A dual version of Reimer's inequality and a proof of Rudich's conjecture

Saks, Michael; Smyth, Clifford

doi:10.1109/ccc.2000.856739

Cited by 27 publications

(36 citation statements)

References 5 publications

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“…They also show that in a more constrained model such a construction is unconditionally impossible. The formal framework of Impagliazzo and Rudich has subsequently been used to address other "implication" questions, such as one-way functions versus one-way permutations [26,19], oneway functions versus collision-resistant hash functions [27], and between key agreement, oblivious transfer, public-key encryption and trapdoor functions and permutations [9,10]. Variants of the framework have also been used to address the issue of the number of rounds in KA protocols [25], of the efficiency of constructions of universal one-way hash functions based on one-way permutations [20,8], of pseudorandom generators based on one-way permutations [8] and of public-key encryption based on trapdoor permutations [7].…”

Section: Introductionmentioning

confidence: 99%

Notions of Reducibility between Cryptographic Primitives

Reingold

Trevisan

Vadhan

2004

Lecture Notes in Computer Science

193

212

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Abstract. Starting with the seminal paper of Impagliazzo and Rudich [17], there has been a large body of work showing that various cryptographic primitives cannot be reduced to each other via "black-box" reductions. The common interpretation of these results is that there are inherent limitations in using a primitive as a black box, and that these impossibility results can be overcome only by explicitly using the code of the primitive in the construction. In this paper we revisit these negative results, give a more careful taxonomy of the ways in which "black-box reductions" can be formalized, strengthen some previous results (in particular giving unconditional impossibility results for reductions that were previously only shown to imply P = NP ), and offer a new interpretation of them: in many cases, there is no limitation in using a primitive as a black box, but there is a limitation in treating adversaries as such. In particular, these negative results may be overcome by using the code of the adversary in the analysis.

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Section: Introductionmentioning

confidence: 99%

Notions of Reducibility between Cryptographic Primitives

Reingold

Trevisan

Vadhan

2004

Lecture Notes in Computer Science

193

212

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“…Following their work, a number of additional black-box impossibility results have appeared [40,41,16,32,17,13]. Kim, Simon, and Tetali [33] initiated work focused on bounding the efficiency of black-box cryptographic constructions (rather than their existence), and their work provided the original inspiration for our research.…”

Section: Introductionmentioning

confidence: 99%

Bounds on the Efficiency of Generic Cryptographic Constructions

Gennaro¹,

Gertner²,

Katz³

et al. 2005

SIAM J. Comput.

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A central focus of modern cryptography is the construction of efficient, "high-level" cryptographic tools (e.g., encryption schemes) from weaker, "low-level" cryptographic primitives (e.g., one-way functions). Of interest are both the existence of such constructions, and their efficiency.Here, we show essentially-tight lower bounds on the best possible efficiency of any black-box construction of some fundamental cryptographic tools from the most basic and widely-used cryptographic primitives. Our results hold in an extension of the model introduced by Impagliazzo and Rudich, and improve and extend earlier results of Kim, Simon, and Tetali. We focus on constructions of pseudorandom generators, universal one-way hash functions, and digital signatures based on one-way permutations, as well as constructions of public-and private-key encryption schemes based on trapdoor permutations. In each case, we show that any black-box construction beating our efficiency bound would yield the unconditional existence of a one-way function and thus, in particular, prove P = N P .

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“…A line of subsequent works used this methodology or new variants to show black-box separations among various other cryptographic primitives (c.f. [34,6,36,24,16,17]), and to show that blackbox constructions suffer from inherent efficiency limitations [25,14,15].…”

Section: Black-box Reductions and Separationsmentioning

confidence: 99%

Towards a Separation of Semantic and CCA Security for Public Key Encryption

Gertner

Malkin

Myers

Theory of Cryptography

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Abstract.We address the question of whether or not semantically secure public-key encryption primitives imply the existence of chosen ciphertext attack (CCA) secure primitives. We show a black-box separation, following the methodology introduced by Impagliazzo and Rudich [23], for a large non-trivial class of constructions. In particular, we show that if the proposed CCA construction's decryption algorithm does not query the semantically secure primitive's encryption algorithm, then the proposed construction cannot be CCA secure.

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A dual version of Reimer's inequality and a proof of Rudich's conjecture

Cited by 27 publications

References 5 publications

Notions of Reducibility between Cryptographic Primitives

Notions of Reducibility between Cryptographic Primitives

Bounds on the Efficiency of Generic Cryptographic Constructions

Towards a Separation of Semantic and CCA Security for Public Key Encryption

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