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Pseudorandom generators in . . .

by Michael Alekhnovich, Eli Ben-sasson, Alexander A. Razborov, Avi Wigderson , 2003
"... We call a pseudorandom generator Gn: {0, 1} n → {0, 1} m hard for a propositional proof system P if P can not efficiently prove the (properly encoded) statement Gn(x1,..., xn) = b for any string b ∈ {0, 1} m. We consider a variety of “combinatorial” pseudorandom generators inspired by the Nisan-Wig ..."
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We call a pseudorandom generator Gn: {0, 1} n → {0, 1} m hard for a propositional proof system P if P can not efficiently prove the (properly encoded) statement Gn(x1,..., xn) = b for any string b ∈ {0, 1} m. We consider a variety of “combinatorial” pseudorandom generators inspired by the Nisan

Pseudorandom Generators

by n.n.
"... Our accomplishments in derandomization from the previous chapters include the following: • Derandomizing specific algorithms, such as the ones for MaxCut and Undirected S-T Connectivity; • Giving explicit (efficient, deterministic) constructions of various pseudorandom objects, such as expanders, ex ..."
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Our accomplishments in derandomization from the previous chapters include the following: • Derandomizing specific algorithms, such as the ones for MaxCut and Undirected S-T Connectivity; • Giving explicit (efficient, deterministic) constructions of various pseudorandom objects, such as expanders

Pseudorandom generators for space-bounded computation

by Noam Nisan - Combinatorica , 1992
"... Pseudorandom generators are constructed which convert O(SlogR) truly random bits to R bits that appear random to any algorithm that runs in SPACE(S). In particular, any randomized polynomial time algorithm that runs in space S can be simulated using only O(Slogn) random bits. An application of these ..."
Abstract - Cited by 237 (10 self) - Add to MetaCart
Pseudorandom generators are constructed which convert O(SlogR) truly random bits to R bits that appear random to any algorithm that runs in SPACE(S). In particular, any randomized polynomial time algorithm that runs in space S can be simulated using only O(Slogn) random bits. An application

Extractors and Pseudorandom Generators

by Luca Trevisan - Journal of the ACM , 1999
"... We introduce a new approach to constructing extractors. Extractors are algorithms that transform a "weakly random" distribution into an almost uniform distribution. Explicit constructions of extractors have a variety of important applications, and tend to be very difficult to obtain. ..."
Abstract - Cited by 104 (6 self) - Add to MetaCart
We introduce a new approach to constructing extractors. Extractors are algorithms that transform a "weakly random" distribution into an almost uniform distribution. Explicit constructions of extractors have a variety of important applications, and tend to be very difficult to obtain.

Pseudorandom Generators for Combinatorial Checkerboards

by Thomas Watson , 2011
"... We define a combinatorial checkerboard to be a function f: {1,...,m} d → {1, −1} of the form f(u1,...,ud) = ∏d i=1 fi(ui) for some functions fi: {1,...,m} → {1, −1}. This is a variant of combinatorial rectangles, which can be defined in the same way but using {0, 1} instead of {1, −1}. We consider ..."
Abstract - Cited by 3 (1 self) - Add to MetaCart
consider the problem of constructing explicit pseudorandom generators for combinatorial checkerboards. This is a generalization of small-bias generators, which correspond to the case m = 2. We construct a pseudorandom generator that ǫ-fools all combinatorial checkerboards with seed length O () 3/2 1 log m

Pseudorandom generators for combinatorial shapes.

by Parikshit Gopalan , Raghu Meka , Omer Reingold , David Zuckerman - In STOC, , 2011
"... ABSTRACT We construct pseudorandom generators for combinatorial shapes, which substantially generalize combinatorial rectangles, -biased spaces, 0/1 halfspaces, and 0/1 modular sums. A function f : [m] n → {0, 1} is an (m, n)-combinatorial shape if there exist sets A1, . . . , An ⊆ [m] and a symm ..."
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ABSTRACT We construct pseudorandom generators for combinatorial shapes, which substantially generalize combinatorial rectangles, -biased spaces, 0/1 halfspaces, and 0/1 modular sums. A function f : [m] n → {0, 1} is an (m, n)-combinatorial shape if there exist sets A1, . . . , An ⊆ [m] and a

State Recovery Attacks on Pseudorandom Generators

by Andrey Sidorenko, Berry Schoenmakers
"... Abstract: State recovery attacks comprise an important class of attacks on pseudorandom generators. In this paper we analyze resistance of pseudorandom generators against these attacks in terms of concrete security. We show that security of the Blum-Micali pseudorandom generator against state recove ..."
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Abstract: State recovery attacks comprise an important class of attacks on pseudorandom generators. In this paper we analyze resistance of pseudorandom generators against these attacks in terms of concrete security. We show that security of the Blum-Micali pseudorandom generator against state

On pseudorandom generators in NC0?

by unknown authors
"... Abstract. In this paper we consider the question of whether NC0 circuits can generate pseudorandom distributions. While we leave the general question unanswered, we show* Generators computed by NC0 circuits where each output bit depends on at most 3 input bits (i.e, NC03 circuits) and with stretch f ..."
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Abstract. In this paper we consider the question of whether NC0 circuits can generate pseudorandom distributions. While we leave the general question unanswered, we show* Generators computed by NC0 circuits where each output bit depends on at most 3 input bits (i.e, NC03 circuits) and with stretch

Language Compression and Pseudorandom Generators

by Harry Buhrman , Troy Lee , Dieter Van Melkebeek
"... The language compression problem asks for succinct descriptions of the strings in a language A such that the strings can be efficiently recovered from their description when given a mem-bership oracle for A. We study randomized and nondeterministic decompression schemes andinvestigate how close we ..."
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string. The latter lower bound is tight up to an additiveterm of O(log n).The key ingredient for our upper bounds is the relativizable hardness versus randomness tradeoffs based on the Nisan-Wigderson pseudorandom generator construction.

Robust Pseudorandom Generators

by Yuval Ishai, Eyal Kushilevitz, Xin Li, Rafail Ostrovsky, Manoj Prabhakaran, Amit Sahai, David Zuckerman , 2013
"... Let G: {0, 1} n → {0, 1} m be a pseudorandom generator. We say that a circuit implementation of G is (k, q)-robust if for every set S of at most k wires anywhere in the circuit, there is a set T of at most q|S | outputs, such that conditioned on the values of S and T the remaining outputs are pseudo ..."
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Let G: {0, 1} n → {0, 1} m be a pseudorandom generator. We say that a circuit implementation of G is (k, q)-robust if for every set S of at most k wires anywhere in the circuit, there is a set T of at most q|S | outputs, such that conditioned on the values of S and T the remaining outputs
Results 1 - 10 of 1,893