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On Deniability in the Common Reference String and Random Oracle Model

Rafael Pass

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

Abstract. We revisit the definitions of zero-knowledge in the Common Reference String (CRS) model and the Random Oracle (RO) model. We argue that even though these definitions syntactically mimic the standard zero-knowledge definition, they loose some of its spirit. In particular, we show that there exist a specific natural security property that is not captured by these definitions. This is the property of deniability. We formally define the notion of deniable zero-knowledge in these models and investigate the possibility of achieving it. Our results are different for the two models: – Concerning the CRS model, we rule out the possibility of achieving deniable zero-knowledge protocols in “natural ” settings where such protocols cannot already be achieved in plain model. – In the RO model, on the other hand, we construct an efficient 2-round deniable zero-knowledge argument of knowledge, that preserves both the zero-knowledge property and the proof of knowledge property under concurrent executions (concurrent zero-knowledge and concurrent proof-of knowledge). 1

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Annual Symposium on Foundations of Computer Science•Oct 1, 2006•86 citations
Abstract. We revisit the definitions of zero-knowledge in the Common Reference String (CRS) model and the Random Oracle (RO) model. We argue that even though these definitions syntactically mimic the standard zero-knowledge definition, they loose some of its spirit. In particular, we show that there exist a specific natural security property that is not captured by these definitions. This is the property of deniability. We formally define the notion of deniable zero-knowledge in these models and investigate the possibility of achieving it. Our results are different for the two models: – Concerning the CRS model, we rule out the possibility of achieving deniable zero-knowledge protocols in “natural ” settings where such protocols cannot already be achieved in plain model. – In the RO model, on the other hand, we construct an efficient 2-round deniable zero-knowledge argument of knowledge, that preserves both the zero-knowledge property and the proof of knowledge property under concurrent executions (concurrent zero-knowledge and concurrent proof-of knowledge). 1
Abstract It is well known that several cryptographic primitives cannot be achieved without a common reference string (CRS). Those include, for instance, non-interactive zero-knowledge for NP, or maliciously secure computation in fewer than four rounds. The security of those primitives heavily relies on the assumption that the trusted authority, who generates the CRS, does not misuse the randomness used in the CRS generation. However, we argue that there is no such thing as an unconditionally trusted authority and every authority must be held accountable for any trust to be well-founded. Indeed, a malicious authority can, for instance, recover private inputs of honest parties given transcripts of the protocols executed with respect to the CRS it has generated. While eliminating trust in the trusted authority may not be entirely feasible, can we at least move towards achieving some notion of accountability? We propose a new notion in which, if the CRS authority releases the private inputs of protocol executions to others, we can then provide a publicly-verifiable proof that certifies that the authority misbehaved. We study the feasibility of this notion in the context of non-interactive zero knowledge and two-round secure two-party computation.
Abstract. Concurrent executions of a zero-knowledge protocol by a single prover (with one or more verifiers) may leak information and may not be zero-knowledge in toto. In this article, we study the problem of maintaining zero-knowledge We introduce the notion of an (α, β) timing constraint: for any two processors P1 and P2, if P1 measures α elapsed time on its local clock and P2 measures β elapsed time on its local clock, and P2 starts after P1 does, then P2 will finish after P1 does. We show that if the adversary is constrained by an (α, β) assumption then there exist four-round almost concurrent zero-knowledge interactive proofs and perfect concurrent zero-knowledge arguments for every language in NP. We also address the more specific problem of Deniable Authentication, for which we propose several particularly efficient solutions. Deniable Authentication is of independent interest, even in the sequential case; our concurrent solutions yield sequential solutions without recourse to timing, that is, in the standard model.
We show that there exist commitment, zero-knowledge and general function evaluation pro-tocols with universally composable security, in a model where all parties and all protocols have access to a single, global, random oracle and no other trusted setup. This model provides sig-nificantly stronger composable security guarantees than the traditional random oracle model of Bellare and Rogaway [CCS’93] or even the common reference string model. Indeed, these latter models provide no security guarantees in the presence of arbitrary protocols that use the same random oracle (or reference string or hash function). Furthermore, our protocols are highly efficient. Specifically, in the interactive setting, our commitment and general computation protocols are much more efficient than the best known ones due to Lindell [Crypto’11,’13] which are secure in the common reference string model. In the non-interactive setting, our protocols are slightly less efficient than the best known ones presented by Afshar et al. [Eurocrypt ’14] but do away with the need to rely on a non-global (programmable) reference string. 1
We define and construct universally composable (UC) Zero-Knowledge Set (ZKS) protocols. A ZKS protocol allows a prover to commit to a secret set S and prove statements of the form x ∈ S or x ∉ S without revealing any other information about S. The universal composability framework initiated by Canetti is very useful as it ensures stronger security such as concurrent composition, adaptive security and non-malleability. In this paper, we propose a UC ZKS protocol and prove its security in the random oracle model. Simultaneously, we give the negative result that a UC ZKS cannot exist in the standard model (without a random oracle). The negative result shows that the random oracle has both compression and extraction, which is a pair of paradoxical properties. To our knowledge, this is the first time this kind of property has been considered.
We provide the first construction of a concurrent and non-malleable zero knowledge argument for every language in NP. We stress that our construction is in the plain model with no common random string, trusted parties, or super-polynomial simulation. That is, we construct a zero knowledge protocol Pi such that for every polynomial-time adversary that can adaptively and concurrently schedule polynomially many executions of Pi, and corrupt some of the verifiers and some of the provers in these sessions, there is a polynomial-time simulator that can simulate a transcript of the entire execution, along with the witnesses for all statements proven by a corrupt prover to an honest verifier Our security model is the traditional model for concurrent zero knowledge, where the statements to be proven by the honest provers are fixed in advance and do not depend on the previous history (but can be correlated with each other); corrupted provers, of course, can chose the statements adaptively. We also prove that there exists some functionality F (a combination of zero knowledge and oblivious transfer) such that it is impossible to obtain a concurrent non-malleable protocol for F in this model. Previous impossibility results for composable protocols ruled out existence of protocols for a wider class of functionalities {including zero knowledge!) but only if these protocols were required to remain secure when executed concurrently with arbitrarily chosen different protocols (Lindell, FOCS 2003) or if these protocols were required to remain secure when the honest parties' inputs in each execution are chosen adaptively based on the results of previous executions (Lindell, TCC2004). We obtain an Otilde(n) -round protocol under the assumption that one-to-one one-way functions exist. This can be improved to Otilde(k log n) rounds under the assumption that there exist k-round statistically hiding commitment schemes. Our protocol is a black-box zero knowledge protocol