The great mathematician Carl Friedrich Gauss believed that he had devised an

# The great mathematician carl friedrich gauss believed

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The Playfair algorithm is based on the use of a 5 x 5 matrix of letters constructed using a keyword. Here is an example, solved by Lord Peter Wimsey in Dorothy Sayers's Have His Carcase: M O N A R C H Y B D E F G I/J K L P Q S T U V W X Z In this case, the keyword is monarchy. The matrix is constructed by filling in the letters of the keyword (minus duplicates) from left to right and from top to bottom, and then filling in the remainder of the matrix with the remaining letters in alphabetic order. The letters I and J count as one letter. Plaintext is encrypted two letters at a time, according to the following rules: 1. Repeating plaintext letters that are in the same pair are separated with a filler letter, such as x, so that balloon would be treated as ba lx lo on. 2. Two plaintext letters that fall in the same row of the matrix are each replaced by the letter to the right, with the first element of the row circularly following the last. For example, ar is encrypted as RM. 3. Two plaintext letters that fall in the same column are each replaced by the letter beneath, with the top element of the column circularly following the last. For example, mu is encrypted as CM. 4. Otherwise, each plaintext letter in a pair is replaced by the letter that lies in its own row and the column occupied by the other plaintext letter. Thus, hs becomes BP and ea becomes IM (or JM, as the enciphered wishes). The Playfair cipher is a great advance over simple Monoalphabetic ciphers. For one thing, whereas there are only 26 letters, there are 26 x 26 = 676 diagrams, so that identification of individual diagrams is more difficult. Furthermore, the relative frequencies of individual letters exhibit a much greater range than that of diagrams, making frequency analysis much more difficult. For these reasons, the Playfair cipher was for a long time considered unbreakable. Hill Cipher Hill cipher was developed by the mathematician Lester Hill in 1929. The encryption algorithm takes m successive plaintext letters and substitutes for them m ciphertext letters. The substitution is determined by m linear equations in which each character is assigned a numerical value (a = 0, b = 1 ... z = 25). For m = 3, the system can be described as follows:

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• Summer '14
• Cryptography, Public-key cryptography, Pretty Good Privacy, public keys