Perfect Zero-knowledge Proof Research Articles

On the Power of Statistical Zero Knowledge

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 18 December 2017Accepted: 29 October 2018Published online: 22 October 2019Keywordsoracle separation, statistical zero knowledge proof, perfect zero knowledge proof, hardness amplificationAMS Subject Headings68Q05, 68Q15Publication DataISSN (print): 0097-5397ISSN (online): 1095-7111Publisher: Society for Industrial and Applied MathematicsCODEN: smjcat

A new certificateless multiple key agreement scheme

Recently, by changing security requirements of computer networks, many public key schemes are introduced. One major shortcoming of identity-based cryptosystems is key screw. Certificateless public key cryptosystems were introduced to solve this problem. In this paper, a certificateless, public-key, multiple-key-agreement scheme will be offered which has some significant security properties such as perfect forward secrecy, strong security, and zero-knowledge proof. This scheme produces far more shared hidden keys per session in comparison with many existing schemes. In this paper, the security and the efficiency of the proposed scheme will be compared with some well-known current schemes.

How to Achieve Perfect Simulation and a Complete Problem for Non-interactive Perfect Zero-Knowledge

This paper studies perfect zero-knowledge proofs. Such proofs do not allow any simulation errors, and therefore techniques from the study of statistical zero-knowledge (where a small error is allowed) do not apply to them. We introduce a new error shifting technique for building perfect simulators. Using this technique we give the first complete problem for the class of problems admitting non-interactive perfect zero-knowledge (NIPZK) proofs, a hard problem for the class of problems admitting public-coin PZK proofs, and other applications.

Fully anonymous multi-service subscription system without random oracles

Lately,Canard et al.(CANARD S,JAMBERT A.Untraceability and profiling are not mutually exclusive [C]// TrustBus 2010:Proceedings of the 7th International Conference on Trust,Privacy and Security in Digital Business,LNCS 6264.Berlin:Springer-Verlag,2010:117-128) introduced the notion of multi-service subscription and proposed several instantiations.Unfortunately,their systems only satisfied a weaker variant of anonymity called revocable-anonymity and they were not fit for "pay-per-use" services.To this end,a revised multi-service subscription system was put forward to extending Canard et al's system.The new system achieved pay-per-use subscriptions by incorporating the anonymous payment system raised by Liu et al.(LIU J K,AU M H,SUSILO W,et al.Enhancing location privacy for electric vehicles(at the right time).[2012-08-01].http://eprint.iacr.org/2012/342).To allow users to prove in zero-knowledge that their account balance is enough for making a payment for the required access,it also utilized the Peng-Bao range proof for small ranges.Furthermore,it was constructed on several 4-round perfect zero-knowledge proofs of knowledge,which were obtained by applying a technique by Cramer et al.to the underlying Sigma-protocols.Compared with typical systems in the literature,the new solution gains advantages in terms of security.Concretely,it can be proved secure in the standard model.Moreover,it matches the strongest level of three crucial security notions,such as inseparability for spendable tokens,anonymity for users,and zero-knowledge for underlying proof systems.

On Monotone Formula Composition of Perfect Zero-Knowledge Languages

We investigate structural properties of interactive perfect zero-knowledge (PZK) proofs. Specifically, we look into the closure properties of PZK languages under monotone boolean formula composition. This gives rise to new protocol techniques. We show that interactive PZK for random self-reducible (RSR) (and for co-RSR) languages is closed under monotone boolean formula composition. Namely, we present PZK proofs for monotone boolean formulae whose atoms are statements about membership in a PZK language which is RSR (or whose complement is RSR). We also discuss extensions, recent applications, and generalizations of the techniques.

