J. Hastad, R. Impagliazzo, L.A. Levin and M. Luby. Construction of Pseudorandom Generator from any One-Way Function. To appear in SIAM J. on Computing. Preliminary versions by Impagliazzo et. al. in 21st STOC (1989. Home/Search Document Details and Download
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....remarkable property of yielding nothing beyond the validity of the assertion being proved. The generality of zero knowledge proofs has been demonstrated by Goldreich, Micali and Wigderson [13] who showed that every NP statement can be proved in zero knowledge provided that one way functions exist [16, 20]. Since then, zero knowledge proofs have turned out to be an extremely useful tool in the design of various cryptographic protocols. The original setting in which zero knowledge proofs were investigated consisted of a single prover and verifier which execute only one instance of the protocol at a ....
J. Hastad, R. Impagliazzo, L.A. Levin and M. Luby. Construction of Pseudorandom Generator from any One-Way Function. SIAM Jour. on Computing, Vol. 28 (4), pages 1364-- 1396, 1999.
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....kinds of pseudorandom functions we want. So how can one construct (variable length input) pseudorandom function families A traditional approach constructs pseudorandom function families from pseudorandom generators [8] Pseudorandom generators are in turn constructed from any one way function [10]. Recently a different construction of pseudorandom function families from trapdoor functions was proposed [14] In these works pseudorandom function families are regarded as a compound primitive, whereas oneway functions (or trapdoor functions) are the building blocks. In all cases, the ....
....ffl (i) is negligible. In contrast, F obtains, using this notation, ffl = lqffl (q) In the typical cases where ffl (1) is much smaller than ffl (q) F does significantly better than F . 1. 5 Related work In comparison to constructions based on one way or trapdoor functions [10, 8, 14], ours are more efficient in practice. Let us now turn to constructions based on FI PRFs. The first construction of VI PRFs from FI PRFs is in [4] They analyze another popular construction (namely, Cipher Block Chaining, or CBC) and show that it yields a VI PRF if the underlying functions are ....
J. H ASTAD, R. IMPAGLIAZZO, L. LEVIN AND M. LUBY, "Construction of a pseudo-random generator from any one-way function, " Manuscript. Earlier versions in STOC 89 and STOC 90.
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....modular multiplications as f N;g;r ) remained open. We denote by n the size (in bits) of N , and by x the value of x mod N . What GGM have actually demonstrated is how to construct exponentially long, easily accessible, pseudorandom strings based on any one way function (following [16]) However, this does not imply that the specific BBS bit sequence remains pseudorandom given direct access to exponentially many of its bits. 2.1.3 The NR Constructions About a decade after the GGM paper appeared, Naor and Reingold (NR) 19] suggested a parallel construction of pseudorandom ....
J. Hastad, R. Impagliazzo, L.A. Levin and M. Luby. Construction of Pseudorandom Generator from any One-Way Function. SIAM Jour. on Computing, Vol. 28 (4), pages 1364--1396, 1999.
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J. Hastad, R. Impagliazzo, L. A. Levin and M. Luby, Construction of a pseudo-random generator from any one-way function, To appear in SIAM J. Comput. Preliminary versions by Impagliazzo et. al. in 21st STOC,
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J. Hastad, R. Impagliazzo, L.A. Levin and M. Luby. Construction of Pseudorandom Generator from any One-Way Function. To appear in SIAM J. on Computing. Preliminary versions by Impagliazzo et. al. in 21st STOC (1989.
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J. Hastad, R. Impagliazzo, L.A. Levin, and M. Luby. Construction of pseudorandom generator from any one-way function. To appear in SIAM J. on Computing . Preliminary versions by Impagliazzo et. al. in 21st STOC (1989) and Hastad in 22nd STOC (1990).
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J. H ASTAD, R. IMPAGLIAZZO, L. LEVIN, AND M. LUBY, Construction of pseudorandom generator from any one-way function. SIAM Journal on Computing. Preliminary versions by Impagliazzo et. al. in 21st STOC (1989) and Hastad in 22nd STOC (1990).
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J. Hastad, R. Impagliazzo, L.A. Levin and M. Luby. Construction of Pseudorandom Generator from any One-Way Function. SIAM Jour. on Computing, Vol. 28 (4), pages 1364--1396, 1999. BIBLIOGRAPHY 119
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