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1,239
Random Oracles are Practical: A Paradigm for Designing Efficient Protocols
, 1995
"... We argue that the random oracle model  where all parties have access to a public random oracle  provides a bridge between cryptographic theory and cryptographic practice. In the paradigm we suggest, a practical protocol P is produced by first devising and proving correct a protocol P R for the ..."
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Cited by 1646 (70 self)
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We argue that the random oracle model  where all parties have access to a public random oracle  provides a bridge between cryptographic theory and cryptographic practice. In the paradigm we suggest, a practical protocol P is produced by first devising and proving correct a protocol P R for the random oracle model, and then replacing oracle accesses by the computation of an "appropriately chosen" function h. This paradigm yields protocols much more efficient than standard ones while retaining many of the advantages of provable security. We illustrate these gains for problems including encryption, signatures, and zeroknowledge proofs.
A Digital Signature Scheme Secure Against Adaptive ChosenMessage Attacks
, 1995
"... We present a digital signature scheme based on the computational diculty of integer factorization. The scheme possesses the novel property of being robust against an adaptive chosenmessage attack: an adversary who receives signatures for messages of his choice (where each message may be chosen in a ..."
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Cited by 959 (40 self)
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We present a digital signature scheme based on the computational diculty of integer factorization. The scheme possesses the novel property of being robust against an adaptive chosenmessage attack: an adversary who receives signatures for messages of his choice (where each message may be chosen in a way that depends on the signatures of previously chosen messages) can not later forge the signature of even a single additional message. This may be somewhat surprising, since the properties of having forgery being equivalent to factoring and being invulnerable to an adaptive chosenmessage attack were considered in the folklore to be contradictory. More generally, we show how to construct a signature scheme with such properties based on the existence of a "clawfree" pair of permutations  a potentially weaker assumption than the intractibility of integer factorization. The new scheme is potentially practical: signing and verifying signatures are reasonably fast, and signatures are compact.
PseudoRandom Generation from OneWay Functions
 PROC. 20TH STOC
, 1988
"... Pseudorandom generators are fundamental to many theoretical and applied aspects of computing. We show howto construct a pseudorandom generator from any oneway function. Since it is easy to construct a oneway function from a pseudorandom generator, this result shows that there is a pseudorandom gene ..."
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Cited by 861 (18 self)
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Pseudorandom generators are fundamental to many theoretical and applied aspects of computing. We show howto construct a pseudorandom generator from any oneway function. Since it is easy to construct a oneway function from a pseudorandom generator, this result shows that there is a pseudorandom generator iff there is a oneway function.
Universally composable security: A new paradigm for cryptographic protocols
, 2013
"... We present a general framework for representing cryptographic protocols and analyzing their security. The framework allows specifying the security requirements of practically any cryptographic task in a unified and systematic way. Furthermore, in this framework the security of protocols is preserved ..."
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Cited by 833 (37 self)
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We present a general framework for representing cryptographic protocols and analyzing their security. The framework allows specifying the security requirements of practically any cryptographic task in a unified and systematic way. Furthermore, in this framework the security of protocols is preserved under a general protocol composition operation, called universal composition. The proposed framework with its securitypreserving composition operation allows for modular design and analysis of complex cryptographic protocols from relatively simple building blocks. Moreover, within this framework, protocols are guaranteed to maintain their security in any context, even in the presence of an unbounded number of arbitrary protocol instances that run concurrently in an adversarially controlled manner. This is a useful guarantee, that allows arguing about the security of cryptographic protocols in complex and unpredictable environments such as modern communication networks.
Proof verification and hardness of approximation problems
 IN PROC. 33RD ANN. IEEE SYMP. ON FOUND. OF COMP. SCI
, 1992
"... We show that every language in NP has a probablistic verifier that checks membership proofs for it using logarithmic number of random bits and by examining a constant number of bits in the proof. If a string is in the language, then there exists a proof such that the verifier accepts with probabilit ..."
