TY - JOUR
T1 - Extractors and pseudo-random generators with optimal seed length
AU - Impagliazzo, Russell
AU - Shaltiel, Ronen
AU - Wigderson, Avi
PY - 2000
Y1 - 2000
N2 - We give the first construction of a pseudo-random generator with optimal seed length that uses (essentially) arbitrary hardness. It builds on the novel recursive use of the NW-generator in [8], which produced many optimal generators one of which was pseudo-random. This is achieved in two stages - first significantly reducing the number of candidate generators, and then efficiently combining them into one. We also give the first construction of an extractor with optimal seed length, that can handle sub-polynomial entropy levels. It builds on the fundamental connection between extractors and pseudo-random generators discovered by Trevisan, combined with construction above. Moreover, using Kolmogorov Complexity rather than circuit size in the analysis gives super-polynomial savings for our construction, and renders our extractors better than known for all entropy levels.
AB - We give the first construction of a pseudo-random generator with optimal seed length that uses (essentially) arbitrary hardness. It builds on the novel recursive use of the NW-generator in [8], which produced many optimal generators one of which was pseudo-random. This is achieved in two stages - first significantly reducing the number of candidate generators, and then efficiently combining them into one. We also give the first construction of an extractor with optimal seed length, that can handle sub-polynomial entropy levels. It builds on the fundamental connection between extractors and pseudo-random generators discovered by Trevisan, combined with construction above. Moreover, using Kolmogorov Complexity rather than circuit size in the analysis gives super-polynomial savings for our construction, and renders our extractors better than known for all entropy levels.
UR - http://www.scopus.com/inward/record.url?scp=0033692219&partnerID=8YFLogxK
U2 - 10.1145/335305.335306
DO - 10.1145/335305.335306
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AN - SCOPUS:0033692219
SP - 1
EP - 10
JO - Unknown Journal
JF - Unknown Journal
T2 - 32nd Annual ACM Symposium on Theory of Computing
Y2 - 21 May 2000 through 23 May 2000
ER -