Non-interactive Provably Secure Attestations for Arbitrary RSA Prime Generation Algorithms

RSA public keys are central to many cryptographic applications; hence their validity is of primary concern to the scrupulous cryptographer. The most relevant properties of an RSA public key (n, e) depend on the factors of n: are they properly generated primes? are they large enough? is e co-prime with φ(n)? etc. And of course, it is out of question to reveal n’s factors. Generic non-interactive zero-knowledge (NIZK) proofs can be used to prove such properties. However, NIZK proofs are not practical at all. For some very specific properties, specialized proofs exist but such ad hoc proofs are naturally hard to generalize. This paper proposes a new type of general-purpose compact non-interactive proofs, called attestations, allowing the key generator to convince any third party that n was properly generated. The proposed construction applies to any prime generation algorithm, and is provably secure in the Random Oracle Model. As a typical implementation instance, for a 138-bit security, verifying or generating an attestation requires k = 1024 prime generations. For this instance, each processed message will later need to be signed or encrypted 14 times by the final users of the attested moduli.