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Cybersecurity

Simultaneously resettable zero knowledge protocol in Public Key model

Wei Zhu, Yi Deng

Published Nov 17, 2024• 0 citations
Publisher

Abstract

Abstract In this paper, we construct a 6-round simultaneously resettable sound resettable $$(T, \epsilon )$$ ( T , ϵ ) -zero knowledge protocol for $$\mathsf {NP \cap coNP}$$ NP ∩ coNP in the Public Key model under standard assumptions, comparing with the 27-round simultaneously resettable zero knowledge protocol in the BPK model by Deng et al. in 2011, we have achieved a significant reduction in the round complexity. Our model assumes that both prover and verifier hold public keys, we call it the Public Key model. It is a variation of the traditional BPK model where only the verifier is assumed to hold public keys. In the original BPK model, under the sub-exponential hardness assumption of factoring, we construct a 2-round simultaneously resettable sound resettable $$(T,\epsilon )$$ ( T , ϵ ) -zero knowledge protocol for $$\textsf{NP}$$ NP .

DOI
10.1186/s42400-024-00253-5

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Resettable zero-knowledge (extended abstract)

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We introduce the notion of Resettable Zero-Knowledge (rZK), a new security measure for cryptographic protocols which strengthens the classical notion of zero-knowledge.In essence, an rZK protocol is one that remains zero knowledge even if an adversary can interact with the prover many times, each time resetting the prover to its initial state and forcing it to use the same random tape.All known examples of zero-knowledge proofs and arguments are trivially breakable in this setting.Moreover, by definition, all zero-knowledge proofs of knowledge are breakable in this setting.Under general complexity assumptions, which hold for example if the Discrete Logarithm Problem is hard, we construct: • Resettable Zero-Knowledge proof-systems for NP with non-constant number of rounds.* Five-round Resettable Witness-Indistinguishable proofsystems for NP. e Four-round Resettabie Zero-Knowledge arguments for NP in the public key model: where verifiers have fixed, public keys associated with them.In addition to shedding new light on what makes zero knowledge possible (by constructing ZK protocols that use randomness in a dramatically weaker way than before), rZK has great relevance to applications.Firstly, rZK protocols are closed under parallel and concurrent execution and thus are guaranteed to be secure when implemented in fully asynchronous networks, even if an adversary schedules the arrival of every message sent so as to foil security.Secondly, rZK protocols enlarge the range of physical ways in which provers of ZK protocols can be securely implemented, including devices which cannot reliably toss coins on line, nor keep state *A subset of this work is included in patent application [21].

ACM Symposium on Theory of Computing (STOC)•May 1, 2000•204 citations
Abstract In this paper, we construct a 6-round simultaneously resettable sound resettable (T,ϵ)(T, \epsilon )(T,ϵ) ( T , ϵ ) -zero knowledge protocol for NP∩coNP\mathsf {NP \cap coNP}NP∩coNP NP ∩ coNP in the Public Key model under standard assumptions, comparing with the 27-round simultaneously resettable zero knowledge protocol in the BPK model by Deng et al. in 2011, we have achieved a significant reduction in the round complexity. Our model assumes that both prover and verifier hold public keys, we call it the Public Key model. It is a variation of the traditional BPK model where only the verifier is assumed to hold public keys. In the original BPK model, under the sub-exponential hardness assumption of factoring, we construct a 2-round simultaneously resettable sound resettable (T,ϵ)(T,\epsilon )(T,ϵ) ( T , ϵ ) -zero knowledge protocol for NP\textsf{NP}NP NP .
In this paper we resolve an open problem regarding resettable zero knowledge in the bare public-key (BPK for short) model: Does there exist constant round resettable zero knowledge argument with concurrent soundness for NP\mathcal{NP}NP in BPK model without assuming \emph{sub-exponential hardness}? We give a positive answer to this question by presenting such a protocol for any language in NP\mathcal{NP}NP in the bare public-key model assuming only collision-resistant hash functions against \emph{polynomial-time} adversaries.
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
Abstract. In resetting attacks against a proof system, a prover or a verifier is reset and enforced to use the same random tape on various inputs as many times as an adversary may want. Recent deployment of cloud computing gives these attacks a new importance. This paper shows that argument systems for any NP language that are both resettably-sound and resettable zero-knowledge are possible by a constant-round protocol in the BPK model. For that sake, we define and construct a resettablyextractable conditional commitment scheme.
We introduce the notion of Resettable Zero-Knowledge (rZK), a new security measure for cryptographic protocols which strengthens the classical notion of zero-knowledge. In essence, an rZK protocol is one that remains zero knowledge even if an adversary can interact with the prover many times, each time resetting the prover to its initial state and forcing it to use the same random tape. Under general complexity assumptions, which hold for example if the Discrete Logarithm Problem is hard, we construct (non-constant round) Resettable Zero-Knowledge proof-systems for NP constant-round Resettable Witness-Indistinguishable proof-systems for NP constant-round Resettable Zero-Knowledge arguments for NP in the public key model: where veriers have fixed, public keys associated with them. In addition to shedding new light on what makes zero knowledge possible (by constructing ZK protocols that use randomness in a dramatically weaker way than before), rZK has great relevance to applications. Firstly, we show that rZK protocols are closed under parallel and
We introduce the notion of Resettable Zero-Knowledge (rZK), a new security measure for cryptographic protocols which strengthens the classical notion of zero-knowledge.In essence, an rZK protocol is one that remains zero knowledge even if an adversary can interact with the prover many times, each time resetting the prover to its initial state and forcing it to use the same random tape.All known examples of zero-knowledge proofs and arguments are trivially breakable in this setting.Moreover, by definition, all zero-knowledge proofs of knowledge are breakable in this setting.Under general complexity assumptions, which hold for example if the Discrete Logarithm Problem is hard, we construct: • Resettable Zero-Knowledge proof-systems for NP with non-constant number of rounds.* Five-round Resettable Witness-Indistinguishable proofsystems for NP. e Four-round Resettabie Zero-Knowledge arguments for NP in the public key model: where verifiers have fixed, public keys associated with them.In addition to shedding new light on what makes zero knowledge possible (by constructing ZK protocols that use randomness in a dramatically weaker way than before), rZK has great relevance to applications.Firstly, rZK protocols are closed under parallel and concurrent execution and thus are guaranteed to be secure when implemented in fully asynchronous networks, even if an adversary schedules the arrival of every message sent so as to foil security.Secondly, rZK protocols enlarge the range of physical ways in which provers of ZK protocols can be securely implemented, including devices which cannot reliably toss coins on line, nor keep state *A subset of this work is included in patent application [21].