How to Forge DES-Encrypted Messages in $2^{28}$ Steps

In this paper we suggest key-collision attacks, and show that the theoretic strength of a cipher cannot exceed the square root of the size of the key space. As a result, in some circumstances, some DES keys can be recovered while they are still in use, and these keys can then be used to forge messages: in particular, one key of DES can be recovered with complexity 2 28 , and one key of (three-key) triple-DES can be recovered with complexity 2 84 .

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