From the minimal assumption of post-quantum semi-honest oblivious transfers, we build the first $\epsilon$-simulatable two-party computation (2PC) against quantum polynomial-time (QPT) adversaries that is both constant-round and black-box (for both the construction and security reduction). A recent work by Chia, Chung, Liu, and Yamakawa (FOCS'21) shows that post-quantum 2PC with standard simulation-based security is impossible in constant rounds, unless either $\mathbf{NP} \subseteq \mathbf{BQP}$ or relying on non-black-box simulation. The $\epsilon$-simulatability we target is a relaxation of the standard simulation-based security that allows for an arbitrarily small noticeable simulation error $\epsilon$. Moreover, when quantum communication is allowed, we can further weaken the assumption to post-quantum secure one-way functions (PQ-OWFs), while maintaining the constant-round and black-box property. Our techniques also yield the following set of constant-round and black-box two-party protocols secure against QPT adversaries, only assuming black-box access to PQ-OWFs: - extractable commitments for which the extractor is also an $\epsilon$-simulator; - $\epsilon$-zero-knowledge commit-and-prove whose commit stage is extractable with $\epsilon$-simulation; - $\epsilon$-simulatable coin-flipping; - $\epsilon$-zero-knowledge arguments of knowledge for $\mathbf{NP}$ for which the knowledge extractor is also an $\epsilon$-simulator; - $\epsilon$-zero-knowledge arguments for $\mathbf{QMA}$. At the heart of the above results is a black-box extraction lemma showing how to efficiently extract secrets from QPT adversaries while disturbing their quantum state in a controllable manner, i.e., achieving $\epsilon$-simulatability of the after-extraction state of the adversary.
翻译:从后夸、钟、刘和山川(FOCS'21)的最低假设来看,以标准模拟基基安全为基础的后夸2PC不可能在固定回合中实现,除非(mathbf{NP}) 和(subset) 美元(mathbfredial-modial-modial-modial-modial-mode-modial-modial-modial-modition-modition-modial-modia-modial-modial-modition-modition-modial-modition-moudio-modireal-modia-modia-modition-moditional-modition-modition-moudiocial-mocial-mocial-mocial-mocial-mocial-mocial-mocial-mocial-motional-motional-motion-moto-moto-mocal-mocal-mocal-motional-motion-motion-motion-motion-motion-mocal-moto-moto-mocal-mocal-momotion-motion-motional-motional-motional-motional-motional-mocal-mocal-mocal-mocal-mocal-moto-moto-motomotomotost-motost-moto motost-motost-mocal-mocal-mocal-mocal-motion-motos-mo-moto moto-motion-motosts-motos-moal-sal-moto-moto-moto-moto-moto-moto-moto-moto-moto-moto-moal-mocal-motional-moal-moal-motos-motos-motos-moto-moto-moto-most-most-motos-motost,我们,我们),我们,我们,我们,我们,也只能,我们,也只能,也只能,也以固定的