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+<article id="content">
+<header>
+<h1 class="title">Module <code>szyfrow.affine</code></h1>
+</header>
+<section id="section-intro">
+<p>Enciphering and deciphering using the <a href="https://en.wikipedia.org/wiki/Affine_cipher">affine cipher</a>.
+Also attempts to break messages that use an affine cipher.</p>
+<p>The affine cipher operates one letter at a time. It converts each letter to a
+number, then enciphers that number using a multiplier and a number. The result
+is taken mod 26 and converted back into a letter.</p>
+<p>For a multiplier <em>m</em> and adder <em>a</em>, a letter converted to number <em>x</em> is
+enciphered as <em>E(x)</em> = (<em>m</em> <em>x</em> + <em>a</em>) mod 26. Deciphering uses the modular
+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>
+<p>If <code>one_based</code> is <code>True</code>, the conversion between letters and numbers maps
+'a' → 1, 'b' → 2, … 'z'→ 26 and the <code>mod</code> function is adjusted to keep
+numbers in this range during enciphering and deciphering. If <code>one_based</code> is
+<code>False</code>, the conversion maps 'a' → 0, 'b' → 1, … 'z'→ 25 and <code>mod</code> behaves
+normally.</p>
+<details class="source">
+<summary>
+<span>Expand source code</span>
+</summary>
+<pre><code class="python">"""Enciphering and deciphering using the [affine cipher](https://en.wikipedia.org/wiki/Affine_cipher).
+Also attempts to break messages that use an affine cipher.
+
+The affine cipher operates one letter at a time. It converts each letter to a
+number, then enciphers that number using a multiplier and a number. The result
+is taken mod 26 and converted back into a letter.
+
+For a multiplier _m_ and adder _a_, a letter converted to number _x_ is
+enciphered as _E(x)_ = (_m_ _x_ + _a_) mod 26. Deciphering uses the modular
+inverse of _m_, _m_⁻¹, so that _D(x)_ = _m_⁻¹ (_x_ - _a_) mod 26.
+
+If `one_based` is `True`, the conversion between letters and numbers maps
+'a' → 1, 'b' → 2, … 'z'→ 26 and the `mod` function is adjusted to keep
+numbers in this range during enciphering and deciphering. If `one_based` is
+`False`, the conversion maps 'a' → 0, 'b' → 1, … 'z'→ 25 and `mod` behaves
+normally.
+"""
+
+from szyfrow.support.utilities import *
+from szyfrow.support.language_models import *
+
+modular_division_table = {
+ (multiplier, (multiplier * plaintext) % 26): plaintext
+ for plaintext in range(26)
+ for multiplier in range(26)
+ }
+
+
+def affine_encipher_letter(accented_letter, multiplier=1, adder=0, one_based=True):
+ """Encipher a letter, given a multiplier and adder.
+
+ Accented version of latin letters (such as é and ö) are converted to their
+ non-accented versions before encryption.
+
+ >>> cat(affine_encipher_letter(l, 3, 5, True) \
+ for l in string.ascii_letters)
+ 'hknqtwzcfiloruxadgjmpsvybeHKNQTWZCFILORUXADGJMPSVYBE'
+ >>> cat(affine_encipher_letter(l, 3, 5, False) \
+ for l in string.ascii_letters)
+ 'filoruxadgjmpsvybehknqtwzcFILORUXADGJMPSVYBEHKNQTWZC'
+ """
+ letter = unaccent(accented_letter)
+ if letter in string.ascii_letters:
+ letter_number = pos(letter)
+ if one_based: letter_number += 1
+ cipher_number = (letter_number * multiplier + adder) % 26
+ if one_based: cipher_number -= 1
+ if letter in string.ascii_uppercase:
+ return unpos(cipher_number).upper()
+ else:
+ return unpos(cipher_number)
+ else:
+ return letter
+
+def affine_decipher_letter(letter, multiplier=1, adder=0, one_based=True):
+ """Encipher a letter, given a multiplier and adder
+
+ >>> cat(affine_decipher_letter(l, 3, 5, True) \
+ for l in 'hknqtwzcfiloruxadgjmpsvybeHKNQTWZCFILORUXADGJMPSVYBE')
+ 'abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ'
+ >>> cat(affine_decipher_letter(l, 3, 5, False) \
+ for l in 'filoruxadgjmpsvybehknqtwzcFILORUXADGJMPSVYBEHKNQTWZC')
+ 'abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ'
+ """
+ if letter in string.ascii_letters:
+ cipher_number = pos(letter)
+ if one_based: cipher_number += 1
+ plaintext_number = (
+ modular_division_table[multiplier, (cipher_number - adder) % 26]
+ )
+ if one_based: plaintext_number -= 1
+ if letter in string.ascii_uppercase:
+ return unpos(plaintext_number).upper()
+ else:
+ return unpos(plaintext_number)
+ else:
+ return letter
+
+def affine_encipher(message, multiplier=1, adder=0, one_based=True):
+ """Encipher a message
+
+ >>> affine_encipher('hours passed during which jerico tried every ' \
+ 'trick he could think of', 15, 22, True)
+ 'lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg jfaoe ls omytd jlaxe mh'
+ """
+ enciphered = [affine_encipher_letter(l, multiplier, adder, one_based)
+ for l in message]
+ return cat(enciphered)
+
+def affine_decipher(message, multiplier=1, adder=0, one_based=True):
+ """Decipher a message
+
+ >>> affine_decipher('lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg ' \
+ 'jfaoe ls omytd jlaxe mh', 15, 22, True)
+ 'hours passed during which jerico tried every trick he could think of'
+ """
+ enciphered = [affine_decipher_letter(l, multiplier, adder, one_based)
+ for l in message]
+ return cat(enciphered)
+
+
+
+def affine_break(message, fitness=Pletters):
+ """Breaks an affine cipher using frequency analysis.
