Forgery-Resilience for Digital Signature Schemes

We introduce the notion of forgery-resilience for digital signature schemes, a new paradigm for digital signature schemes exhibiting desirable legislative properties. It evolves around the idea that, for any message, there can only be a unique valid signature, and exponentially many acceptable signatures, all but one of them being spurious. This primitive enables a judge to verify whether an alleged forged signature is indeed a forgery. In particular, the scheme considers an adversary who has access to a signing oracle and an oracle that solves a “hard” problem, and who tries to produce a signature that appears to be acceptable from a verifier’s point of view. However, a judge can tell apart such a spurious signature from a signature that is produced by an honest signer. This property is referred to as validatibility. Moreover, the scheme provides undeniability against malicious signers who try to fabricate spurious signatures and deny them later by showing that they are not valid. Last but not least, trustability refers to the inability of a malicious judge trying to forge a valid signature. This notion for signature schemes improves upon the notion of fail-stop signatures in different ways. For example, it is possible to sign more than one messages with forgery-resilient signatures and once a forgery is found, the credibility of a previously signed signature is not under question. A concrete instance of a forgery-resilient signature scheme is constructed based on the hardness of extracting roots of higher residues, which we show to be equivalent to the factoring assumption. In particular, using collision-free accumulators, we present a tight reduction from malicious signers to adversaries against the factoring problem. Meanwhile, a secure pseudorandom function ensures that no polynomially-bounded cheating verifier, who can still solve hard problems, is able to forge valid signatures. Security against malicious judges is based on the RSA assumption.