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Bit Commitment Using PseudoRandomness
 Journal of Cryptology
, 1991
"... We show how a pseudorandom generator can provide a bit commitment protocol. We also analyze the number of bits communicated when parties commit to many bits simultaneously, and show that the assumption of the existence of pseudorandom generators suffices to assure amortized O(1) bits of communicat ..."
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Cited by 282 (16 self)
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We show how a pseudorandom generator can provide a bit commitment protocol. We also analyze the number of bits communicated when parties commit to many bits simultaneously, and show that the assumption of the existence of pseudorandom generators suffices to assure amortized O(1) bits of communication per bit commitment.
Perfect ZeroKnowledge Arguments for NP Can Be Based on General Complexity Assumptions (Extended Abstract)
 JOURNAL OF CRYPTOLOGY
, 1998
"... "Zeroknowledge arguments" is a fundamental cryptographic primitive which allows one polynomialtime player to convince another polynomialtime player of the validity of an NP statement, without revealing any additional information in the informationtheoretic sense. Despite their practi ..."
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Cited by 42 (11 self)
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"Zeroknowledge arguments" is a fundamental cryptographic primitive which allows one polynomialtime player to convince another polynomialtime player of the validity of an NP statement, without revealing any additional information in the informationtheoretic sense. Despite their practical and theoretical importance, it was only known how to implement zeroknowledge arguments based on specific algebraic assumptions; basing them on a general complexity assumption was open since their introduction in 1986 [BCC, BC, CH]. In this paper, we finally show a general construction, which can be based on any oneway permutation. We stress that our scheme is efficient: both players can execute only polynomialtime programs during the protocol. Moreover, the security achieved is online: in order to cheat and validate a false theorem, the prover must break a cryptographic assumption online during the conversation, while the verifier can not find (ever!) any information unconditionally (in the i...
Minimallatency secure function evaluation
 In Proc. EUROCRYPT 2000
, 2000
"... Abstract. Sander, Young and Yung recently exhibited a protocol for computing on encrypted inputs, for functions computable in NC 1. In their variant of secure function evaluation, Bob (the “CryptoComputer”) accepts homomorphicallyencrypted inputs (x) from client Alice, and then returns a string fro ..."
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Cited by 22 (0 self)
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Abstract. Sander, Young and Yung recently exhibited a protocol for computing on encrypted inputs, for functions computable in NC 1. In their variant of secure function evaluation, Bob (the “CryptoComputer”) accepts homomorphicallyencrypted inputs (x) from client Alice, and then returns a string from which Alice can extract f(x, y) (where y is Bob’s input, or e.g. the function f itself). Alice must not learn more about y than what f(x, y) reveals by itself. We extend their result to encompass NLOGSPACE (nondeterministic logspace functions). In the domain of multiparty computations, constantround protocols have been known for years [BB89,FKN95]. This paper introduces novel parallelization techniques that, coupled with the [SYY99] methods, reduce the constant to 1 with preprocessing. This resolves the conjecture that NLOGSPACE subcomputations (including logslices of circuit computation) can be evaluated with latency 1 (as opposed to just O(1)). 1
Simulatable Commitments and Efficient Concurrent ZeroKnowledge
 In EUROCRYPT’03, volume 2656 of LNCS
, 2003
"... Abstract. We define and construct simulatable commitments. These are commitment schemes such that there is an efficient interactive proof system to show that a given string c is a legitimate commitment on a given value v, and furthermore, this proof is efficiently simulatable given any proper pair ( ..."
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Abstract. We define and construct simulatable commitments. These are commitment schemes such that there is an efficient interactive proof system to show that a given string c is a legitimate commitment on a given value v, and furthermore, this proof is efficiently simulatable given any proper pair (c, v). Our construction is provably secure based on the Decisional DiffieHellman (DDH) assumption. Using simulatable commitments, we show how to efficiently transform any public coin honest verifier zero knowledge proof system into a proof system that is concurrent zeroknowledge with respect to any (possibly cheating) verifier via black box simulation. By efficient we mean that our transformation incurs only an additive overhead (both in terms of the number of rounds and the computational and communication complexity of each round), and the additive term is close to optimal (for black box simulation): only ω(log n) additional rounds, and ω(log n) additional public key operations for each round of the original protocol, where n is a security parameter, and ω(log n) can be any superlogarithmic function of n independent of the complexity of the original protocol. The transformation preserves (up to negligible additive terms) the soundness and completeness error probabilities, and the new proof system is proved secure based on the DDH assumption, in the standard model of computation, i.e., no random oracles, shared random strings, or public key infrastructure is assumed. 1
Efficient and Concurrent ZeroKnowledge from any public coin HVZK protocol
, 2002
"... We show how to efficiently transform any public coin honest verifier zero knowledge proof system into a proof system that is concurrent zeroknowledge with respect to any (possibly cheating) verifier via black box simulation. By efficient we mean that our transformation incurs only an additive overh ..."
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We show how to efficiently transform any public coin honest verifier zero knowledge proof system into a proof system that is concurrent zeroknowledge with respect to any (possibly cheating) verifier via black box simulation. By efficient we mean that our transformation incurs only an additive overhead, both in terms of the number of rounds and the computational and communication complexity of each round, independently of the complexity of the original protocol. Moreover, the transformation preserves (up to negligible additive terms) the soundness and completeness error probabilities. The new proof system is proved secure based on the Decisional DieHellman (DDH) assumption, in the standard model of computation, i.e., no random oracles, shared random strings, or public key infrastructure is assumed. In addition to the introduction of a practical protocol, this construction provides yet another example of ideas in plausibility results that turn into ideas in the construction of practical protocols.