Blockchain Papers

Oded Goldreich, Amit Sahai, Salil Vadhan

No abstract is available for this record.

Giovanni Di Crescenzo, Rafail Ostrovsky

No abstract is available for this record.

Ran Canetti, Oded Goldreich, S. Goldwasser, Silvio Micali

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

Khanh Quoc Nguyen, Yi Mu, Vijay Varadharajan

No abstract is available for this record.

Khanh Quoc Nguyen, Feng Bao, Yi Mu, Vijay Varadharajan

No abstract is available for this record.

Ransom Richardson, Joe Kilian

No abstract is available for this record.

Uriel Feige, Dror Lapidot, Adi Shamir

In this paper we show how to construct noninteractive zero knowledge proofs for any NP statement under general (rather than number theoretic) assumptions, and how to enable polynomially many provers to give polynomially many such proofs based on a single random string. Our constructions can be used in cryptographic applications in which the prover is restricted to polynomial time.

Jan Camenisch, Markus Michels

<p>This paper presents the first efficient statistical zero-knowledge protocols to prove statements such as:<br />A committed number is a pseudo-prime.<br />A committed (or revealed) number is the product of two safe primes, i.e., primes p and q such that (p - 1)=2 and (q - 1)=2 are primes as well.<br />A given value is of large order modulo a composite number that consists of two safe prime factors.</p><p>So far, no methods other than inefficient circuit-based proofs are known for proving such properties. Proving the second property is for instance necessary in many recent cryptographic schemes that rely on both the hardness of computing discrete logarithms and of difficulty computing roots modulo a composite.<br />The main building blocks of our protocols are statistical zero-knowledge proofs that are of independent interest. Mainly, we show how to prove the correct computation of a modular addition, a modular multiplication, or a modular exponentiation, where all values including the modulus are committed but not<br />publicly known. Apart from the validity of the computation, no other information about the modulus (e.g., a generator which order equals the modulus) or any other operand is given. Our technique can be generalized to prove in zeroknowledge<br />that any multivariate polynomial equation modulo a certain modulus is satisfied, where only commitments to the variables of the polynomial and a commitment to the modulus must be known. This improves previous results,<br />where the modulus is publicly known.<br />We show how a prover can use these building blocks to convince a verifier that a committed number is prime. This finally leads to efficient protocols for proving that a committed (or revealed) number is the product of two safe primes. As a consequence, it can be shown that a given value is of large order modulo a<br />given number that is a product of two safe primes.</p><p> </p><p>Keywords. RSA-based protocols, zero-knowledge proofs of knowledge, primality tests.</p>

Giovanni Di Crescenzo, Kouichi Sakurai, Moti Yung

No abstract is available for this record.

Gerrit Bleumer

. In this paper, we establish the notion of divertibility as a protocol property as opposed to the existing notion as a language property (see Okamoto, Ohta [OO90]). We give a definition of protocol divertibility that applies to arbitrary 2-party protocols and is compatible with Okamoto and Ohta's definition in the case of interactive zero-knowledge proofs. Other important examples falling under the new definition are blind signature protocols. A su#cient criterion for divertibility is presented and found to be satisfied by many examples of protocols in the literature. The generality of the definition is further demonstrated by examples from protocol classes that have not been considered for divertibility before. We show diverted El-Gamal encryption and diverted Di#e-Hellman key exchange. Keywords: interactive protocol, divertibility, zero-knowledge proof, Fiat-Shamir identification, blind signature, Di#e-Hellman key-exchange, El-Gamal encryption. 1

Donald Beaver

No abstract is available for this record.

Uwe Schöning, Randall Pruim

No abstract is available for this record.

Liqun Chen

No abstract is available for this record.

Julien P. Stern

No abstract is available for this record.

Guillaume Poupard, Jacques Stern

No abstract is available for this record.

Alfredo De Santis, Giovanni Di Crescenzo, Giuseppe Persiano, Moti Yung

No abstract is available for this record.

Cynthia Dwork, Amit Sahai

. An interactive proof system (or argument) (P; V ) is concurrent zero-knowledge if whenever the prover engages in polynomially many concurrent executions of (P; V ), with (possibly distinct) colluding polynomial time bounded veriers V1 ; : : : ; V poly(n) , the entire undertaking is zero-knowledge. Dwork, Naor, and Sahai recently showed the existence of a large class of concurrent zero-knowledge arguments, including arguments for all of NP, under a reasonable assumption on the behavior of clocks of nonfaulty processors. In this paper, we continue the study of concurrent zero-knowledge arguments. After observing that, without recourse to timing, the existence of a trusted center considerably simpli- es the design and proof of many concurrent zero-knowledge arguments (again including arguments for all of NP), we design a preprocessing protocol, making use of timing, to simulate the trusted center for the purposes of achieving concurrent zero-knowledge. Once a particular p...

Matt Blaze, Gerrit Bleumer, Martin J. Strauss

No abstract is available for this record.

Oded Goldreich, Amit Sahai, Salil Vadhan

We show how to transform any interactive proof system which is statistical zero-knowledge with respect to the honest-verifier, into a proof systemwhich is statistical zero-knowledgewith respect to any verifier. This is done by limiting the behavior of potentially cheating verifiers, without using computational assumptions or even referring to the complexity of such verifier strategies. (Previous transformations have either relied on computational assumptions or were applicable only to constant-round public-coin proof systems.) Our transformation also applies to public-coin (aka Arthur-Merlin) computational zero-knowledge proofs: We transform any ArthurMerlin proof system which is computational zero-knowledge with respect to the honest-verifier, into an Arthur-Merlin proof system which is computational zero-knowledge with respect to any probabilistic polynomial-time verifier. A crucial ingredient in our analysis is a new lemma regarding 2-universal hashing functions. 1 Introduction Zer...

Giovanni Di Crescenzo, Kouichi Sakurai, Moti Yung

No abstract is available for this record.

Cynthia Dwork, Moni Naor, Amit Sahai

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 P 1 and P 2 , if P 1 measures α elapsed time on its local clock and P 2 measures β elapsed time on its local clock, and P 2 starts after P 1 does, then P 2 will finish after P 1 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.

Joe Kilian, Erez Petrank

No abstract is available for this record.

Rosario Gennaro, Daniele Micciancio, Tal Rabin

We present efficient zero-knowledge proof systems for quasi-safe prime products and other related languages. Quasi-safe primes are a relaxation of safe primes, a class of prime numbers useful in many cryptographic applications. Our proof systems achieve higher security and better efficiency than all previously known ones. In particular, all our proof systems are perfect or statistical zero-knowledge, meaning that even a computationally unbounded adversary cannot extract any information from the proofs. Moreover, our proof systems are extremely efficient because they do not use general reductions to NP-complete problems, can be easily parallelized preserving zero-knowledge, and are non-interactive for computationally unbounded provers. The prover can also be efficiently implemented given some trapdoor information and using very little interaction. We demonstrate the applicability of quasi-safe primes by showing how they can be effectively used in the context of RSA based undeniable signatures to enforce the use of "good" public keys, i.e., keys such that if a signer can convince a recipient of the validity of a signature, then he won't be able to subsequently deny the same signature in case of a dispute.

Donald Beaver, Joan Feigenbaum, Joe Kilian, Phillip Rogaway

No abstract is available for this record.