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So, 6 is a perfect number because the proper divisors of 6 are 1, 2, and 3, and 1 + 2 + 3 = 6. [2] [4] Euclid proved c. 300 BCE that every prime expressed as M p = 2 p − 1 has a corresponding perfect number M p × (M p +1)/2 = 2 p − 1 × (2 p − 1). For example, the Mersenne prime 2 2 − 1 = 3 leads to the corresponding perfect number 2 2 ...
Their "Deep Crack" machine cost U.S. $250,000 to build and decrypted the DES Challenge II-2 test message after 56 hours of work. The only other confirmed DES cracker was the COPACOBANA machine (Cost-Optimized PArallel COde Breaker) built in 2006. Unlike Deep Crack, COPACOBANA consists of commercially available FPGAs (reconfigurable logic gates).
Lord Playfair, who heavily promoted its use.. Playfair cipher was the first cipher to encrypt pairs of letters in cryptologic history. [2] Wheatstone invented the cipher for secrecy in telegraphy, but it carries the name of his friend Lord Playfair, first Baron Playfair of St. Andrews, who promoted its use.
In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number itself. For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfect number. The next perfect number is 28, since 1 + 2 + 4 + 7 + 14 = 28.
The Beaufort cipher can be described algebraically. For example, using an encoding of the letters A – Z as the numbers 0–25 and using addition modulo 26, let = … be the characters of the message, = … be the characters of the cipher text and = …
In the example, the message 13 26 39 can be cracked by dividing each number by 13 and then ranking them alphabetically. However, the focus of codebook cryptanalysis is the comparative frequency of the individual code elements matching the same frequency of letters within the plaintext messages using frequency analysis .
In classical cryptography, the running key cipher is a type of polyalphabetic substitution cipher in which a text, typically from a book, is used to provide a very long keystream. The earliest description of such a cipher was given in 1892 by French mathematician Arthur Joseph Hermann (better known for founding Éditions Hermann ).
A book cipher is a cipher in which each word or letter in the plaintext of a message is replaced by some code that locates it in another text, the key. A simple version of such a cipher would use a specific book as the key, and would replace each word of the plaintext by a number that gives the position where that word occurs in that book.