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  1. PO
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    <p>It is not possible (in general case, for affine cipher, see update below). That's why module operation is so frequently used in security algorithms - it is not reversible. But, why don't we try?</p> <pre><code>result = (k1 * input + k2) % 27 (*1) </code></pre> <p>Let's take the first letter:</p> <pre><code>result = (7 * 8 + 5) % 27 = 7 </code></pre> <p>That's cool. Now, because we said, that:</p> <pre><code>result = (k1 * input + k2) % 27 </code></pre> <p>the following is also true:</p> <pre><code>k1 * input + k2 = 27 * div + result (*2) </code></pre> <p>where</p> <pre><code>div = (k1 * input + k2) / 27 (integral division) </code></pre> <p>It is quite obvious (if a % b = c, then a = b*n + c, where n is the result of integer division a/b).</p> <p>You know the values of k1 (which is 7), k2 (5) and result (7). So, when we put these values to (*2), we get the following:</p> <pre><code>7 * input + 5 = 27 * div + 7 //You need to solve this </code></pre> <p>As you can see, it is impossible to solve this, because you would need to know also the result of the integral division - translating this to your function's language, you would need the value of</p> <pre><code>numberback / 27 </code></pre> <p>which is unknown. So answer is: <strong>you cannot reverse your function's results, using only output it returns</strong>.</p> <hr> <p>** UPDATE **</p> <hr> <p>I focused too much on the question's title, so the answer above is not fully correct. I decided not to remove it, however, but write an update.</p> <p>So, the answer <strong>for your particular case</strong> (affine cipher) is: YES, you can reverse it.</p> <p>As you can see on the wiki, decryption function for affine cipher for the following encrytption function:</p> <pre><code>E(input) = a*input + b mod m </code></pre> <p>is defined as:</p> <pre><code>D(enc) = a^-1 * (enc - b) mod m </code></pre> <p>The only possible problem here can be computation of a^-1, which is modular multiplicative inverse.</p> <p>Read about it on <a href="http://en.wikipedia.org/wiki/Modular_multiplicative_inverse" rel="nofollow">wiki</a>, I will provide only example.</p> <p>In your case a = k1 = 7 and m = 27. So:</p> <pre><code>7^-1 = p mod 27 7p = 1 mod 27 </code></pre> <p>In other words, you need to find p, which satisfies the following: 7p % 27 = 1. p can be computed using extended euclidean algorithm and I computed it to be 4 (4 * 7 = 28, 28 % 27 = 1).</p> <p>Check, if can decipher your output now:</p> <pre><code>E(8) = 7*8 + 5 mod 27 = 7 D(7) = 4 * (7 - 5) mod 27 = 8 </code></pre> <p>Hope that helps :)</p>
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    1. POHow to calculate the modular multiplicative inverse for the Affine Cipher
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    1. USMateusz Grzejek
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    1. POHow to calculate the modular multiplicative inverse for the Affine Cipher
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    1. COthanks for the answer.
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    2. CO@icebox19 The answer is incorrect though. The Cipher required coprimes.
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      1. USflindeberg
    3. COYou are making the same assumption as @Stefan, the numbers are not random. `k1` and `m` (27) are coprime, do not forget that.
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