By Elad Barkan, Eli Biham, Adi Shamir (auth.), Cynthia Dwork (eds.)
This ebook constitutes the refereed complaints of the twenty sixth Annual overseas Cryptology convention, CRYPTO 2006, held in Santa Barbara, California, united states in August 2006.
The 34 revised complete papers offered including 2 invited lectures have been conscientiously reviewed and chosen from 250 submissions. The papers tackle all present foundational, theoretical and study facets of cryptology, cryptography, and cryptanalysis in addition to complicated applications.
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Example text
In practice, it is not necessarily sufficient that a reduction translates polynomial security into polynomial security. In order for reductions to be of any practical use, the concrete overhead introduced by the reduction comes into play. There are various factors involved in determining the security of a reduction. In this discussion, however, we focus only on one central parameter, which is the length m of the generator’s seed compared to the length n of the input to the underlying one-way function.
Efficient pseudorandom generators from exponentially hard one-way functions. In ICALP 2006, 2006. J. H˚ astad, R. Impagliazzo, L. A. Levin, and M. Luby. A pseudorandom generator from any one-way function. SIAM Journal of Computing, 29(4):1364–1396, 1999. A. Herzberg and M. Luby. Pubic randomness in cryptography. In CRYPTO ’92, LNCS, volume 740, pages 421–432. Springer, 1992. T. Holenstein. Pseudorandom generators from one-way functions: A simple construction for any hardness. In TCC ’06, LNCS. Springer, 2006.
Therefore we use only the first randomized iterate of a function, that is x1 = f (h(f (x))). Denote the degeneracy of y by Df (y) = log f −1 (y) (this is a measure that divides the images of f to n categories according to their preimage size). Let b denote a hardcore-bit (again we take the Goldreich-Levin hardcore-bit [GL89]). Loosely speaking, we consider the bit b(x0 ) when given the value (x1 , h) (recall that x0 = f (x)) and make the following observation: When Df (x0 ) ≥ Df (x1 ) then b(x0 ) is (almost) fully determined by (x1 , h), as opposed to when Df (x0 ) < Df (x1 ) where b(x0 ) is essentially uniform.