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Chinese Journal of Electronics

Some Constant-Round Zero-KnowledgeProtocols

Liu Hanwu, Dongdai Lin

Published Jan 5, 2010• 0 citations
OpenAlex

Abstract

The concept of zero-knowledge has been extensively used in the design of cryptographic protocols since being introduced. The round complexity of zero- knowledge protocols is a very important e±ciency con- sideration, and in general it is desirable to have zero- knowledge protocols with constant numbers of rounds. In this paper, we suggest a novel method to use the program of the veri¯er and use the method to construct some con- stant round honest-veri¯er zero-knowledge protocols. The notion of honest-veri¯er zero-knowledge protocols is highly non-trivial and fascinating itself. It also has many other uses.

Related papers

Constant Round Non-Malleable Protocols using One Way Functions.

Vipul Goyal

We provide the first constant round constructions of non-malleable commitment and zero-knowledge protocols based only on one-way functions. This improves upon several previous (incomparable) works which required either: (a) super-constant number of rounds, or, (b) non-standard or sub-exponential hardness assumptions, or, (c) non-black-box simulation and collision resistant hash functions. These constructions also allow us to obtain the first constant round multi-party computation protocol relying only on the existence of constant round oblivious transfer protocols. Our primary technique can be seen as a means of implementing the previous “two-slot simulation ” idea in the area of non-malleability with only black-box simulation. A simple modification of our commitment scheme gives a construction which makes use of the underlying one-way function in a black-box way. The modified construction satisfies the notion of what we call nonmalleability w.r.t. replacement. Non-malleability w.r.t. replacement is a slightly weaker yet natural notion of non-malleability which we believe suffices for many application of non-malleable commitments. We show that a commitment scheme which is non-malleable only w.r.t. replacement is sufficient to obtain a (fully) black-box multi-party computation protocol. This allows us to obtain a constant round multi-party computation protocol making only a black-box use of the standard cryptographic primitives with polynomial-time hardness thus directly improving upon the recent work of Wee (FOCS’10). 0 1

•Jan 1, 2010•0 citations

Achieving Constant Round Leakage-Resilient Zero-Knowledge.

Omkant Pandey

Recently there has been a huge emphasis on constructing cryptographic protocols that maintain their security guarantees even in the presence of side channel attacks. Such attacks exploit the physical characteristics of a cryptographic device to learn useful information about the internal state of the device. Designing protocols that deliver meaningful security even in the presence of such leakage attacks is a challenging task. The recent work of Garg, Jain, and Sahai formulates a meaningful notion of zero-knowledge in presence of leakage; and provides a construction which satisfies a weaker variant of this notion called (1 + ɛ)-leakage-resilient-zero-knowledge, for every constant ɛ> 0. In this weaker variant, roughly speaking, if the verifier learns ℓ bits of leakage during the interaction, then the simulator is allowed to access (1 + ɛ) · ℓ bits of leakage. The round complexity of their protocol is ⌈ n ɛ ⌉. In this work, we present the first construction of leakage-resilient zero-knowledge satisfying the ideal requirement of ɛ = 0. While our focus is on a feasibility result for ɛ = 0, our construction also enjoys a constant number of rounds. At the heart of our construction is a new “public-coin preamble ” which allows the simulator to recover arbitrary information from a (cheating) verifier in a “straight line. ” We use non-black-box simulation techniques to accomplish this goal. 1

•Jan 1, 2012•1 citation

Resettable Cryptography in Constant Rounds - the Case of Zero Knowledge.

Yi Deng, Dengguo Feng, Vipul Goyal +3 more

A fundamental question in cryptography deals with understanding the role that randomness plays in cryptographic protocols and to what extent it is necessary. One particular line of works was initiated by Canetti, Goldreich, Goldwasser, and Micali (STOC 2000) who introduced the notion of resettable zero-knowledge, where the protocol must be zeroknowledge even if a cheating verifier can reset the prover and have several interactions in which the prover uses the same random tape. Soon afterwards, Barak, Goldreich, Goldwasser, and Lindell (FOCS 2001) studied the setting where the verifier uses a fixed random tape in multiple interactions. Subsequent to these works, a number of papers studied the notion of resettable protocols in the setting where only one of the participating parties uses a fixed random tape multiple times. The notion of resettable security has been studied in two main models: the plain model and the bare public key model (also introduced in the above paper by Canetti et. al.). In a recent work, Deng, Goyal and Sahai (FOCS 2009) gave the first construction of a simultaneous resettable zero-knowledge protocol where both participants of the protocol can reuse a fixed random tape in any (polynomial) number of executions. Their construction however required O(nɛ) rounds of interaction between the prover and the verifier. Both in the plain as well as the BPK model, this construction remain the only known simultaneous resettable zero-knowledge protocols. In this work, we study the question of round complexity of simultaneous resettable zeroknowledge in the BPK model. We present a constant round protocol in such a setting based on standard cryptographic assumptions. Our techniques are significantly different from the ones used by Deng, Goyal and Sahai. 1

