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#### Caesar Cipher: Explain How It Was Broken With "Frequency Analysis"

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### Caesar Cipher

Caesar Cipher also known as shift cipher is considered to be one of the most simple and widely known technique, which is used for encryption in cryptography. This comes under the category of substitution cipher, where each letter from the plaintext is changed with a letter by a specific number of positions down the phonemes in the alphabet. The example can be given by a replacement of the letter E, with a left shift of 3 would change it to B. Julius Caesar used to communicate privately using this technique from where the name originated. The process of encryptions done in a Caesar Cipher is included, with complex schemes like the Vigenere Cipher, with inclusion in modern applications like ROT13 system. However, with the advent of modern technology, Caesar Cipher is easily decoded and provides no security in communications.

During encryption with Cipher Text the procedure, which is used is generally aligning two alphabets, the plain text and the cipher text, rotated from position to the left or right by some given number or positions. The easiest way to understand Caesar Cipher, where it has been using a left rotation of three positions, which is equal to a shift towards the right, where the shift parameter is used as the key.

Plain Text: ABCDEFGHIJKLMNOPQRSTUVWXYZ

Cipher Text: XYZABCDEFGHIJKLMNOPQRSTUVW

When the process of encryption takes place, the person decoding the cipher look into each specific letter present within the message of the plain line and subsequently writes the letter in the cipher line. Another example of such a plain line to cipher line, where there is a rotation to the right with a shift of 3, is given by:

Plain Line: THE QUICK BROWN FOX JUMPS OVER THE LAZY DOG

Cipher Line: QEB NRFZH YOLTK CLU GRJMP LSBO QEB IXWV ALD

Expressions can also be presented with the help of modular arithmetic, where the letters are transformed into numbers, and based on this scheme, A is transformed to 0, B to 1 and so on. This shift of an encryption of a given letter y by a shift of n can be given mathematically with,

En (y) = (y + n) mod 26

Decryption on the other hand occurs by,

Dn (y) = (y – n) mod 26

This above process has different types of definitions, the result can be in the range of 0 to 25, which is if ( y + n ) or ( y – n) is not within the range of 0 to 25, then subtraction or addition of 26 is done to it based on the text taken for encryption. This replacement is similar from the beginning till the end of the message, thus this is classified as mono-alphabetic substitution and not polyalphabetic substitution.

The cipher was broken with substitution cipher techniques like frequency analysis, which is the study of frequency of letters or a series or groups of letter in a cipher text. There is a frequency of each letter present in the English language. This information of frequencies of letters in the English language is used to decode mono-alphabetic substitution ciphers like the Caesar cipher. This technique works very efficiently in decoding simple cipher texts, for example if the letter “e” has been encrypted with “y” then wherever the letter y was e, the most frequent presence of the cipher text should be y, which is used to replace x in the cipher text.

The frequencies of letter in the cipher text in descending order are:

e = 12.7, t = 9.1 , a = 8.2, o = 7.5, i = 7.0, n = 6.7, s = 6.3, h = 6.1, r = 6.0, d = 4.3, l = 4.0, c = 2.8, u = 2.8, m = 2.4, w = 2.4, f = 2.2, g = 2.0, y = 2.0, p = 1.9, b = 1.5, v = 1.0, k = 0.8, j = 0.15, x = 0.15, q = 0.10, z = 0.07.

Thus, when a piece of encoded information, which is in cipher text, let us consider that the most common letter, which is used is “p” with “e” then every letter is replaced with the said alphabet. This process of frequency analysis use certain properties of a language due to which, the entire work of decoding a cipher text is not possible to be computed with a machine. Human intervention is inevitable to make the process easier to understand, based on which the required letters or alphabets are decoded and changed using frequency analysis of Caesar Cipher text.

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