On the impossbility of proving security of equivalence class signatures from computational assumptions

Abstract

Equivalence class signatures (EQS) are digital signatures which provide the additional functionality that lets users adapt a given signature to a related message without knowledge of the secret key. They have been used to instantiate numerous cryptographic primitives and increased their efficiency.Unforgeability of the original EQS construction is proven in the generic group model, a theoretical model that treats the underlying group as "ideal". There exist constructions from standard assumptions but those only achieve weak security notions.In this work we strive to answer the question whether EQS schemes which satisfy the original model can be proved secure under standard assumptions with standard techniques. We answer in the negative. There cannot be an efficient security reduction which runs an adversary breaking unforgeability to then break a non-interactive computational assumption. This will be shown by construction of efficient meta-reductions that either break the security of the scheme or said computational problem directly.