•Jan 1, 2011•0 citations

New and improved constructions of non-malleable cryptographic protocols

Rafael Pass, Alon Rosen

We present a new constant round protocol for non-malleable zero-knowledge. Using this protocol as a subroutine, we obtain a new constant-round protocol for non-malleable commitments. Our constructions rely on the existence of (standard) collision resistant hash functions. Previous constructions either relied on the existence of trapdoor permutations and hash functions that are collision resistant against sub-exponential sized circuits, or required a super-constant number of rounds.Additional results are the first construction of a non-malleable commitment scheme that is statistically hiding (with respect to opening), and the first non-malleable protocols that satisfy a strict polynomial-time simulation requirement. The latter are constructed by additionally assuming the existence of trapdoor permutations.Our approach differs from the approaches taken in previous works in that we view non-malleable zero-knowledge as a building-block rather than an end goal. This gives rise to a modular construction of non-malleable commitments and results in a somewhat simpler analysis.The techniques that we use to construct our zero-knowl-edge protocol are non black-box, but are different than the non black-box techniques previously used in the context of non-malleable coin-tossing.

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Rafael Pass, Alon Rosen

We present a new constant-round protocol for nonmalleable zero-knowledge. Using this protocol as a subroutine, we obtain a new constant-round protocol for nonmalleable commitments. Our constructions rely on the existence of (standard) collision-resistant hash functions. Previous constructions either relied on the existence of trapdoor permutations and hash functions that are collision resistant against subexponential-sized circuits or required a superconstant number of rounds. Additional results are the first construction of a nonmalleable commitment scheme that is statistically hiding (with respect to opening) and the first nonmalleable commitments that satisfy a strict polynomial-time simulation requirement. Our approach differs from the approaches taken in previous works in that we view nonmalleable zero-knowledge as a building block rather than an end goal. This gives rise to a modular construction of nonmalleable commitments and results in a somewhat simpler analysis.

SIAM Journal on Computing•Jan 1, 2008•47 citations

Constant round non-malleable protocols using one way functions

Vipul Goyal

We provide the first constant round constructions of non-malleable commitment and zero-knowledge protocols based only on one-way functions. This improves upon several previous (incomparable) works which required either: (a) super-constant number of rounds, or, (b) non-standard or sub-exponential hardness assumptions, or, (c) non-black-box simulation and collision resistant hash functions. These constructions also allow us to obtain the first constant round multi-party computation protocol relying only on the existence of constant round oblivious transfer protocols. Our primary technique can be seen as a means of implementing the previous "two-slot simulation" idea in the area of non-malleability with only black-box simulation.

