## Cryptology ePrint Archive: Report 2021/1516

Post-Quantum Simulatable Extraction with Minimal Assumptions: Black-Box and Constant-Round

Nai-Hui Chia and Kai-Min Chung and Xiao Liang and Takashi Yamakawa

Abstract: 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 $NP \subseteq BQP$ 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 $NP$ for which the knowledge extractor is also an $\epsilon$-simulator;

- $\epsilon$-zero-knowledge arguments for $QMA$.

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.

Category / Keywords: foundations / Simulation, Extraction, Post-Quantum

Date: received 16 Nov 2021

Contact author: naichia at iu edu, kmchung at iis sinica edu tw, xiao crypto at gmail com, takashi yamakawa ga at hco ntt co jp

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2021/1516

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