Cryptography and Cryptanalysis

The purpose of cryptography is to hide the contents of messages by encrypting them so as to make them unrecognizable except by someone who has been given a special decryption key. The purpose of cryptanalysis is then to defeat this by finding ways to decrypt messages without being given the key.

The picture below shows a standard method of encrypting messages represented by sequences of black and white squares. The basic idea is to have an encrypting sequence, shown as column (b) on the left, and from the original message (a) to get an encrypted version of the message (c) by reversing the color of every square for which the corresponding square in the encrypting sequence (b) is black.

So if one receives the encrypted message (c), how can one recover the original message (a)? If one knows the encrypting sequence (b) then it is straightforward. For all one need do is to repeat the process that was used for encryption, and reverse the color of every square in (c) for which the corresponding square in (b) is black.

But how can one arrange that only the intended recipient of the message knows the encrypting sequence (b)? In some situations it may be feasible to transmit the whole encrypting sequence in some secure way. But much more common is to be able to transmit only some short key in a secure way, and then to have to generate the encrypting sequence from this key.

So what kind of procedure might one use to get an encrypting sequence from a key? The picture at the top of the facing page shows an extremely simple approach that was widely used in practical cryptography until less than a century ago. The idea is just to form an encrypting sequence by repeatedly cycling through the elements in the key. And as the picture demonstrates, combining this with the original message leads to an encrypted message in which at least some of the structure in the original message is obscured.

But perhaps not surprisingly it is fairly easy to do cryptanalysis in such a case. For if one can find out what any sufficiently long segment in the encrypting sequence was, then this immediately gives the key,

Example of a scheme for encryption. From the original message (a) an encrypted message (c) is generated by reversing the color of each square for which the corresponding square in the encrypting sequence (b) is black. This scheme is the basis for essentially all practical stream ciphers.

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From Stephen Wolfram: A New Kind of Science [citation]