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IEEE International Conference on Progress in Informatics and Computing

A constant-round perfect parallel coin-tossing protocol

Xiaolan Zhang, Hong-xiang Sun, Hua Zhang, Qiaoyan Wen, Haixia Xu

Published Dec 1, 2010• 0 citations
Publisher

Abstract

A coin-tossing protocol lets two parties decide on a string that should be a random (or at least pseudorandom) string. In this paper, we focus on taking advantage of the perfectly hiding commitment scheme, constant-round perfect zero-knowledge arguments and arguments of knowledge to construct a two-party constant-round perfect protocol for secure coin-tossing, where both of two parties can obtain the common resulting coins and the resulting coins are guaranteed to be statistically close to uniform. The security of our protocol is obtained against malicious non-uniform adversaries that may arbitrarily deviate from the protocol specification. Comparing with the Barak's protocol, we utilize the black-box reduction in the process of security proof and the rounds of our protocol decrease obviously.

DOI
10.1109/pic.2010.5687591

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A coin-tossing protocol lets two parties decide on a string that should be a random (or at least pseudorandom) string. In this paper, we focus on taking advantage of the perfectly hiding commitment scheme, constant-round perfect zero-knowledge arguments and arguments of knowledge to construct a two-party constant-round perfect protocol for secure coin-tossing, where both of two parties can obtain the common resulting coins and the resulting coins are guaranteed to be statistically close to uniform. The security of our protocol is obtained against malicious non-uniform adversaries that may arbitrarily deviate from the protocol specification. Comparing with the Barak's protocol, we utilize the black-box reduction in the process of security proof and the rounds of our protocol decrease obviously.
Abstract. In this paper we show that any two-party functionality can be securely computed in a constant number of rounds, where security is obtained against malicious adversaries that may arbitrarily deviate from the protocol specification. This is in contrast to Yao’s constant-round protocol that ensures security only in the face of semi-honest adversaries, and to its malicious adversary version that requires a polynomial number of rounds. In order to obtain our result, we present a constant-round protocol for secure coin-tossing of polynomially many coins (in parallel). We then show how this protocol can be used in conjunction with other existing constructions in order to obtain a constant-round protocol for securely computing any two-party functionality. On the subject of coin-tossing, we also present a constant-round perfect coin-tossing protocol, where by “perfect ” we mean that the resulting coins are guaranteed to be statistically close to uniform (and not just pseudorandom). 1
We present the first constant-round non-malleable commitment scheme and the first constant-round non-malleable zero-knowledge argument system, as defined by Dolev, Dwork and Naor (1991). Previous constructions either used a non-constant number of rounds, or were only secure under stronger setup assumptions. An example of such an assumption is the shared random string model where we assume all parties have access to a reference string that was chosen uniformly at random by a trusted dealer. We obtain these results by defining an adequate notion of non-malleable coin-tossing, and presenting a constant-round protocol that satisfies it. This protocol allows us to transform protocols that are non-malleable in (a modified notion of) the shared random string model into protocols that are non-malleable in the plain model (without any trusted dealer or setup assumptions). Observing that known constructions of a non-interactive non-malleable zero-knowledge argument systems in the shared random string model (De Santis et. al., 2001) are in fact non-malleable in the modified model, and combining them with our coin-tossing protocol we obtain the results mentioned above. The techniques we use are different from those used in previous constructions of non-malleable protocols. In particular our protocol uses diagonalization and a non-black-box proof of security (in a sense similar to Barak's zero-knowledge argument (2001)).
In coin tossing two remote participants want to share a uniformly distributed random bit. At the least in the quantum version, each participant test whether or not the other has attempted to create a bias on this bit. It is requested that, for b = 0,1, the probability that Alice gets bit b and pass the test is smaller than 1/2 whatever she does, and similarly for Bob. If the bound 1/2 holds perfectly against any of the two participants, the task realised is called an exact coin tossing. If the bound is actually 1/2+ξ1/2 + ξ1/2+ξ where the bias ξξξ vanishes when a security parameter m defined by the protocol increases, the task realised is a (non exact) coin tossing. It is found here that exact coin tossing is impossible. At the same time, an unconditionally secure quantum protocol that realises a (non exact) coin tossing is proposed. The protocol executes m biased quantum coin tossing procedures at the same time. It executes the first round in each of these m procedures sequentially, then the second rounds are executed, and so on until the end of the n procedures. Each procedure requires 4n particles where n∈O(lg⁡m)n \in O(\lg m)n∈O(lgm). The final bit x is the parity of the m random bits. The information about each of these m bits is announced a little bit at a time which implies that the principle used against bit commitment does not apply. The bias on x is smaller than 1/m1/m1/m. The result is discussed in the light of the impossibility result for exact coin tossing.
Non-malleable commitment is one of the most fundamental cryptographic primitives in that it is often used as a basic building block in modern cryptography. Briefly, a commitment scheme allows a sender to commit to a value while keeping the value secret from the receiver. In addition, when the commitment is opened in a later stage, the scheme guarantees that the sender can reveal only the unique value being committed to in the previous stage. A commitment scheme is said to be non-malleable if no adversary can succeed in committing to a related massage m', after seeing a commitment of a message m. In this dissertation, we study the construction of non-malleable commitments and some of their applications.A black-box construction of non-malleable commitment is presented in the first part of this dissertation. Our protocol requires only a constant number of rounds and satisfies the standard notion of non-malleability w.r.t. commitment. Our technique is based on ideas from the ``zero-knowledge from secure multi-party computation'' paradigm by Ishai, Kushilevitz, Ostrovsky, and Sahai (STOC 2007). Furthermore, our construction only uses one-way functions as a black-box and thus does not depend on the actual implementation details of the functions. Prior to our result, under the standard notion of security, no black-box construction of constant-round non-malleable commitment was known. Hence, our main result closes the gap between black-box and non-black-box constructions for the problem of non-malleable commitment.In the second part of this dissertation, we show that our technique can be applied to multiple applications. Specifically, we extend our work to obtain a constant-round concurrent non-malleable commitment, a constant-round multi-party parallel coin tossing, and a non-malleable statistically hiding commitment (according to the notion of non-malleability w.r.t. opening.) Additionally, all results mentioned above are based only on a black-box use of one-way functions.
We propose a coin-flip protocol which yields a string of strong, random coins and is fully simulatable against poly-sized quantum adversaries on both sides. It can be implemented with quantum-computational security without any set-up assumptions, since our construction only assumes mixed commitment schemes which we show how to construct in the given setting. We then show that the interactive generation of random coins at the beginning or during outer protocols allows for quantum-secure realizations of classical schemes, again without any set-up assumptions. As example applications we discuss quantum zero-knowledge proofs of knowledge and quantum-secure two-party function evaluation. Both applications assume only fully simulatable coin-flipping and mixed commitments. Since our framework allows to construct fully simulatable coin-flipping from mixed commitments, this in particular shows that mixed commitments are complete for quantum-secure two-party function evaluation. This seems to be the first completeness result for quantum-secure two-party function evaluation from a generic assumption.