Introduction to Algebraic Attacks

What do you mean by the term Algebraic Attacks?

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Algebraic attacks are the class of methods which rely for their success on some block cipher showing a high degree of mathematical structure.

For example, it is conceivable that a block cipher may show what is termed a group structure. If this were the case, then encrypting the plaintext beneath one key and then encrypting the result beneath the other key would always be equal to single encryption beneath some other single key. If so, then block cipher would be considerably weaker and the use of multiple encryptions would provide no additional security over the single encryption. For most of the block ciphers, the question of whether they form a group is still open. For DES, though, it is well-known that the cipher is not a group.

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