Impagliazzo, R., Levin, L. and Luby, M, "Pseudo-random number generation from one-way functions", 21 STOC, 1989, pp 12-24.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....to generate hard satisfiable instances. Besides practical importance, more interestingly, the problem of generating random hard satisfiable instances is related to some open problems in cryptography, e.g. computing a one way function, generating pseudo random numbers and private key cryptography [9, 13, 15]. 7 In fact, for constraint satisfaction and Boolean satisfiability problems, there is a natural strategy to generate instances that are guaranteed to have at least one satisfying assignment. The strategy is as follows [2] first generate a random truth assignment t, and then generate a certain ....

R. Impagliazzo, L. Levin, and M. Luby. Pseudo-random number generation from one-way functions. In: Proceedings of STOC-89, pp.12-24.

....state that D and E are R l n computationally indistinguishable if there is no R l n breaking adversary for distinguishing them. An alternative de nition is to use sp1n (A) sp n (A) because it more accurately re ects the trade o between the running time of A and its success probability [5]. Now we can proceed to de ne a pseudorandom generator as P time function ensemble where l n t n . f is a R l n secure pseudorandom generator if the function (probability) ensembles f(U t n ) and U l n are R l n secure computationally indistinguishable. Here we must note that the ....

....in the de nition of a PRG) and being a permutation the function will not lose information (f(x) uniquely determines x) so it will follow that the output of the OWP is uniformly distributed and no change in entropy will occur. This is enough for us to claim that the following construct holds [5]: one way permutation. Let x; r2U f0; 1g . De ne the P time function ensemble g(x) f(x)jrjx r. Then g is a pseudorandom generator. The reduction is linear preserving with respect to the de nition of computationally indistinguishable. The proof may be outlined as follows: Let and ....

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R. Impagliazzo, L. A. Levin, and M. Luby. Pseudo-random number generation from oneway functions. Proc. of the 21st Annu. ACM Symp. on the Theory of Computing, pages 12-24, 1989.

.... For any positive integer k, given a 2 universal function family F from D to R, a 2 universal function family with the same domain and range R k can be de ned as follows: F k = D R k (x) 1 (x) 2(x) k (x) for some 1 ; k 2 F : The following lemma (see [12]) asserts that 2 universal hash function families can be used to smooth the min entropy of a random variable X. Lemma 1 (Leftover Hash Lemma) Let H be a 2 universal hash function family with domain D and range R and let X be a random variable over D. The distribution hUH ; UH (X)i, satis es ....

R. Impagliazzo, L. Levin and M. Luby, \Pseudorandom number generation from one-way functions", STOC, 1989, pp. 12-24

....information in larger combinatorial structures is of interest to the computer science theory community since successful techniques for doing so may eventually lead to more effective cryptographic methods. Cryptographic problems do suggest one way of creating hard satisfiable problem instances (Impagliazzo et al. 1989). For example, Crawford and Kearns (1993) created SAT encodings of the noisy parity problem. The instances are guaranteed to have a satisfying assignment but are extremely hard to solve using current SAT procedures. In recent work Massacci (1999) also provides a way of translating the DES crypto ....

Impagliazzo, R., Levin, L., and Luby, M. (1989). Pseudo-random number generation from one-way functions. Proc. 21st STOC, 1989, 12-24.

....for two party coin flipping. A commitment by one party, followed by a guess by the second party, followed by a revelation by the first party, is equivalent to the flip of a coin. Naor [62] shows a general construction for basing bit commitment on any one way function, based on earlier reductions [53] [51] A more specific example of a bit commitment scheme is based on quadratic residuosity. If n = pq, p = q = 3 mod 4, then a bit is committed by sending a quadratic residue modulo n (for a zero) or a quadratic nonresidue modulo n (for a one) The scheme is unalterable, since no element can be ....

.... constructed circuit consists of a number of gates, each of which enables a single decryption key (output) to be recovered from the knowledge of two decryption keys (inputs) The input decryption keys serve as seeds for a pseudorandom number generator (which can be based on any one way function [53] [51] that returns the output decryption key (yet another seed for the generator) Kilian [57] shows how to further reduce the complexity assumption for oblivious circuit evaluation to just Oblivious Transfer. In an earlier section, we showed Cr epeau s bit commitment scheme based on Oblivious ....

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R. Impagliazzo, L. Levin, and M. Luby, "Pseudorandom number generation from one-way functions," ACM STOC 1989, 12-24.

