Tight Parallel Repetition for Private-Coin Arguments

Abstract: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.

Quantum Physics (quant-ph); Cryptography and Security (cs.CR)

arXiv:2609.38941 [quant-ph]

(or arXiv:2609.38941v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.38941 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.