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3.5.6 Is DES a group?

It has been frequently asked whether DES encryption is closed under composition; i.e., is encrypting a plaintext under one DES key and then encrypting the result under another key always equivalent to a single encryption under a single key? Algebraically, is DES a group? If so, then DES might be weaker than would otherwise be the case. However, the answer is no, DES is not a group; this issue was settled only recently, after many years of speculation and circumstantial evidence. This result seems to imply that techniques such as triple encryption do in fact increase the security of DES.

Denis Arnaud