We construct a succinct non-interactive publicly-verifiable delegation scheme for any logspace uniform circuit under the sub-exponential Learning With Errors (LWE) assumption. For a circuit C : {0, 1} N \u2192 {0, 1} of size S and depth D, the prover runs in time poly(S), the communication complexity is D \u00b7 polylog(S), and the verifier runs in time (D + N) \u00b7 polylog(S). To obtain this result, we introduce a new cryptographic primitive: lossy correlation-intractable hash functions. We use this primitive to soundly instantiate the Fiat-Shamir transform for a large class of interactive proofs, including the interactive sum-check protocol and the GKR protocol, assuming the sub-exponential hardness of LWE. By relying on the result of Choudhuri et al. (STOC 2019), we also establish the subexponential average-case hardness of PPAD, assuming the sub-exponential hardness of LWE.<\/p>\n","protected":false},"excerpt":{"rendered":"
We construct a succinct non-interactive publicly-verifiable delegation scheme for any logspace uniform circuit under the sub-exponential Learning With Errors (LWE) assumption. For a circuit C : {0, 1} N \u2192 {0, 1} of size S and depth D, the prover runs in time poly(S), the communication complexity is D \u00b7 polylog(S), and the verifier runs […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"IACR.org 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