This paper introduces a natural paradigm for fair exchange protocols, called ID-based partial proxy signature scheme. A security model with precise and formal definitions is presented, and an efficient and provably secure partial proxy signature scheme is proposed. This is a full ID-based optimistic fair exchange protocol. Unlike the vast majority of previously proposed protocols, this approach does not use any zero knowledge proofs, and thus avoids most of the costly computations.
We present two universally composable and practical protocols by which a dealer can, verifiably and non-interactively, secret-share an integer among a set of players. Moreover, at small extra cost and using a distributed verifier proof, it can be shown in zero-knowledge that three shared integers a, b, c satisfy ab = c. This implies by known reductions non-interactive zero-knowledge proofs that a shared integer is in a given interval, or that one secret integer is larger than another. Such primitives are useful, e.g., for supplying inputs to a multiparty computation protocol, such as an auction or an election. The protocols use various set-up assumptions, but do not require the random oracle model.
Abstract. We show an efficient secure two-party protocol, based on Yao’s construction, which provides security against malicious adversaries. Yao’s original protocol is only secure in the presence of semi-honest adversaries. Security against malicious adversaries can be obtained by applying the compiler of Goldreich, Micali and Wigderson (the “GMW compiler”). However, this approach does not seem to be very practical as it requires using generic zero-knowledge proofs. Our construction is based on applying cut-and-choose techniques to the original circuit and inputs. Security is proved according to the ideal/real simulation paradigm, and the proof is in the standard model (with no random oracle model or common reference string assumptions). The resulting protocol is computationally efficient: the only usage of asymmetric cryptography is for running O(1) oblivious transfers for each input bit (or for each bit of a statistical security parameter, whichever is larger). Our protocol combines techniques from folklore (like cut-and-choose) along with new techniques for efficiently proving consistency of inputs. We remark that a naive implementation of the cut-and-choose technique with Yao’s protocol does not yield a secure protocol. This is the first paper to show how to properly implement these techniques, and to provide a full proof of security. Our protocol can also be interpreted as a constant-round black-box reduction of secure two-party com-putation to oblivious transfer and perfectly-hiding commitments, or a black-box reduction of secure two-party computation to oblivious transfer alone, with a number of rounds which is linear in a sta-tistical security parameter. These two reductions are comparable to Kilian’s reduction, which uses OT alone but incurs a number of rounds which is linear in the depth of the circuit [18]. 1
In this paper, a new forward secure threshold signature scheme is presented, which is the first one from bilinear pairings. Compared with the known schemes against malicious adversary, the new scheme needs the fewest interactions and is very efficient. As an additional contribution, we present a new interactive zero-knowledge proof protocol and convert it into a non-interactive protocol to verify the validity of part signatures in this scheme. The scheme is robust against malicious adversary and forward secure in the random oracle model
A multi-signature scheme enables a group of signers to produce a compact, joint signature on a common document, and has many potential uses. However, existing schemes impose key setup or PKI requirements that make them impractical, such as requiring a dedicated, distributed key generation protocol amongst potential signers, or assuming strong, concurrent zero-knowledge proofs of knowledge of secret keys done to the CA at key registration. These requirements limit the use of the schemes. We provide a new scheme that is proven secure in the plain public-key model, meaning requires nothing more than that each signer has a (certified) public key. Furthermore, the important simplification in key management achieved is not at the cost of efficiency or assurance: our scheme matches or surpasses known ones in terms of signing time, verification time and signature size, and is proven secure in the random-oracle model under a standard (not bilinear map related) assumption. The proof is based on a simplified and general Forking Lemma that may be of independent interest.
Let Lambda : {0, 1}ntimes {0,1}mrarr {0,1} be a Boolean formula of size d, or more generally, an arithmetic circuit of degree d, known to both Alice and Bob, and let y isin {0,1}mbe an input known only to Alice. Assume that Alice and Bob interacted in the past in a preamble phase (that is, applied a preamble protocol that depends only on the parameters, and not on Lambday). We show that Alice can (non-interactively) commit to y, by a message of size poly(m, log d), and later on prove to Bob any N statements of the form Lambda (x1, y) = z1,..., Lambda(xN,y) = zNby a (computationally sound) non-interactive zero-knowledge proof of size poly(d, log N). (Note the logarithmic dependence on N). We give many applications and motivations for this result. In particular, assuming that Alice and Bob applied in the past the (poly-logarithmic size) preamble protocol: 1. given a CNF formula Psi(w1,..., wm) of size N, Alice can prove the satisfiability of Psi by a (computationally sound) non-interactive zero-knowledge proof of size poly(m). That is, the size of the proof depends only on the size of the witness and not on the size of the formula. 2. Given a language L in the class LOGSNP and an input x isin {0, 1}n, Alice can prove the membership x isin L by a (computationally sound) non-interactive zero-knowledge proof of size polylog n. 3. Alice can commit to a Boolean formula y of size m, by a message of size poly(m), and later on prove to Bob any N statements of the form y(x1) = z1,..., y(xN) = zNby a (computationally sound) non-interactive zero-knowledge proof of size poly(m, log N). Our cryptographic assumptions include the existence of a poly-logarithmic symmetric-private-information-retrieval (SPIR) scheme, as defined in (C. Cachin et. al, 1999), and the existence of commitment schemes, secure against circuits of size exponential in the security parameter
An identity-based signcryption scheme with (t,n) shared unsigncryption is proposed, which is the integration of the signcryption scheme, the (t,n) threshold scheme and zero knowledge proof for the equality of two discrete logarithms based on the bilinear map. In this scheme, any third party can verify the validity of the signature, but only more than t members in the recipient group can cooperatively recover the message m. As compared to the Zhang et al.'s signcryption scheme with (t,n) shared unsigncryption based on discrete logarithms, the proposed scheme has the following advantages: it provides both public verifiability and forward security; the key management problem is simplified because of using identity-based cryptosystem.