+
+ It tries all possible combinations of multiplier, adder, and one_based,
+ scores the fitness of the text decipherd with each combination, and returns
+ the key that produces the most fit deciphered text.
+
+ >>> 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
+ ((15, 22, True), -340.601181913...)
+ """
+ sanitised_message = sanitise(message)
+ best_multiplier = 0
+ best_adder = 0
+ best_one_based = True
+ best_fit = float("-inf")
+ for one_based in [True, False]:
+ for multiplier in [x for x in range(1, 26, 2) if x != 13]:
+ for adder in range(26):
+ plaintext = affine_decipher(sanitised_message,
+ multiplier, adder, one_based)
+ fit = fitness(plaintext)
+ if fit > best_fit:
+ best_fit = fit
+ best_multiplier = multiplier
+ best_adder = adder
+ best_one_based = one_based
+
+ return (best_multiplier, best_adder, best_one_based), best_fit</code></pre>
+</details>
+</section>
+<section>
+</section>
+<section>
+</section>
+<section>
+<h2 class="section-title" id="header-functions">Functions</h2>
+<dl>
+<dt id="szyfrow.affine.affine_break"><code class="name flex">
+<span>def <span class="ident">affine_break</span></span>(<span>message, fitness=<function Pletters>)</span>
+</code></dt>
+<dd>
+<div class="desc"><p>Breaks an affine cipher using frequency analysis.</p>
+<p>It tries all possible combinations of multiplier, adder, and one_based,
+scores the fitness of the text decipherd with each combination, and returns
+the key that produces the most fit deciphered text.</p>
+<pre><code class="language-python-repl">>>> 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
+((15, 22, True), -340.601181913...)
+</code></pre></div>
+<details class="source">
+<summary>
+<span>Expand source code</span>
+</summary>
+<pre><code class="python">def affine_break(message, fitness=Pletters):
+ """Breaks an affine cipher using frequency analysis.
+
+ It tries all possible combinations of multiplier, adder, and one_based,
+ scores the fitness of the text decipherd with each combination, and returns
+ the key that produces the most fit deciphered text.
+
+ >>> 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
+ ((15, 22, True), -340.601181913...)
