Post-Quantum Simulatable Extraction with Minimal Assumptions: Black-Box and Constant-Round
Nai-Hui Chia
Kai-Min Chung
Xiao Liang
Takashi Yamakawa
Abstract
From the minimal assumption of post-quantum semi-honest oblivious transfers, we build the first -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 or relying on non-black-box simulation. The -simulatability we target is a relaxation of the standard simulation-based security that allows for an arbitrarily small noticeable simulation error . 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 -simulator;
- -zero-knowledge commit-and-prove whose commit stage is extractable with -simulation;
- -simulatable coin-flipping;
- -zero-knowledge arguments of knowledge for for which the knowledge extractor is also an -simulator;
- -zero-knowledge arguments for .
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 -simulatability of the post-extraction state of the adversary.
@misc{cryptoeprint:2021/1516,
author = {Nai-Hui Chia and Kai-Min Chung and Xiao Liang and Takashi Yamakawa},
title = {Post-Quantum Simulatable Extraction with Minimal Assumptions: Black-Box and Constant-Round},
howpublished = {Cryptology {ePrint} Archive, Paper 2021/1516},
year = {2021},
url = {https://eprint.iacr.org/2021/1516}
}
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