On the (In)security of Fischlin’s Paradigm

Abstract

The Fiat-Shamir paradigm was proposed as a way to remove interaction from 3-round proof of knowledge protocols and derive secure signature schemes. This generic transformation leads to very efficient schemes and has thus grown quite popular. However, this transformation is proven secure only in the random oracle model. In FOCS 2003, Goldwasser and Kalai showed that this transformation is provably insecure in the standard model by presenting a counterexample of a 3-round protocol, the Fiat-Shamir transformation of which is (although provably secure in the random oracle model) insecure in the standard model, thus showing that the random oracle is uninstantiable. In particular, for every hash function that is used to replace the random oracle, the resulting signature scheme is existentially forgeable. This result was shown by relying on the non-black-box techniques of Barak (FOCS 2001). An alternative to the Fiat-Shamir paradigm was proposed by Fischlin in Crypto 2005. Fischlin’s transformation can be applied to any so called 3-round “Fiat-Shamir proof of knowledge’ ’ and can be used to derive non-interactive zero-knowledge proofs of knowledge as well as signature schemes. An attractive property of this transformation is that it provides online extractability (i.e., the extractor works without having to rewind the prover). Fischlin remarks that in comparison to the Fiat-Shamir transformation, his construction tries to