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Cited by 797 (39 self)
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We show that every language in NP has a probablistic verifier that checks membership proofs for it using logarithmic number of random bits and by examining a constant number of bits in the proof. If a string is in the language, then there exists a proof such that the verifier accepts with probability 1 (i.e., for every choice of its random string). For strings not in the language, the verifier rejects every provided “proof " with probability at least 1/2. Our result builds upon and improves a recent result of Arora and Safra [6] whose verifiers examine a nonconstant number of bits in the proof (though this number is a very slowly growing function of the input length). As a consequence we prove that no MAX SNPhard problem has a polynomial time approximation scheme, unless NP=P. The class MAX SNP was defined by Papadimitriou and Yannakakis [82] and hard problems for this class include vertex cover, maximum satisfiability, maximum cut, metric TSP, Steiner trees and shortest superstring. We also improve upon the clique hardness results of Feige, Goldwasser, Lovász, Safra and Szegedy [42], and Arora and Safra [6] and shows that there exists a positive ɛ such that approximating the maximum clique size in an Nvertex graph to within a factor of N ɛ is NPhard.
A Threshold of ln n for Approximating Set Cover
 JOURNAL OF THE ACM
, 1998
"... Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NPhar ..."
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Cited by 776 (5 self)
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Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NPhard. We prove that (1 \Gamma o(1)) ln n is a threshold below which set cover cannot be approximated efficiently, unless NP has slightly superpolynomial time algorithms. This closes the gap (up to low order terms) between the ratio of approximation achievable by the greedy algorithm (which is (1 \Gamma o(1)) ln n), and previous results of Lund and Yannakakis, that showed hardness of approximation within a ratio of (log 2 n)=2 ' 0:72 lnn. For max kcover we show an approximation threshold of (1 \Gamma 1=e) (up to low order terms), under the assumption that P != NP .
NonMalleable Cryptography
 SIAM Journal on Computing
, 2000
"... The notion of nonmalleable cryptography, an extension of semantically secure cryptography, is defined. Informally, in the context of encryption the additional requirement is that given the ciphertext it is impossible to generate a different ciphertext so that the respective plaintexts are related. ..."
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Cited by 480 (20 self)
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The notion of nonmalleable cryptography, an extension of semantically secure cryptography, is defined. Informally, in the context of encryption the additional requirement is that given the ciphertext it is impossible to generate a different ciphertext so that the respective plaintexts are related. The same concept makes sense in the contexts of string commitment and zeroknowledge proofs of possession of knowledge. Nonmalleable schemes for each of these three problems are presented. The schemes do not assume a trusted center; a user need not know anything about the number or identity of other system users. Our cryptosystem is the first proven to be secure against a strong type of chosen ciphertext attack proposed by Rackoff and Simon, in which the attacker knows the ciphertext she wishes to break and can query the decryption oracle on any ciphertext other than the target.
Security and Composition of Multiparty Cryptographic Protocols
 JOURNAL OF CRYPTOLOGY
, 1998
"... We present general definitions of security for multiparty cryptographic protocols, with focus on the task of evaluating a probabilistic function of the parties' inputs. We show that, with respect to these definitions, security is preserved under a natural composition operation. The definiti ..."
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Cited by 463 (19 self)
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We present general definitions of security for multiparty cryptographic protocols, with focus on the task of evaluating a probabilistic function of the parties' inputs. We show that, with respect to these definitions, security is preserved under a natural composition operation. The definitions follow the general paradigm of known definitions; yet some substantial modifications and simplifications are introduced. The composition operation is the natural `subroutine substitution' operation, formalized by Micali and Rogaway. We consider several standard settings for multiparty protocols, including the cases of eavesdropping, Byzantine, nonadaptive and adaptive adversaries, as well as the informationtheoretic and the computational models. In particular, in the computational model we provide the first definition of security of protocols that is shown to be preserved under composition.
Reconciling Two Views of Cryptography (The Computational Soundness of Formal Encryption)
, 2000
"... Two distinct, rigorous views of cryptography have developed over the years, in two mostly separate communities. One of the views relies on a simple but effective formal approach; the other, on a detailed computational model that considers issues of complexity and probability. ..."
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Cited by 378 (11 self)
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Two distinct, rigorous views of cryptography have developed over the years, in two mostly separate communities. One of the views relies on a simple but effective formal approach; the other, on a detailed computational model that considers issues of complexity and probability.