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Malleable Commitments from Group Actions and Zero-Knowledge Proofs for Circuits Based on Isogenies

par Chen, Mingjie;Lai, Yi-Fu;Laval, Abel ;Marco, Laurane;Petit, Christophe
Référence Lecture notes in computer science, 14459 LNCS, page (221-243)
Publication Publié, 2024-06-01

Article révisé par les pairs

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Résumé :

Zero-knowledge proofs for NP statements are an essential tool for building various cryptographic primitives and have been extensively studied in recent years. In a seminal result from Goldreich, Micali and Wigderson [17], zero-knowledge proofs for NP statements can be built from any one-way function, but this construction leads very inefficient proofs. To yield practical constructions, one often uses the additional structure provided by homomorphic commitments. In this paper, we introduce a relaxed notion of homomorphic commitments, called malleable commitments, which requires less structure to be instantiated. We provide a malleable commitment construction from the ElGamal-type isogeny-based group action from Eurocrypt’22 [5]. We show how malleable commitments with a group structure in the malleability can be used to build zero-knowledge proofs for NP statements, improving on the naive construction from one-way functions. We compare three different approaches, namely from arithmetic circuits, rank-1 constraint systems and branching programs.