Concurrent Statistical Zero-Knowledge Arguments for NP from One Way Functions

Goyal, Vipul; Moriarty, Ryan; Ostrovsky, Rafail; Sahai, Amit

doi:10.1007/978-3-540-76900-2_27

Cited by 8 publications

(6 citation statements)

References 25 publications

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“…The round complexity of our statistical CNMZK argument-poly(n) rounds when only the existence of one-way functions is assumed and ω(log n) rounds when the existence of a family of collision-resistant hash functions is assumed-is the same as the round complexity of the known statistical CZK arguments [GMOS07]. Thus, our result closes the gap between statistical CNMZK arguments and statistical CZK arguments.…”

Section: Our Resultssupporting

confidence: 65%

Statistical Concurrent Non-Malleable Zero-Knowledge from One-Way Functions

Kiyoshima

2020

J Cryptol

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Concurrent non-malleable zero-knowledge (CNMZK) protocols are zero-knowledge protocols that provides security even when adversaries interacts with multiple provers and verifiers simultaneously. It is known that CNMZK arguments for NP can be constructed in the plain model. Furthermore, it was recently shown that statistical CNMZK arguments for NP can also be constructed in the plain model. However, although the former requires only the existence of one-way functions, the latter requires the DDH assumption. In this paper, we construct a statistical CNMZK argument for NP assuming only the existence of one-way functions. The security is proven via black-box simulation, and the round complexity is poly(n). Under the existence of collision-resistant hash functions, the round complexity is reduced to ω(log n), which is essentially optimal for black-box concurrent zero-knowledge protocols.

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Section: Our Resultssupporting

confidence: 65%

Statistical Concurrent Non-Malleable Zero-Knowledge from One-Way Functions

Kiyoshima

2020

J Cryptol

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“…This information can be used by an unbounded distinguisher to establish certain correlations among the values used in different executions, ultimately breaking the statistical ZK property. Because of these restrictions, previously known techniques, which were sufficient for resettable [CGGM00,BGGL01] and statistical ZK [MOSV06,GMOS07,GOS06a] independently, turn out to be insufficient for achieving both of them simultaneously.…”

Section: Technical Difficulties and New Techniquesmentioning

confidence: 99%

Resettable Statistical Zero Knowledge

Garg¹,

Ostrovsky

Visconti

et al. 2012

Lecture Notes in Computer Science

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sub-exponentially hard one-way functions exist, rSZK = SZK. In other words, every language that admits a Statistical Zero-Knowledge (SZK) proof system also admits a Resettable Statistical ZeroKnowledge (rSZK) proof system. (Further, the result can be re-stated unconditionally provided there exists a sub-exponentially hard language in SZK). Moreover, under the assumption that (standard) one-way functions exist, all languages L such that the complement of L is random self reducible, admit a rSZK, in other words: co-RSR ⊆ rSZK. The round complexity of all our proof systems isÕ(log κ), where κ is the security parameter, and all our simulators are black-box.

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“…-Have the verifier commit using a trapdoor commitment scheme and the prover use a statistically binding commitment scheme (implicit in [33,38,41,23] 2 ). -Have both the prover and verifier commit using a computationally hiding commitment scheme, but have the prover prove that it "knows" the values underlying its commitments (e.g., by using a zero-knowledge proof of knowledge) before the verifier opens the commitment to its challenge [17, Sec 4.9.2.2].…”

Section: Overview Of Our Constructionsmentioning

confidence: 99%

Black-Box Constructions of Two-Party Protocols from One-Way Functions

Pass

Wee

2009

Lecture Notes in Computer Science

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We exhibit constructions of the following two-party cryptographic protocols given only black-box access to a one-way function: constant-round zero-knowledge arguments (of knowledge) for any language in NP; constant-round trapdoor commitment schemes; constant-round parallel coin-tossing. Previous constructions either require stronger computational assumptions (e.g. collision-resistant hash functions), non-black-box access to a one-way function, or a super-constant number of rounds. As an immediate corollary, we obtain a constant-round black-box construction of secure two-party computation protocols starting from only semi-honest oblivious transfer. In addition, by combining our techniques with recent constructions of concurrent zero-knowledge and nonmalleable primitives, we obtain black-box constructions of concurrent zeroknowledge arguments for NP and non-malleable commitments starting from only one-way functions.

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Concurrent Statistical Zero-Knowledge Arguments for NP from One Way Functions

Cited by 8 publications

References 25 publications

Statistical Concurrent Non-Malleable Zero-Knowledge from One-Way Functions

Statistical Concurrent Non-Malleable Zero-Knowledge from One-Way Functions

Resettable Statistical Zero Knowledge

Black-Box Constructions of Two-Party Protocols from One-Way Functions

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