....will be used for each instance of the O.A. protocol. Let sig be a signature scheme that is existentially unforgeable against a chosen message attack; such a scheme exists if one way functions exist [26] 35] Let E be a symmetric key encryption function, which also exists if one way functions exist[22, 23, 20]. row row link link wind half wind half window window Delta Delta Delta Delta Delta Delta Delta Delta Delta Delta Delta Delta Delta Delta Omega Omega Omega Omega Omega Omega Omega Omega Omega Omega Omega OE Phi Phi Phi Phi Phi Phi Phi P P P P P P Pq Omega ....

R. Impagliazzo, L. Levin, and M. Luby, "Pseudorandom number generation from one-way functions," ACM STOC 1989, 12--24.

....for two party coin flipping. A commitment by one party, followed by a guess by the second party, followed by a revelation by the first party, is equivalent to the flip of a coin. Naor [114] shows a general construction for basing bit commitment on any one way function, based on earlier reductions [92] [88] A more specific example of a bit commitment scheme is based on quadratic residuosity. If n = pq, p = q = 3 mod 4, then a bit is committed by sending a quadratic residue modulo n (for a zero) or a quadratic nonresidue modulo n (for a one) The scheme is unalterable, since no element can ....

.... constructed circuit consists of a number of gates, each of which enables a single decryption key (output) to be recovered from the knowledge of two decryption keys (inputs) The input decryption keys serve as seeds for a pseudorandom number generator (which can be based on any one way function [92] [88] that returns the output decryption key (yet another seed for the generator) Kilian [96] shows how to base oblivious circuit evaluation solely on Oblivious Transfer as a primitive (black box reduction) In Section 2.2.2, we showed Cr epeau s bit commitment scheme based on Oblivious Transfer ....

[Article contains additional citation context not shown here]

R. Impagliazzo, L. Levin, and M. Luby, "Pseudorandom number generation from one-way functions," ACM STOC 1989, 12--24.

....for two party coin flipping. A commitment by one party, followed by a guess by the second party, followed by a revelation by the first party, is equivalent to the flip of a coin. Naor [79] shows a general construction for basing bit commitment on any one way function, based on earlier reductions [66] [63] A more specific example of a bit commitment scheme is based on quadratic residuosity. If n = pq, p = q = 3 mod 4, then a bit is committed by sending a quadratic residue modulo n (for a zero) or a quadratic nonresidue modulo n (for a one) The scheme is unalterable, since no element can ....

.... constructed circuit consists of a number of gates, each of which enables a single decryption key (output) to be recovered from the knowledge of two decryption keys (inputs) The input decryption keys serve as seeds for a pseudorandom number generator (which can be based on any one way function [66] [63] that returns the output decryption key (yet another seed for the generator) Kilian [70] shows how to base oblivious circuit evaluation solely on Oblivious Transfer as a primitive (black box reduction) In Section 2.2.2, we showed Cr epeau s bit commitment scheme based on Oblivious Transfer ....

[Article contains additional citation context not shown here]

R. Impagliazzo, L. Levin, and M. Luby, "Pseudorandom number generation from one-way functions," ACM STOC 1989, 12-24.

....related to a traditional problem in cryptography theory. More precisely, Russell Impagliazzo has pointed out that generating hard solved instances of 3 SAT is equivalent to computing a one way function, which in turn is equivalent to generating pseudo random numbers and private key cryptography [ILL89, Luby96] It may be easier to generate hard satisfiable instances than hard solved instances, but we have no insight on this. FINDING HARD INSTANCES OF THE SATISFIABILITY PROBLEM 13 The problem of generating hard solved instances can be explained as follows: Find a polytime function h which ....

R. Impagliazzo, L. Levin, and M. Luby. Pseudo-random number generation from oneway functions. Proc. 21st STOC, 1989, pp 12-24.

.... positive integer k, given a 2 universal function family F from D to R, a 2 universal function family with the same domain and range R k can be defined as follows: F k = n : D R k j (x) OE 1 (x) OE 2 (x) OE k (x) for some OE 1 ; OE k 2 F o : The following lemma (see [12]) asserts that 2 universal hash function families can be used to smooth the min entropy of a random variable X . Lemma 1 (Leftover Hash Lemma) Let H be a 2 universal hash function family with domain D and range R and let X be a random variable over D. The distribution hUH ; UH (X)i, satisfies ....

