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Caesar cipher, is one of the simplest and most widely known encryption techniques.The transformation can be represented by aligning two alphabets, the cipher alphabet is the plain alphabet rotated left or right by some number of positions.

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We can find the name of these samples and determine the clusters they are closer (neighbor cluster), as follow: All the above elements can be used to evaluate the internal quality of clustering.

In the following sections, we’ll compute the clustering quality statistics for k-means.

This number comes from the fact there are 12 numbers that are coprime with 26 that are less than 26 (these are the possible values of a).

Each value of a can have 26 different addition shifts (the b value) ; therefore, there are 12*26 or 312 possible keys.

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Hence without the restriction on a decryption might not be possible.

It can be shown as follows that decryption function is the inverse of the encryption function, Read more ...

Plaintext: The decryption function is where a - 1 is the modular multiplicative inverse of a modulo m.

I.e., it satisfies the equation The multiplicative inverse of a only exists if a and m are coprime.

In classical cryptography, a permutation cipher is a transposition cipher in which the key is a permutation.

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