Certain RSA-based protocols, for instance in the domain of group signatures, require a prover to convince a verifier that a set of RSA parameters is well-structured (e.g., that the modulus is the product of two distinct primes and that the exponent is co-prime to the group order). Various corresponding proof systems have been proposed in the past, with different levels of generality, efficiency, and interactivity.

This paper proposes two new proof systems for a wide set of properties that RSA and related moduli might have. The protocols are particularly efficient: The necessary computations are simple, the communication is restricted to only one round, and the exchanged messages are short. While the first protocol is based on prior work (improving on it by reducing the number of message passes from four to two), the second protocol is novel. Both protocols require a random oracle.