Two long-standing open problems exist on the fringe of complexity theory and cryptography: (1) Does there exist a reduction from an NP-complete problem to a one-way function? (2) Do parallelized versions of classical constant-round zero-knowledge proofs for NP conceal every "hard" bit of the witness to the statement proved? We show that, unless the polynomial-hierarchy collapses, black-box reductions cannot be used to provide positive answers to both questions
We prove that every problem in NP that has a zero-knowledge proof also has a zero-knowledge proof where the prover can be implemented in probabilistic polynomial time given an NP witness. Moreover, if the original proof system is statistical zero knowledge, so is the resulting efficient-prover proof system. An equivalence of zero knowledge and efficient-prover zero knowledge was previously known only under the assumption that one-way functions exist (whereas our result is unconditional), and no such equivalence was known for statistical zero knowledge. Our results allow us to translate the many general results and characterizations known for zero knowledge with inefficient provers to zero knowledge with efficient provers.
We propose cryptographic primitives for reading and assigning the (shared) secret found at a secret index in a vector of secrets. The problem can also be solved in constant round with existing general techniques based on arithmetic circuits and the “equality test” in [4]. However the proposed technique requires to exchange less bits. The proposed primitives require a number of rounds that is independent of the size N of the vector, and only depends (linearly) on the number t of computing servers. A previously known primitive for reading a vector at a secret index works only for 2party computations. Our primitives work for any number of computing participants/servers. The proposed techniques are secure against passive attackers, and zero knowledge proofs are provided to show that exactly one index of the array is read/written. The techniques work both with multiparty computations based on secret sharing and with multiparty computations based on threshold homomorphic encryption.
Abstract The notion of non-interactive zero-knowledge (NIZK) is of fundamental importance incryptography. Despite the vast attention the concept of NIZK has attracted since its introduction, one question has remained very resistant: Is it possible to construct NIZK schemesfor any NP-language with statistical or even perfect ZK? Groth, Ostrovsky and Sahai recently positively answers to the question by presenting a couple of elegant constructions. However,their schemes pose a limitation on the length of the proof statement to achieve adaptive soundness against dishonest provers who may choose the target statement depending on thecommon reference string (CRS). In this work, we first present a very simple and efficient adaptively-sound perfect NIZKargument system for any NP-language. Besides being the first adaptively-sound statistical NIZK argument for all NP that does not pose any restriction on the statements to be proven,it enjoys a number of additional desirable properties: it allows to re-use the CRS, it can handle arithmetic circuits, and the CRS can be set-up very efficiently without the need foran honest party. We then show an application of our techniques in constructing efficient NIZK schemes for proving arithmetic relations among committed secrets, whereas previousmethods required expensive generic NP-reductions. The security of the proposed schemes is based on a strong non-standard assumption,an extended version of the so-called Knowledge-of-Exponent Assumption (KEA) over bilinear groups. We give some justification for using such an assumption by showing that thecommonly-used approach for proving NIZK arguments sound does not allow for adaptivelysound statistical NIZK arguments (unless NP ae P/poly). Furthermore, we show that theassumption used in our construction holds with respect to generic adversaries that do not exploit the specific representation of the group elements. We also discuss how to avoid thenon-standard assumption in a pre-processing model.
This paper proves that several interactive proof systems are zero-knowledge against general quantum attacks. This includes the well-known Goldreich–Micali–Wigderson classical zero-knowledge protocols for graph isomorphism and graph 3-coloring (assuming the existence of quantum computationally concealing commitment schemes in the second case). Also included is a quantum interactive proof system for a complete problem for the complexity class of problems having honest verifier quantum statistical zero-knowledge proofs, which therefore establishes that honest verifier and general quantum statistical zero-knowledge are equal: $\mathrm{QSZK}= \mathrm{QSZK}_{\mathrm{HV}}$. Previously no nontrivial interactive proof systems were known to be zero-knowledge against quantum attacks, except in restricted settings such as the honest verifier and common reference string models. This paper therefore establishes for the first time that true zero-knowledge is indeed possible in the presence of quantum information and computation.
Blum integers (BL), which has extensively been used in the domain of cryptography, are integers with form p , where p and q are di#erent primes both 3 mod 4 and k 1 and k 2 are odd integers. These integers can be divided two types: 1) M = pq, 2) M = p at least one of k 1 and k 2 is greater than 1.
The aim of this work is to investigate the possibility of designing zero-knowledge identification schemes based on hard-on-average problems. It includes a new two-party identification protocol whose security relies on a discrete mathematics problem classified as DistNP-Complete under the average-case analysis, the so-called Distributional Matrix Representability Problem. Thanks to the use of the search version of the mentioned problem, the zero-knowledge property is formally proved by black-box simulation, and consequently the security of the proposed scheme is actually guaranteed. Furthermore, with the proposal of a new zero-knowledge proof based on a problem never used before for this purpose, the set of tools for designing cryptographic applications is enlarged.
An efficient computational Zero-Knowledge Proof of Knowledge whose security relies on the NP-completeness of the Independent Set Problem is presented here. The proposed algorithm is constructed from a bit commitment scheme based on the hardness of the Discrete Logarithm Problem, which guarantees the fulfillment of soundness, completeness and computational zero-knowledge properties, and allows avoiding the use of the Graph Isomorphism Problem, which is present in every known Zero-Knowledge Proofs for the Independent Set Problem.
Cryptography and Data Security
Complexity and Algorithms in Graphs
Physical Unclonable Functions (PUFs) and Hardware Security