TY - JOUR

T1 - Efficiency improvements in constructing pseudorandom generators from one-way functions

AU - Haitner, Iftach

AU - Reingold, Omer

AU - Vadhan, Salil

PY - 2013

Y1 - 2013

N2 - We give a new construction of pseudorandom generators from any one-way function. The construction achieves better parameters and is simpler than that given in the seminal work of Hastad, Impagliazzo, Levin, and Luby [SIAM J. Comput., 28 (1999), pp. 1364.1396]. The key to our construction is a new notion of next-block pseudoentropy, which is inspired by the notion of inaccessible entropy±; recently introduced in [I. Haitner, O. Reingold, S. Vadhan, and H. Wee, Proceedings of the 41st Annual ACM Symposium on Theory of Computing (STOC), 2009, pp. 611. 620]. An additional advantage over previous constructions is that our pseudorandom generators are parallelizable and invoke the one-way function in a nonadaptive manner. Using [B. Applebaum, Y. Ishai, and E. Kushilevitz, SIAM J. Comput., 36 (2006), pp. 845.888], this implies the existence of pseudorandom generators in NC0 based on the existence of one-way functions in NC1.

AB - We give a new construction of pseudorandom generators from any one-way function. The construction achieves better parameters and is simpler than that given in the seminal work of Hastad, Impagliazzo, Levin, and Luby [SIAM J. Comput., 28 (1999), pp. 1364.1396]. The key to our construction is a new notion of next-block pseudoentropy, which is inspired by the notion of inaccessible entropy±; recently introduced in [I. Haitner, O. Reingold, S. Vadhan, and H. Wee, Proceedings of the 41st Annual ACM Symposium on Theory of Computing (STOC), 2009, pp. 611. 620]. An additional advantage over previous constructions is that our pseudorandom generators are parallelizable and invoke the one-way function in a nonadaptive manner. Using [B. Applebaum, Y. Ishai, and E. Kushilevitz, SIAM J. Comput., 36 (2006), pp. 845.888], this implies the existence of pseudorandom generators in NC0 based on the existence of one-way functions in NC1.

KW - One-way functions

KW - Pseudoentropy

KW - Pseudorandom generators

UR - http://www.scopus.com/inward/record.url?scp=84883024171&partnerID=8YFLogxK

U2 - 10.1137/100814421

DO - 10.1137/100814421

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AN - SCOPUS:84883024171

VL - 42

SP - 1405

EP - 1430

JO - SIAM Journal on Computing

JF - SIAM Journal on Computing

SN - 0097-5397

IS - 3

ER -