TY - CHAP
T1 - Why “Fiat-Shamir for Proofs” Lacks a Proof
T2 - Theory of Cryptography
Y1 - 2013
A1 - Bitansky, Nir
A1 - Dana Dachman-Soled
A1 - Garg, Sanjam
A1 - Jain, Abhishek
A1 - Kalai, Yael Tauman
A1 - López-Alt, Adriana
A1 - Wichs, Daniel
ED - Sahai, Amit
KW - Algorithm Analysis and Problem Complexity
KW - Computation by Abstract Devices
KW - Data Encryption
KW - Systems and Data Security
AB - The Fiat-Shamir heuristic [CRYPTO ’86] is used to convert any 3-message public-coin proof or argument system into a non-interactive argument, by hashing the prover’s first message to select the verifier’s challenge. It is known that this heuristic is sound when the hash function is modeled as a random oracle. On the other hand, the surprising result of Goldwasser and Kalai [FOCS ’03] shows that there exists a computationally sound argument on which the Fiat-Shamir heuristic is never sound, when instantiated with any actual efficient hash function. This leaves us with the following interesting possibility: perhaps we can securely instantiates the Fiat-Shamir heuristic for all 3-message public-coin statistically sound proofs, even if we must fail for some computationally sound arguments. Indeed, this has been conjectured to be the case by Barak, Lindell and Vadhan [FOCS ’03], but we do not have any provably secure instantiation under any “standard assumption”. In this work, we give a broad black-box separation result showing that the security of the Fiat-Shamir heuristic for statistically sound proofs cannot be proved under virtually any standard assumption via a black-box reduction. More precisely: –If we want to have a “universal” instantiation of the Fiat-Shamir heuristic that works for all 3-message public-coin proofs, then we cannot prove its security via a black-box reduction from any assumption that has the format of a “cryptographic game”. –For many concrete proof systems, if we want to have a “specific” instantiation of the Fiat-Shamir heuristic for that proof system, then we cannot prove its security via a black box reduction from any “falsifiable assumption” that has the format of a cryptographic game with an efficient challenger.
JA - Theory of Cryptography
T3 - Lecture Notes in Computer Science
PB - Springer Berlin Heidelberg
SN - 978-3-642-36593-5, 978-3-642-36594-2
UR - http://link.springer.com/chapter/10.1007/978-3-642-36594-2_11
ER -