私密币论证的紧致并行重复
Tight Post-Quantum Parallel Repetition for Private-Coin Arguments
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- Weizmann Institute of Science（魏茨曼科学研究所）
- University of California, Berkeley（加州大学伯克利分校）
- Massachusetts Institute of Technology（麻省理工学院）
- Cornell University（康奈尔大学）
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中文总结 AI 辅助
本文证明在同态加密下，交互式论证的并行重复可紧致指数降低可靠性误差，并推广至阈值验证者，进而构造首个仅需量子同态加密的QMA常数轮简洁论证。
中文摘要 AI 辅助
我们证明，在假设同态加密存在的情况下，所有交互式论证（在同态加密下运行后）的并行重复能够以紧致的指数速率降低可靠性误差，即使在量子后设定下也是如此。此外，我们将此结果推广到阈值验证者的情况，其中并行重复的验证者当且仅当至少$t$次执行被接受时才接受（对于某个阈值$t$）。在此工作之前，这些结果仅在作弊证明者被假定为经典的情况下已知，并且不知道如何实现紧致界限。作为推论，我们构造了第一个仅假设量子同态加密存在的、具有可忽略完备性和可靠性误差的$\textsf{QMA}$的常数轮简洁论证。
英文摘要
We show that assuming the existence of homomorphic encryption, parallel repetition of all interactive arguments (after being run under homomorphic encryption) reduces the soundness error at a tight exponential rate even in the post-quantum setting. Moreover, we generalize this result to hold for threshold verifiers, where the parallel repeated verifier accepts if and only if at least $t$ of the executions are accepted (for some threshold $t$). Prior to this work, these results were known only when the cheating prover was assumed to be classical, and it was not known how to achieve tight bounds. As a corollary, we construct the first constant-round succinct argument for $\mathsf{QMA}$ with negligible completeness and soundness errors assuming only the existence of quantum homomorphic encryption.
