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In a Caesar cipher, each letter of the alphabet is shifted along some number of places. For example, in a Caesar cipher of shift 3, a would become D, b would become E, y would become B and so on. The Vigenère cipher has several Caesar ciphers in sequence with different shift values.
The number of "coincidences" goes up sharply when the bottom message is shifted by a multiple of the key length, because then the adjacent letters are in the same language using the same alphabet. Having found the key length, cryptanalysis proceeds as described above using frequency analysis .
The Alberti cipher by Leon Battista Alberti around 1467 was an early polyalphabetic cipher. Alberti used a mixed alphabet to encrypt a message, but whenever he wanted to, he would switch to a different alphabet, indicating that he had done so by including an uppercase letter or a number in the cryptogram.
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A crossword grid taken from a 1941 newspaper. The distribution of grilles, an example of the difficult problem of key exchange, can be eased by taking a readily-available third-party grid in the form of a newspaper crossword puzzle. Although this is not strictly a grille cipher, it resembles the chessboard with the black squares shifted and it ...