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An Efficient Existentially Unforgeable Signature Scheme and its Applications
 Journal of Cryptology
, 1994
"... A signature scheme is existentially unforgeable if, given any polynomial (in the security parameter) number of pairs (m 1 ; S(m 1 )); (m 2 ; S(m 2 )); : : : (m k ; S(m k )) where S(m) denotes the signature on the message m, it is computationally infeasible to generate a pair (m k+1 ; S(m k+1 )) fo ..."
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Cited by 51 (5 self)
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A signature scheme is existentially unforgeable if, given any polynomial (in the security parameter) number of pairs (m 1 ; S(m 1 )); (m 2 ; S(m 2 )); : : : (m k ; S(m k )) where S(m) denotes the signature on the message m, it is computationally infeasible to generate a pair (m k+1 ; S(m k+1 )) for any message m k+1 = 2 fm 1 ; : : : m k g. We present an existentially unforgeable signature scheme that for a reasonable setting of parameters requires at most 6 times the amount of time needed to generate a signature using "plain" RSA (which is not existentially unforgeable). We point out applications where our scheme is desirable. Preliminary version appeared in Crypto'94 y IBM Research Division, Almaden Research Center, 650 Harry Road, San Jose, CA 95120. Research supported by a BSF Grant 32000321. Email: dwork@almaden.ibm.com. z Incumbent of the Morris and Rose Goldman Career Development Chair, Dept. of Applied Mathematics and Computer Science, Weizmann Institute of Science, Re...
A composition theorem for universal oneway hash functions
 In Eurocrypt ’00
, 2000
"... Abstract. In this paper we present a new scheme for constructing universal oneway hash functions that hash arbitrarily long messages out of universal oneway hash functions that hash fixedlength messages. The new construction is extremely simple and is also very efficient, yielding shorter keys th ..."
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Cited by 49 (5 self)
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Abstract. In this paper we present a new scheme for constructing universal oneway hash functions that hash arbitrarily long messages out of universal oneway hash functions that hash fixedlength messages. The new construction is extremely simple and is also very efficient, yielding shorter keys than previously proposed composition constructions. 1
Cryptographic Hash Functions: A Survey
, 1995
"... This paper gives a survey on cryptographic hash functions. It gives an overview of all types of hash functions and reviews design principals and possible methods of attacks. It also focuses on keyed hash functions and provides the applications, requirements, and constructions of keyed hash functions ..."
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Cited by 47 (7 self)
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This paper gives a survey on cryptographic hash functions. It gives an overview of all types of hash functions and reviews design principals and possible methods of attacks. It also focuses on keyed hash functions and provides the applications, requirements, and constructions of keyed hash functions.
Cryptography in NC0
, 2006
"... We study the parallel timecomplexity of basic cryptographic primitives such as oneway functions (OWFs) and pseudorandom generators (PRGs). Specifically, we study the possibility of implementing instances of these primitives by NC 0 functions, namely by functions in which each output bit depends on ..."
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Cited by 47 (11 self)
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We study the parallel timecomplexity of basic cryptographic primitives such as oneway functions (OWFs) and pseudorandom generators (PRGs). Specifically, we study the possibility of implementing instances of these primitives by NC 0 functions, namely by functions in which each output bit depends on a constant number of input bits. Despite previous efforts in this direction, there has been no convincing theoretical evidence supporting this possibility, which was posed as an open question in several previous works. We essentially settle this question by providing strong positive evidence for the possibility of cryptography in NC 0. Our main result is that every “moderately easy ” OWF (resp., PRG), say computable in NC 1, can be compiled into a corresponding OWF (resp., “lowstretch ” PRG) in which each output bit depends on at most 4 input bits. The existence of OWF and PRG in NC 1 is a relatively mild assumption, implied by most numbertheoretic or algebraic intractability assumptions commonly used in cryptography. A similar compiler can also be obtained for other cryptographic primitives such as oneway permutations, encryption, signatures, commitment, and collisionresistant hashing. Our techniques can also be applied to obtain (unconditional) constructions of “noncryptographic ” PRGs. In particular, we obtain ɛbiased generators and a PRG for spacebounded computation in which each output bit depends on only 3 input bits. Our results make use of the machinery of randomizing polynomials (Ishai and Kushilevitz, 41st FOCS, 2000), which was originally motivated by questions in the domain of informationtheoretic secure multiparty computation. 1
Some Plausible Constructions of DoubleBlockLength Hash Functions
 FSE 2006, volume 4047 of LNCS
, 2006
"... Abstract. In this article, it is discussed how to construct a compression function with 2nbit output using a component function with nbit output. The component function is either a smaller compression function or a block cipher. Some constructions are presented which compose collisionresistant ..."
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Cited by 43 (0 self)
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Abstract. In this article, it is discussed how to construct a compression function with 2nbit output using a component function with nbit output. The component function is either a smaller compression function or a block cipher. Some constructions are presented which compose collisionresistant hash functions: Any collisionfinding attack on them is at most as efficient as the birthday attack in the random oracle model or in the ideal cipher model. A new security notion is also introduced, which we call indistinguishability in the iteration, with a construction satisfying the notion. 1
Strongly unforgeable signatures based on computational diffiehellman
 In Public Key Cryptography
, 2006
"... Abstract. A signature system is said to be strongly unforgeable if the signature is existentially unforgeable and, given signatures on some message m, the adversary cannot produce a new signature on m. Strongly unforgeable signatures are used for constructing chosenciphertext secure systems and gro ..."
