Compute the relative frequencies of each letter in a cipher

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Question

In cryptography, a Caesar cipher, also known as Caesar's cipher, the shift cipher, Caesar's code or Caesar shift, is one of the simplest and most widely known encryption techniques. It is a type of substitution cipher in which each letter in the plaintext is replaced by a letter some fixed number of positions down the alphabet. For example, with a left shift of 3, D would be replaced by A, E would become B, and so on. The method is named after Julius Caesar, who used it in his private correspondence.

The encryption step performed by a Caesar cipher is often incorporated as part of more complex schemes, such as the Vigenère cipher, and still has modern application. As with all single alphabet substitution ciphers, the Caesar cipher is easily broken and in modern practice offers essentially no communication security. Generally speaking, it is a great exercise to understand crypto, and for our purposes, it deals with various concepts for learning a new programming language.

The Caesar Cipher, the Multiplication Cipher and the Linear Cipher have one property in common. They all fall in the category of Monoalphabetic Ciphers: "Same plain letters are encoded to the same cipher letter." I.e. in the Caesar Cipher each "a" turned into "d", each "b" turned into "e", etc.

The following holds true for each of the above Ciphers: Although letters are changed the underlying letter frequencies are not! If the plain letter "a" occurs 10 times its cipher letter will do so 10 times. Therefore, ANY Monoalphabetic Cipher can be broken with the aid of letter frequency analysis.

To compute the relative frequencies of each letter in a cipher text simply count the occurrences of the letter in the text. Afterwards compare the letter frequencies with those of the English language (assuming that the cipher text stems from an English plain text). Remember that

a) The most frequent letter of the English language is "e" (with about 12%) followed by t,i,o,a,n,s,r which is very helpful to break the cipher text.

b) The longer the cipher text the better do the counted letter frequencies converge to the actual English plain letter frequencies.

Reference no: EM13756631

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