SZK Proofs for Black-Box Group Problems

In this paper we classify several algorithmic problems in group theory in the complexity classes PZK and SZK (problems with perfect/statistical zero-knowledge proofs respectively). Prior to this, these problems were known to be in $\mbox {\rm AM}\cap \mbox {\rm coAM}$. As $\mbox {\rm PZK}\subseteq \mbox {\rm SZK}\subseteq \mbox {\rm AM}\cap \mbox {\rm coAM}$, we have a tighter upper bound for these problems. Specifically: We show that the permutation group problems Coset Intersection, Double Coset Membership, Group Conjugacy are in PZK. Further, the complements of these problems also have perfect zero knowledge proofs (in the liberal sense). We also show that permutation group isomorphism for solvable groups is in PZK. As an ingredient of this protocol, we design a randomized algorithm for sampling short presentations of solvable permutation groups. We show that the complement of all the above problems have concurrent zero knowledge proofs. We prove that the above problems for black-box groups are in SZK. Finally, we also show that some of the problems have SZK protocols with efficient provers in the sense of Micciancio and Vadhan (Lecture Notes in Comput. Sci. 2729, 282–298, 2003).

Locally random reductions: Improvements and applications

A (t, n)-locally random reduction maps a problem instancex into a set of problem instancesy 1,...,y n in such a way that it is easy to construct the answer tox from the answers toy 1,...,y n, and yet the distribution ont-element subsets ofy 1,...,y n depends only on |x|. In this paper we formalize such reductions and give improved methods for achieving them. Then we give a cryptographic application, showing a new way to prove in perfect zero knowledge that committed bitsx 1,...,x m satisfy some predicateQ. Unlike previous techniques for such perfect zero-knowledge proofs, ours uses an amount of communication that is bounded by a fixed polynomial inm, regardless of the computational complexity ofQ.

The knowledge complexity of quadratic residuosity languages

Noninteractive perfect zero-knowledge (ZK) proofs are very elusive objects. In fact, since the introduction of the noninteractive model of Blum . (1988), the only perfect zero-knowledge proof known...

The knowledge complexity of quadratic residuosity languages

Noninteractive perfect zero-knowledge (ZK) proofs are very elusive objects. In fact, since the introduction of the noninteractive model of Blum . (1988), the only perfect zero-knowledge proof known was the one for quadratic nonresiduosity of Blum . (1991). The situation is no better in the interactive case where perfect zero-knowledge proofs are known only for a handful of particular languages.In this work, we show that a large class of languages related to quadratic residuosity admits noninteractive perfect zero-knowledge proofs. More precisely, we give a protocol for the language of thresholds of quadratic residuosity.Moreover, we develop a new technique for converting noninteractive zero-knowledge proofs into round-optimal zero-knowledge proofs for an even wider class of languages. The transformation preserves perfect zero knowledge in the sense that, if the noninteractive proof we started with is a perfect zero-knowledge proof, then we obtain a round-optimal perfect zero-knowledge proof. The noninteractive perfect zero-knowledge proofs presented in this work can be transformed into 4-round (which is optimal) interactive perfect zero-knowledge proofs. Until now, the only known 4-round perfect ZK proof systems were the ones for quadratic nonresiduosity (Goldwasser et al., 1989) and for graph nonisomorphism (Goldreich et al., 1986) and no 4-round perfect zero-knowledge proof system was known for the simple case of the language of quadratic residues.

Round-optimal perfect zero-knowledge proofs

We give a round-optimal perfect zero-knowledge proofs of membership to the language of q-residuosity.

A perfect zero-knowledge proof system for a problem equivalent to the discrete logarithm

An interactive proof system is called perfect zero-knowledge if the probability distribution generated by any probabilistic polynomial-time verifier interacting with the prover on input theorem , c...

Elliptic curve implementation of zero-knowledge blobs

In [2] the authors show how to construct the building blocks for perfect zero-knowledge proofs called “blobs” using the discrete log problem. Contrary to what they remark on p. 73 of [2], we argue that the Mordell group of an elliptic curve is more suitable than the multiplicative group of a finite field for the construction of a hard cryptographic suite of problems.