Cryptanalysis
Cryptanalysis is the science that studies how to break ciphers, and so it is as ancient as cryptography. Each time a new cipher is developed new strategies are researched to break it and the success of such attempts determines the strenght of the ciphers itself.
Among the first ciphers used by man we have substiution ciphers: it falls in this category every encryption system which encodes a message using a rule to substitute the symbols in the text. An example is the Caesar cipher, developed by Caesar himself during the Gallic war, in which each letter is substiuted by the third following letter in the alphabet. Further refinements of this method include monoalphabetic and polyalphabetic ciphers in which a permutation (or several different) of the whole alphabet is used. Such ciphers were widely used from medieval times up to the beginning of 20th century, especially the "Vigenère chiffre", called the unbreakable cipher.
Substitution ciphers and their variants were largely abandoned in the last century due to their weakness to cryptanalysis and replaced by block ciphers. In fact they are vulnerable to frequency analysis which studies the number of occurrences of symbols and certain patterns to decrpyt the hidden text. This can be carried out in a really fast way nowadays using computers.
In the IT projects section I present a fast algorithm to decrypt monoalphabetic ciphers using a modern computer: by "fast" I mean that it can recover the 99.9% of the original, one-page long text in less than 0.4 seconds on an average computer.
Nowadays ciphers, such as RSA, are either symmetric or asymmetric depending on the applications and expolit the computational complexity of factorizing large numbers. In fact they choose very large prime numbers to genrate key pairs but the attacker cannot recover such keys without the original primes pair and determining whether a large number is prime or not has exponential complexity and no fast algorithm for it is known.
Among the first ciphers used by man we have substiution ciphers: it falls in this category every encryption system which encodes a message using a rule to substitute the symbols in the text. An example is the Caesar cipher, developed by Caesar himself during the Gallic war, in which each letter is substiuted by the third following letter in the alphabet. Further refinements of this method include monoalphabetic and polyalphabetic ciphers in which a permutation (or several different) of the whole alphabet is used. Such ciphers were widely used from medieval times up to the beginning of 20th century, especially the "Vigenère chiffre", called the unbreakable cipher.
Substitution ciphers and their variants were largely abandoned in the last century due to their weakness to cryptanalysis and replaced by block ciphers. In fact they are vulnerable to frequency analysis which studies the number of occurrences of symbols and certain patterns to decrpyt the hidden text. This can be carried out in a really fast way nowadays using computers.
In the IT projects section I present a fast algorithm to decrypt monoalphabetic ciphers using a modern computer: by "fast" I mean that it can recover the 99.9% of the original, one-page long text in less than 0.4 seconds on an average computer.
Nowadays ciphers, such as RSA, are either symmetric or asymmetric depending on the applications and expolit the computational complexity of factorizing large numbers. In fact they choose very large prime numbers to genrate key pairs but the attacker cannot recover such keys without the original primes pair and determining whether a large number is prime or not has exponential complexity and no fast algorithm for it is known.
posted by diev at
6:25 PM
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