Fast Mutual Authentication Using RSA Moduli

We describe a fast three-round mutual authentication protocol for parties A and B belonging to the same coalition group. Parties A and B keep their own independent long-term private keys that are used in the process of authentication and can be used for other purposes. The scheme assumes an initial setup with a trusted third party T. This party initiates another secret information that includes factors of a large RSA modulus. For authentication, both parties must demonstrate each other the knowledge of their private keys without revealing them and the ability to factorize a large RSA modulus. Thus, the protocol based on the suggested scheme provides reciprocal authentication. The scheme possesses all desirable properties of an interactive proof, i.e., completeness, soundness, and zero-knowledge. The security of the protocol relies on assumptions of difficulty of the RSA factorization and existence of a cryptographic hash function.