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Cited by 41 (1 self)
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Abstract. A signature system is said to be strongly unforgeable if the signature is existentially unforgeable and, given signatures on some message m, the adversary cannot produce a new signature on m. Strongly unforgeable signatures are used for constructing chosenciphertext secure systems and group signatures. Current efficient constructions in the standard model (i.e. without random oracles) depend on relatively strong assumptions such as StrongRSA or StrongDiffieHellman. We construct an efficient strongly unforgeable signature system based on the standard Computational DiffieHellman problem in bilinear groups. 1
Two remarks concerning the goldwassermicalirivest signature scheme
 Advances in Cryptology  CRYPTO' 86
, 1987
"... The focus of this note is the GoldwasserMicaliRivest Signature Scheme (presented in the 25th POCS, 1984). The GMR scheme has the salient property that, unless factoring is easy, it is infeasible to forge any signature even through an adaptive chosen message attack. We present two technical contrib ..."
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Cited by 37 (5 self)
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The focus of this note is the GoldwasserMicaliRivest Signature Scheme (presented in the 25th POCS, 1984). The GMR scheme has the salient property that, unless factoring is easy, it is infeasible to forge any signature even through an adaptive chosen message attack. We present two technical contributions with respect to the GMR scheme: 1) The GMR scheme can be made totally \memoryless": That is, the signature generated by the signer on message M does not depend on the previous signed messages. (In the original scheme, the signature to a message depends on the number of messages signed before.) 2) The GMR scheme can be implemented almost as eciently as the RSA: The original implementation of the GMR scheme based on factoring, can be speededup by a factor of jN j. Thus, both signing and verifying take time O(jN j 3 log 2 jN j). (Here N is the moduli.)
Reducing complexity assumptions for statisticallyhiding commitment
 In EUROCRYPT
, 2005
"... We revisit the following question: what are the minimal assumptions needed to construct statisticallyhiding commitment schemes? Naor et al. show how to construct such schemes based on any oneway permutation. We improve upon this by showing a construction based on any approximable preimagesize one ..."
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Cited by 36 (8 self)
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We revisit the following question: what are the minimal assumptions needed to construct statisticallyhiding commitment schemes? Naor et al. show how to construct such schemes based on any oneway permutation. We improve upon this by showing a construction based on any approximable preimagesize oneway function. These are oneway functions for which it is possible to efficiently approximate the number of preimages of a given output. A special case is the class of regular oneway functions where all points in the image of the function have the same number of preimages. We also prove two additional results related to statisticallyhiding commitment. First, we prove a (folklore) parallel composition theorem showing, roughly speaking, that the statistical hiding property of any such commitment scheme is amplified exponentially when multiple independent parallel executions of the scheme are carried out. Second, we show a compiler which transforms any commitment scheme which is statistically hiding against an honestbutcurious receiver into one which is statistically hiding even against a malicious receiver. 1
Applications of SAT solvers to cryptanalysis of hash functions
 In Theory and Applications of Satisfiability Testing 2006
, 2006
"... Several standard cryptographic hash functions were broken in 2005. Some essential building blocks of these attacks lend themselves well to automation by encoding them as CNF formulas, which are within reach of modern SAT solvers. In this paper we demonstrate effectiveness of this approach. In partic ..."
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Cited by 32 (0 self)
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Several standard cryptographic hash functions were broken in 2005. Some essential building blocks of these attacks lend themselves well to automation by encoding them as CNF formulas, which are within reach of modern SAT solvers. In this paper we demonstrate effectiveness of this approach. In particular, we are able to generate full collisions for MD4 and MD5 given only the differential path and applying a (minimally modified) offtheshelf SAT solver. To the best of our knowledge, this is the first example of a SATsolveraided cryptanalysis of a nontrivial cryptographic primitive. We expect SAT solvers to find new applications as a validation and testing tool of practicing cryptanalysts. 1
The Foundations of Modern Cryptography
, 1998
"... In our opinion, the Foundations of Cryptography are the paradigms, approaches and techniques used to conceptualize, define and provide solutions to natural cryptographic problems. In this essay, we survey some of these paradigms, approaches and techniques as well as some of the fundamental result ..."
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Cited by 28 (0 self)
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In our opinion, the Foundations of Cryptography are the paradigms, approaches and techniques used to conceptualize, define and provide solutions to natural cryptographic problems. In this essay, we survey some of these paradigms, approaches and techniques as well as some of the fundamental results obtained using them. Special effort is made in attempt to dissolve common misconceptions regarding these paradigms and results. c flCopyright 1998 by Oded Goldreich. Permission to make copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that new copies bear this notice and the full citation on the first page. Abstracting with credit is permitted. A preliminary version of this essay has appeared in the proceedings of Crypto97 (Springer's Lecture Notes in Computer Science, Vol. 1294). 0 Contents 1 Introduction 2 I Basic Tools 6 2 Central Paradigms 6 2.1 Computati...