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Hill Cipher
In classical cryptography, the Hill cipher is a polygraphic substitution cipher based on linear algebra. Invented by Lester S. Hill in 1929, it was the first polygraphic cipher in which it was practical (though barely) to operate on more than three symbols at once. The following discussion assumes an elementary knowledge of matrices. Encryption Each letter is represented by a number modulo 26. Though this is not an essential feature of the cipher, this simple scheme is often used: To encrypt a message, each block of ''n'' letters (considered as an ''n''-component vector) is multiplied by an invertible ''n'' × ''n'' matrix, against modulus 26. To decrypt the message, each block is multiplied by the inverse of the matrix used for encryption. The matrix used for encryption is the cipher key, and it should be chosen randomly from the set of invertible ''n'' × ''n'' matrices (modulo 26). The cipher can, of course, be adapted to an alphabet with any number of lette ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Hill's Message Protector
Hill's Pet Nutrition, Inc., trading as Hill's, is an American pet food company that produces dog and cat foods. It is a subsidiary of Colgate-Palmolive. History Hill's Pet Nutrition was founded in the spring of 1907 by Burton Hill and started operation as Hill Rendering Works. Hill Rendering Works provided rendering services to Shawnee County, Kansas, and had a contract with Topeka, Kansas, to dispose of dead and lame animals. Hill Rendering Works produced tallow, hides, tankage, meat scraps and farm animal feed including hogs and chicken feed. By the 1930s, the name had changed to Hill Packing Company, which included a milling division, Hill Milling company. At this time the company produced farm animal feed, dog food and horse meat for human consumption, processing 500 head of horse per week. The meat was shipped to markets in Norway, Sweden, Finland and the Netherlands. Much of the horse meat was sold to the east coast as a product called Chopped and Cured and shipped to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Modular Multiplicative Inverse
In mathematics, particularly in the area of arithmetic, a modular multiplicative inverse of an integer is an integer such that the product is congruent to 1 with respect to the modulus .. In the standard notation of modular arithmetic this congruence is written as :ax \equiv 1 \pmod, which is the shorthand way of writing the statement that divides (evenly) the quantity , or, put another way, the remainder after dividing by the integer is 1. If does have an inverse modulo , then there is an infinite number of solutions of this congruence, which form a congruence class with respect to this modulus. Furthermore, any integer that is congruent to (i.e., in 's congruence class) has any element of 's congruence class as a modular multiplicative inverse. Using the notation of \overline to indicate the congruence class containing , this can be expressed by saying that the ''modulo multiplicative inverse'' of the congruence class \overline is the congruence class \overline such that: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Bifid Cipher
In classical cryptography, the bifid cipher is a cipher which combines the Polybius square with transposition, and uses fractionation to achieve diffusion. It was invented around 1901 by Felix Delastelle. Operation First, a mixed alphabet Polybius square is drawn up, where the I and the J share their position: The message is converted to its coordinates in the usual manner, but they are written vertically beneath: They are then read out in rows: Then divided up into pairs again, and the pairs turned back into letters using the square: In this way, each ciphertext character depends on two plaintext characters, so the bifid is a digraphic cipher, like the Playfair cipher. To decrypt, the procedure is simply reversed. Longer messages are first broken up into blocks of fixed length, called the period, and the above encryption procedure is applied to each block. One way to detect the period uses bigram statistics on ciphertext letters separated by half the period. For ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Playfair Cipher
The Playfair cipher or Playfair square or Wheatstone–Playfair cipher is a manual symmetric encryption technique and was the first literal digram substitution cipher. The scheme was invented in 1854 by Charles Wheatstone, but bears the name of Lord Playfair for promoting its use. The technique encrypts pairs of letters (''bigrams'' or ''digrams''), instead of single letters as in the simple substitution cipher and rather more complex Vigenère cipher systems then in use. The Playfair cipher is thus significantly harder to break since the frequency analysis used for simple substitution ciphers does not work with it. The frequency analysis of bigrams is possible, but considerably more difficult. With 600 possible bigrams rather than the 26 possible monograms (single symbols, usually letters in this context), a considerably larger cipher text is required in order to be useful. History Playfair cipher was the first cipher to encrypt pairs of letters in cryptologic history. Whe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
General Linear Group
In mathematics, the general linear group of degree n is the set of n\times n invertible matrices, together with the operation of ordinary matrix multiplication. This forms a group, because the product of two invertible matrices is again invertible, and the inverse of an invertible matrix is invertible, with the identity matrix as the identity element of the group. The group is so named because the columns (and also the rows) of an invertible matrix are linearly independent, hence the vectors/points they define are in general linear position, and matrices in the general linear group take points in general linear position to points in general linear position. To be more precise, it is necessary to specify what kind of objects may appear in the entries of the matrix. For example, the general linear group over \R (the set of real numbers) is the group of n\times n invertible matrices of real numbers, and is denoted by \operatorname_n(\R) or \operatorname(n,\R). More generally ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
