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Pseudorandom generators in . . .
, 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 NisanWig ..."
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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
"... Our accomplishments in derandomization from the previous chapters include the following: • Derandomizing specific algorithms, such as the ones for MaxCut and Undirected ST 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 ST Connectivity; • Giving explicit (efficient, deterministic) constructions of various pseudorandom objects, such as expanders
Pseudorandom generators for spacebounded computation
 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 ..."
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Cited by 237 (10 self)
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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
 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. ..."
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Cited by 104 (6 self)
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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
, 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 ..."
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Cited by 3 (1 self)
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consider the problem of constructing explicit pseudorandom generators for combinatorial checkerboards. This is a generalization of smallbias generators, which correspond to the case m = 2. We construct a pseudorandom generator that ǫfools all combinatorial checkerboards with seed length O () 3/2 1 log m
Pseudorandom generators for combinatorial shapes.
 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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Cited by 10 (1 self)
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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
"... 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 BlumMicali pseudorandom generator against state recove ..."
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Cited by 5 (0 self)
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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 BlumMicali pseudorandom generator against state
On pseudorandom generators in NC0?
"... 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
"... 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 membership oracle for A. We study randomized and nondeterministic decompression schemes andinvestigate how close we ..."
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Cited by 7 (0 self)
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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 NisanWigderson pseudorandom generator construction.
Robust Pseudorandom Generators
, 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 qS  outputs, such that conditioned on the values of S and T the remaining outputs are pseudo ..."
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Cited by 1 (0 self)
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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 qS  outputs, such that conditioned on the values of S and T the remaining outputs
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