Approximating Imperfect Cryptography in a Formal Model

We present a formal view of cryptography that overcomes the usual assumptions of formal models for reasoning about security of computer systems, i.e. perfect cryptography and Dolev-Yao adversary model. In our framework, equivalence among formal cryptographic expressions is parameterized by a computational adversary that may exploit weaknesses of the cryptosystem to cryptanalyze ciphertext with a certain probability of success. To validate our approach, we show that in the restricted setting of ideal cryptosystems, for which the probability of guessing information that the Dolev-Yao adversary cannot derive is negligible, the computational adversary is limited to the allowed behaviors of the Dolev-Yao adversary.