+ """
+ sanitised_message = sanitise(message)
+ best_multiplier = 0
+ best_adder = 0
+ best_one_based = True
+ best_fit = float("-inf")
+ for one_based in [True, False]:
+ for multiplier in [x for x in range(1, 26, 2) if x != 13]:
+ for adder in range(26):
+ plaintext = affine_decipher(sanitised_message,
+ multiplier, adder, one_based)
+ fit = fitness(plaintext)
+ if fit > best_fit:
+ best_fit = fit
+ best_multiplier = multiplier
+ best_adder = adder
+ best_one_based = one_based
+
+ return (best_multiplier, best_adder, best_one_based), best_fit</code></pre>
+</details>
+</dd>
+<dt id="szyfrow.affine.affine_decipher"><code class="name flex">
+<span>def <span class="ident">affine_decipher</span></span>(<span>message, multiplier=1, adder=0, one_based=True)</span>
+</code></dt>
+<dd>
+<div class="desc"><p>Decipher a message</p>
+<pre><code class="language-python-repl">>>> affine_decipher('lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg ' 'jfaoe ls omytd jlaxe mh', 15, 22, True)
+'hours passed during which jerico tried every trick he could think of'
+</code></pre></div>
+<details class="source">
+<summary>
+<span>Expand source code</span>
+</summary>
+<pre><code class="python">def affine_decipher(message, multiplier=1, adder=0, one_based=True):
+ """Decipher a message
+
+ >>> affine_decipher('lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg ' \
+ 'jfaoe ls omytd jlaxe mh', 15, 22, True)
+ 'hours passed during which jerico tried every trick he could think of'
+ """
+ enciphered = [affine_decipher_letter(l, multiplier, adder, one_based)
+ for l in message]
+ return cat(enciphered)</code></pre>
+</details>
+</dd>
+<dt id="szyfrow.affine.affine_decipher_letter"><code class="name flex">
+<span>def <span class="ident">affine_decipher_letter</span></span>(<span>letter, multiplier=1, adder=0, one_based=True)</span>
+</code></dt>
+<dd>
+<div class="desc"><p>Encipher a letter, given a multiplier and adder</p>
+<pre><code class="language-python-repl">>>> cat(affine_decipher_letter(l, 3, 5, True) for l in 'hknqtwzcfiloruxadgjmpsvybeHKNQTWZCFILORUXADGJMPSVYBE')
+'abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ'
+>>> cat(affine_decipher_letter(l, 3, 5, False) for l in 'filoruxadgjmpsvybehknqtwzcFILORUXADGJMPSVYBEHKNQTWZC')
+'abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ'
+</code></pre></div>
+<details class="source">
+<summary>
+<span>Expand source code</span>
+</summary>
+<pre><code class="python">def affine_decipher_letter(letter, multiplier=1, adder=0, one_based=True):
+ """Encipher a letter, given a multiplier and adder
+
+ >>> cat(affine_decipher_letter(l, 3, 5, True) \
+ for l in 'hknqtwzcfiloruxadgjmpsvybeHKNQTWZCFILORUXADGJMPSVYBE')
+ 'abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ'
+ >>> cat(affine_decipher_letter(l, 3, 5, False) \
+ for l in 'filoruxadgjmpsvybehknqtwzcFILORUXADGJMPSVYBEHKNQTWZC')
+ 'abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ'
+ """
+ if letter in string.ascii_letters:
+ cipher_number = pos(letter)
+ if one_based: cipher_number += 1
+ plaintext_number = (
+ modular_division_table[multiplier, (cipher_number - adder) % 26]
+ )
+ if one_based: plaintext_number -= 1
+ if letter in string.ascii_uppercase:
+ return unpos(plaintext_number).upper()
+ else:
+ return unpos(plaintext_number)
+ else:
+ return letter</code></pre>
+</details>
+</dd>
+<dt id="szyfrow.affine.affine_encipher"><code class="name flex">
+<span>def <span class="ident">affine_encipher</span></span>(<span>message, multiplier=1, adder=0, one_based=True)</span>
+</code></dt>
+<dd>
+<div class="desc"><p>Encipher a message</p>
+<pre><code class="language-python-repl">>>> affine_encipher('hours passed during which jerico tried every ' 'trick he could think of', 15, 22, True)
+'lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg jfaoe ls omytd jlaxe mh'
+</code></pre></div>
+<details class="source">
+<summary>
+<span>Expand source code</span>
+</summary>
+<pre><code class="python">def affine_encipher(message, multiplier=1, adder=0, one_based=True):
+ """Encipher a message
+
+ >>> affine_encipher('hours passed during which jerico tried every ' \
+ 'trick he could think of', 15, 22, True)
+ 'lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg jfaoe ls omytd jlaxe mh'
+ """
+ enciphered = [affine_encipher_letter(l, multiplier, adder, one_based)
+ for l in message]
+ return cat(enciphered)</code></pre>
+</details>
+</dd>
+<dt id="szyfrow.affine.affine_encipher_letter"><code class="name flex">
+<span>def <span class="ident">affine_encipher_letter</span></span>(<span>accented_letter, multiplier=1, adder=0, one_based=True)</span>
+</code></dt>
+<dd>
+<div class="desc"><p>Encipher a letter, given a multiplier and adder.</p>
+<p>Accented version of latin letters (such as é and ö) are converted to their
+non-accented versions before encryption.</p>
+<pre><code class="language-python-repl">>>> cat(affine_encipher_letter(l, 3, 5, True) for l in string.ascii_letters)
+'hknqtwzcfiloruxadgjmpsvybeHKNQTWZCFILORUXADGJMPSVYBE'
+>>> cat(affine_encipher_letter(l, 3, 5, False) for l in string.ascii_letters)
+'filoruxadgjmpsvybehknqtwzcFILORUXADGJMPSVYBEHKNQTWZC'
+</code></pre></div>
+<details class="source">
+<summary>
+<span>Expand source code</span>
+</summary>
+<pre><code class="python">def affine_encipher_letter(accented_letter, multiplier=1, adder=0, one_based=True):
+ """Encipher a letter, given a multiplier and adder.
