfrow.affine.lcat">lcat</a></code></li>
 419 <li><code><a title="szyfrow.affine.wcat" href="#szyfrow.affine.wcat">wcat</a></code></li>
 420 </ul>
 421 </li>
 422 </ul>
 423 </nav>
 424 </main>
 425 <footer id="footer">
 426 <p>Generated by <a href="https://pdoc3.github.io/pdoc"><cite>pdoc</cite> 0.9.2</a>.</p>
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