Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing 2021
DOI: 10.1145/3406325.3451055
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SNARGs for bounded depth computations and PPAD hardness from sub-exponential LWE

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Cited by 33 publications
(10 citation statements)
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“…For interactive probabilistic proof protocols with a public randomization coin, whose outcome both the verifier and the prover can see, interaction can be replaced by a cryptographic hash function in the Fiat-Shamir [12] heuristic, which yields a proof of primality/compositeness which can be verified at a later time and whose soundness is justified by the hardness of predicting the hash values. Note that for protocols where interaction is replaced by the Fiat-Shamir idea, a provable soundness requires a special design for the hash functions and cryptographic hardness assumptions [5,19,23]. For Google's Rubik's Cube computation mentioned above, such a proof-of-work certificate could have been produced.…”
Section: Primality Of -Bit Integers 2a 2+ (1)mentioning
confidence: 99%
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“…For interactive probabilistic proof protocols with a public randomization coin, whose outcome both the verifier and the prover can see, interaction can be replaced by a cryptographic hash function in the Fiat-Shamir [12] heuristic, which yields a proof of primality/compositeness which can be verified at a later time and whose soundness is justified by the hardness of predicting the hash values. Note that for protocols where interaction is replaced by the Fiat-Shamir idea, a provable soundness requires a special design for the hash functions and cryptographic hardness assumptions [5,19,23]. For Google's Rubik's Cube computation mentioned above, such a proof-of-work certificate could have been produced.…”
Section: Primality Of -Bit Integers 2a 2+ (1)mentioning
confidence: 99%
“…Row 1c puts Fiat-Shamir in practice by placing the previous hash value as an additional argument to the next hash operation, and may incur a loss of soundness [14], which is mitigated by our protocol of fewer rounds. The papers [5,19,23] prove the hardness of predicting the hash values; Row 1d is for the hash functions in [19].…”
Section: Primality Of -Bit Integers 2a 2+ (1)mentioning
confidence: 99%
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“…For 𝑐 > 0 and 𝐿 : ℕ + → ℕ, let ℛ 𝐿,𝑐 be the same as ℛ 𝐿 , except that the adversaries can run in time 𝗉𝗈𝗅𝗒 (︀ 2 𝜆 𝑐 )︀ instead of 𝗉𝗈𝗅𝗒(𝜆). We denote 𝑐-subexponential hardness [JKKZ21,HLR21] to mean that any 𝗉𝗈𝗅𝗒 (︀ 2 𝜆 𝑐 )︀ -time adversary achieving advantage at most 𝗇𝖾𝗀𝗅 (︀ 2 𝜆 𝑐 )︀ .…”
Section: Bounded-entanglement Soundness From Subexponential Hardnessmentioning
confidence: 99%
“…LWE-based cryptosystems lie at the center of efforts by the National Institute of Standards and Technology (NIST) to develop post-quantum cryptographic standards. LWE has also had applications to learning theory, in the form of hardness results for learning intersections of halfspaces [KS09], and in game theory, where the hardness of LWE implies the hardness of the complexity class PPAD [JKKZ21]. Finally, LWE enjoys remarkable structural properties such as leakage-resilience [GKPV10].…”
Section: Introductionmentioning
confidence: 99%