+
+ Accented version of latin letters (such as é and ö) are converted to their
+ non-accented versions before encryption.
+
+ >>> cat(affine_encipher_letter(l, 3, 5, True) \
+ for l in string.ascii_letters)
+ 'hknqtwzcfiloruxadgjmpsvybeHKNQTWZCFILORUXADGJMPSVYBE'
+ >>> cat(affine_encipher_letter(l, 3, 5, False) \
+ for l in string.ascii_letters)
+ 'filoruxadgjmpsvybehknqtwzcFILORUXADGJMPSVYBEHKNQTWZC'
+ """
+ letter = unaccent(accented_letter)
+ if letter in string.ascii_letters:
+ letter_number = pos(letter)
+ if one_based: letter_number += 1
+ cipher_number = (letter_number * multiplier + adder) % 26
+ if one_based: cipher_number -= 1
+ if letter in string.ascii_uppercase:
+ return unpos(cipher_number).upper()
+ else:
+ return unpos(cipher_number)
+ else:
+ return letter</code></pre>
+</details>
+</dd>
+<dt id="szyfrow.affine.cat"><code class="name flex">
+<span>def <span class="ident">cat</span></span>(<span>iterable, /)</span>
+</code></dt>
+<dd>
+<div class="desc"><p>Concatenate any number of strings.</p>
+<p>The string whose method is called is inserted in between each given string.
+The result is returned as a new string.</p>
+<p>Example: '.'.join(['ab', 'pq', 'rs']) -> 'ab.pq.rs'</p></div>
+</dd>
+<dt id="szyfrow.affine.lcat"><code class="name flex">
+<span>def <span class="ident">lcat</span></span>(<span>iterable, /)</span>
+</code></dt>
+<dd>
+<div class="desc"><p>Concatenate any number of strings.</p>
+<p>The string whose method is called is inserted in between each given string.
+The result is returned as a new string.</p>
+<p>Example: '.'.join(['ab', 'pq', 'rs']) -> 'ab.pq.rs'</p></div>
+</dd>
+<dt id="szyfrow.affine.wcat"><code class="name flex">
+<span>def <span class="ident">wcat</span></span>(<span>iterable, /)</span>
+</code></dt>
+<dd>
+<div class="desc"><p>Concatenate any number of strings.</p>
+<p>The string whose method is called is inserted in between each given string.
+The result is returned as a new string.</p>
+<p>Example: '.'.join(['ab', 'pq', 'rs']) -> 'ab.pq.rs'</p></div>
+</dd>
+</dl>
+</section>
+<section>
+</section>
+</article>
+<nav id="sidebar">
+<h1>Index</h1>
+<div class="toc">
+<ul></ul>
+</div>
+<ul id="index">
+<li><h3>Super-module</h3>
+<ul>
+<li><code><a title="szyfrow" href="index.html">szyfrow</a></code></li>
+</ul>
+</li>
+<li><h3><a href="#header-functions">Functions</a></h3>
+<ul class="">
+<li><code><a title="szyfrow.affine.affine_break" href="#szyfrow.affine.affine_break">affine_break</a></code></li>
+<li><code><a title="szyfrow.affine.affine_decipher" href="#szyfrow.affine.affine_decipher">affine_decipher</a></code></li>
+<li><code><a title="szyfrow.affine.affine_decipher_letter" href="#szyfrow.affine.affine_decipher_letter">affine_decipher_letter</a></code></li>
+<li><code><a title="szyfrow.affine.affine_encipher" href="#szyfrow.affine.affine_encipher">affine_encipher</a></code></li>
+<li><code><a title="szyfrow.affine.affine_encipher_letter" href="#szyfrow.affine.affine_encipher_letter">affine_encipher_letter</a></code></li>
+<li><code><a title="szyfrow.affine.cat" href="#szyfrow.affine.cat">cat</a></code></li>
+<li><code><a title="szyfrow.affine.lcat" href="#szyfrow.affine.lcat">lcat</a></code></li>
+<li><code><a title="szyfrow.affine.wcat" href="#szyfrow.affine.wcat">wcat</a></code></li>
+</ul>
+</li>
+</ul>
+</nav>
+</main>
+<footer id="footer">
+<p>Generated by <a href="https://pdoc3.github.io/pdoc"><cite>pdoc</cite> 0.9.2</a>.</p>
+</footer>
+</body>
+</html>
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projects / szyfrow.git / blobdiff