ACM Symposium on Theory of Computing (STOC)•Jun 6, 2011•119 citations
The concept of zero-knowledge has been extensively used in the design of cryptographic protocols since being introduced. The round complexity of zero- knowledge protocols is a very important e±ciency con- sideration, and in general it is desirable to have zero- knowledge protocols with constant numbers of rounds. In this paper, we suggest a novel method to use the program of the veri¯er and use the method to construct some con- stant round honest-veri¯er zero-knowledge protocols. The notion of honest-veri¯er zero-knowledge protocols is highly non-trivial and fascinating itself. It also has many other uses.
We provide the first constant round constructions of non-malleable commitment and zero-knowledge protocols based only on one-way functions. This improves upon several previous (incomparable) works which required either: (a) super-constant number of rounds, or, (b) non-standard or sub-exponential hardness assumptions, or, (c) non-black-box simulation and collision resistant hash functions. These constructions also allow us to obtain the first constant round multi-party computation protocol relying only on the existence of constant round oblivious transfer protocols. Our primary technique can be seen as a means of implementing the previous “two-slot simulation ” idea in the area of non-malleability with only black-box simulation. A simple modification of our commitment scheme gives a construction which makes use of the underlying one-way function in a black-box way. The modified construction satisfies the notion of what we call nonmalleability w.r.t. replacement. Non-malleability w.r.t. replacement is a slightly weaker yet natural notion of non-malleability which we believe suffices for many application of non-malleable commitments. We show that a commitment scheme which is non-malleable only w.r.t. replacement is sufficient to obtain a (fully) black-box multi-party computation protocol. This allows us to obtain a constant round multi-party computation protocol making only a black-box use of the standard cryptographic primitives with polynomial-time hardness thus directly improving upon the recent work of Wee (FOCS’10). 0 1
Recently there has been a huge emphasis on constructing cryptographic protocols that maintain their security guarantees even in the presence of side channel attacks. Such attacks exploit the physical characteristics of a cryptographic device to learn useful information about the internal state of the device. Designing protocols that deliver meaningful security even in the presence of such leakage attacks is a challenging task. The recent work of Garg, Jain, and Sahai formulates a meaningful notion of zero-knowledge in presence of leakage; and provides a construction which satisfies a weaker variant of this notion called (1 + ɛ)-leakage-resilient-zero-knowledge, for every constant ɛ> 0. In this weaker variant, roughly speaking, if the verifier learns ℓ bits of leakage during the interaction, then the simulator is allowed to access (1 + ɛ) · ℓ bits of leakage. The round complexity of their protocol is ⌈ n ɛ ⌉. In this work, we present the first construction of leakage-resilient zero-knowledge satisfying the ideal requirement of ɛ = 0. While our focus is on a feasibility result for ɛ = 0, our construction also enjoys a constant number of rounds. At the heart of our construction is a new “public-coin preamble ” which allows the simulator to recover arbitrary information from a (cheating) verifier in a “straight line. ” We use non-black-box simulation techniques to accomplish this goal. 1
A fundamental question in cryptography deals with understanding the role that randomness plays in cryptographic protocols and to what extent it is necessary. One particular line of works was initiated by Canetti, Goldreich, Goldwasser, and Micali (STOC 2000) who introduced the notion of resettable zero-knowledge, where the protocol must be zeroknowledge even if a cheating verifier can reset the prover and have several interactions in which the prover uses the same random tape. Soon afterwards, Barak, Goldreich, Goldwasser, and Lindell (FOCS 2001) studied the setting where the verifier uses a fixed random tape in multiple interactions. Subsequent to these works, a number of papers studied the notion of resettable protocols in the setting where only one of the participating parties uses a fixed random tape multiple times. The notion of resettable security has been studied in two main models: the plain model and the bare public key model (also introduced in the above paper by Canetti et. al.). In a recent work, Deng, Goyal and Sahai (FOCS 2009) gave the first construction of a simultaneous resettable zero-knowledge protocol where both participants of the protocol can reuse a fixed random tape in any (polynomial) number of executions. Their construction however required O(nɛ) rounds of interaction between the prover and the verifier. Both in the plain as well as the BPK model, this construction remain the only known simultaneous resettable zero-knowledge protocols. In this work, we study the question of round complexity of simultaneous resettable zeroknowledge in the BPK model. We present a constant round protocol in such a setting based on standard cryptographic assumptions. Our techniques are significantly different from the ones used by Deng, Goyal and Sahai. 1
We present a new constant round protocol for non-malleable zero-knowledge. Using this protocol as a subroutine, we obtain a new constant-round protocol for non-malleable commitments. Our constructions rely on the existence of (standard) collision resistant hash functions. Previous constructions either relied on the existence of trapdoor permutations and hash functions that are collision resistant against sub-exponential sized circuits, or required a super-constant number of rounds.Additional results are the first construction of a non-malleable commitment scheme that is statistically hiding (with respect to opening), and the first non-malleable protocols that satisfy a strict polynomial-time simulation requirement. The latter are constructed by additionally assuming the existence of trapdoor permutations.Our approach differs from the approaches taken in previous works in that we view non-malleable zero-knowledge as a building-block rather than an end goal. This gives rise to a modular construction of non-malleable commitments and results in a somewhat simpler analysis.The techniques that we use to construct our zero-knowl-edge protocol are non black-box, but are different than the non black-box techniques previously used in the context of non-malleable coin-tossing.
We present a new constant-round protocol for nonmalleable zero-knowledge. Using this protocol as a subroutine, we obtain a new constant-round protocol for nonmalleable commitments. Our constructions rely on the existence of (standard) collision-resistant hash functions. Previous constructions either relied on the existence of trapdoor permutations and hash functions that are collision resistant against subexponential-sized circuits or required a superconstant number of rounds. Additional results are the first construction of a nonmalleable commitment scheme that is statistically hiding (with respect to opening) and the first nonmalleable commitments that satisfy a strict polynomial-time simulation requirement. Our approach differs from the approaches taken in previous works in that we view nonmalleable zero-knowledge as a building block rather than an end goal. This gives rise to a modular construction of nonmalleable commitments and results in a somewhat simpler analysis.
We provide the first constant round constructions of non-malleable commitment and zero-knowledge protocols based only on one-way functions. This improves upon several previous (incomparable) works which required either: (a) super-constant number of rounds, or, (b) non-standard or sub-exponential hardness assumptions, or, (c) non-black-box simulation and collision resistant hash functions. These constructions also allow us to obtain the first constant round multi-party computation protocol relying only on the existence of constant round oblivious transfer protocols. Our primary technique can be seen as a means of implementing the previous "two-slot simulation" idea in the area of non-malleability with only black-box simulation.