R. Impagliazzo, L. Levin and M. Luby, "Pseudo-random number generation from one-way functions", STOC, 1989, pp. 12-24

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Impagliazzo, R., Levin, L. and Luby, M, "Pseudo-random number generation from one-way functions", 21 STOC, 1989, pp 12-24.

....more intricate constructions, starting with constructions for one way functions with a lot of structure and finishing with the constructions for one way functions with no required structural properties. The current paper is a combination of the results announced in the conference papers [ILL89] and [H90] 1.1. Concepts and tools. Previous methods, following [BM82] rely on constructing a function that has an output bit that is computationally unpredictable given the other bits of the output, but is nevertheless statistically correlated with these other bits. GL89] provide a simple and ....

....It turns out to be easier to construct a false entropy generator f where f 0 is not necessarily P time computable from a one way function than it is to construct a false entropy generator f where f 0 is P time samplable. Using this approach and a non uniform version of Proposition 4. 12, [ILL89] describe a non uniform reduction from a one way function to a pseudorandom generator. However, a uniform reduction using Proposition 4.12 requires that f 0 be P time computable. Thus, one of the main difficulties in our constructions below is to build a false entropy generator f where f 0 is ....

Impagliazzo, R., Levin, L. and Luby, M., Pseudo-random number generation from one-way functions, 21 rst ACM Symp. on Th. of Comp., 1989, pp. 12--24.

....more intricate constructions, starting with constructions for 3 one way functions with a lot of structure and finishing with the constructions for one way functions with no required structural properties. The current paper is a combination of the results announced in the conference papers [ILL : 89] and [Has : 90] 1.1 Concepts and tools Previous methods, following [BM : 82] rely on constructing a function that has an output bit that is computationally unpredictable given the other bits of the output, but is nevertheless statistically correlated with these other bits. GL : 89] provide a ....

....It turns out to be easier to construct a false entropy generator f where f 0 is not necessarily P time computable from a one way function than it is to construct a false entropy generator f where f 0 is P time samplable. Using this approach and a non uniform version of Proposition 4.6. 2, ILL : 89] describe a non uniform reduction from a one way function to a pseudorandom generator. However, a uniform reduction using Proposition 4.6.2 requires that f 0 be P time computable. Thus, one of the main difficulties in our constructions below is to build a false entropy generator f where f 0 ....

Impagliazzo, R., Levin, L. and Luby, M, "Pseudo-random number generation from one-way functions", 21 rst ACM Symposium on Theory of Computing, 1989, pp. 12--24.

....results. In a conditional result (of the above type) the quality of the generator is based on some complexity theoretic assumption, which is believed but is not known to hold. Such results exist for very strong models, specifically polynomial time computation, under various assumptions [BM82, Yao82, GKL88, ILL89, Has90, NW88, BFNW]. The unconditional results use no unproven assumption, and typically demonstrate that weaker computational models can be fooled by pseudorandom generators. To this class of results belong the pseudorandom generators for various constant depth circuits [AW85, Nis91, LVW93] and for space bounded ....

R. Impagliazzo, L. Levin, and M. Luby. Pseudo-random number generation from one-way functions. In 21st STOC, pages 12--24, 1989.

....results. In a conditional result (of the above type) the quality of the generator is based on some complexity theoretic assumption, which is believed but is not known to hold. Such results exist for very strong models, specifically polynomial time computation, under various assumptions [BM82, Yao82, GKL88, ILL89, Has90, NW88, BFNW]. The unconditional results use no unproven assumption, and typically demonstrate that weaker computational models can be fooled by pseudorandom generators. To this class of results belong the pseudorandom generators for various constant depth circuits [AW85, Nis91, LVW93] and for space bounded ....

R. Impagliazzo, L. Levin, and M. Luby. Pseudo-random number generation from one-way functions. In 21st STOC, pages 12--24, 1989.

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Impagliazzo, R., Levin, L. and Luby, M, "Pseudo-random number generation from one-way functions", 21 rst STOC, 1989, pp 12-24.

No context found.

R. Impagliazzo, L. A. Levin, and M. Luby. Pseudo-random number generation from one-way functions. In Proc. of the 21st ACM Symp. on the Theory of Computing, pages 12-24, 1989.

No context found.

R. Impagliazzo, L. A. Levin, and M. Luby. Pseudo-random number generation from one-way functions. In Proc. of the 21st Annu. ACM Symp. on the Theory of Computing, pages 12-24, 1989.

No context found.

Impagliazzo, R., Levin, L., Luby, L.: Pseudo-Random Number Generation from One-Way Functions. Proc. of STOC (1989) 12--24

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