Machine-Checked Security Proofs of Cryptographic Signature Schemes

Formal methods have been extensively applied to the certification of cryptographic protocols. However, most of these works make the perfect cryptography assumption, i.e. the hypothesis that there is no way to obtain knowledge about the plaintext pertaining to a ciphertext without knowing the key. A model that does not require the perfect cryptography assumption is the generic model and the random oracle model. These models provide non-standard computational models in which one may reason about the computational cost of breaking a cryptographic scheme. Using the machine-checked account of the Generic Model and the Random Oracle Model formalized in Coq, we prove the safety of cryptosystems that depend on a cyclic group (like ElGamal cryptosystem), against interactive generic attacks and we prove the security of blind signatures against interactive attacks. To prove the last step, we use a generic parallel attack to create a forgery signature.