Provably secure fail-stop signature schemes based on RSA

The security of ordinary digital signature schemes relies on a computational assumption. Fail-stop signature (FSS) schemes provide security for a forger with unlimited computational power by enabling the sender to provide a proof of forgery if it occurs. An attractive construction of FSS scheme based on factorisation is the RSA-based FSS schemes published in IWSEC '99, which allows the signer to provide a non-trivial factor of the modulus in the case of forgery. In this paper, firstly we review some remarks on the RSA-based FSS schemes, including a recently proposed 'attack' which is incorrect. We note that the proposed scheme is not provably secure. Then we incorporate Hensel lifting techniques to create a provably secure variant of the scheme. As a result, our scheme is provably secure and has an explicit proof of forgery by allowing the sender to reveal the non-trivial factor of the modulus in the case of forgery. Among the existing FSS schemes based on the factorisation, our scheme is the only scheme which provides an explicit proof of forgery together with a provable security. We provide a complete security proof of our scheme.