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Formal models for security protocols often rely on assumptions not to be found in computational models. A first assumption is the perfect encryption one: encrypted data can not be manipulated in any way unless the decryption key is known. Another usual assumption is the free algebra one: only a few cryptographic primitives are considered in the model, and these must form a free algebra. We study these assumptions, and relax them to define more general models. We then define static analysis techniques for veryfing protocols secure in our models.