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A general cryptanalysis method is presented based on statistical estimation theory. It is applied to two systems of practical interest: rotor machines and substitution-permutation networks. To cryptanalyze these systems, the finite keyspace is imbedded in a continuous set and the key estimate is a proper quantization of the continuous maximum likelihood estimate. Promising cryptanalysis results of a rotor machine under a ciphertext only attack and a substitution-permutation network under a known plaintext attack are presented.