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Hardness vs. randomness
 JOURNAL OF COMPUTER AND SYSTEM SCIENCES
, 1994
"... We present a simple new construction of a pseudorandom bit generator, based on the constant depth generators of [N]. It stretches a short string of truly random bits into a long string that looks random to any algorithm from a complexity class C (eg P, NC, PSPACE,...) using an arbitrary function tha ..."
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Cited by 298 (27 self)
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We present a simple new construction of a pseudorandom bit generator, based on the constant depth generators of [N]. It stretches a short string of truly random bits into a long string that looks random to any algorithm from a complexity class C (eg P, NC, PSPACE,...) using an arbitrary function
Pseudorandom generators without the XOR Lemma (Extended Abstract)
, 1998
"... Impagliazzo and Wigderson [IW97] have recently shown that if there exists a decision problem solvable in time 2 O(n) and having circuit complexity 2 n) (for all but finitely many n) then P = BPP. This result is a culmination of a series of works showing connections between the existence of har ..."
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Cited by 138 (23 self)
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of hard predicates and the existence of good pseudorandom generators. The construction of Impagliazzo and Wigderson goes through three phases of "hardness amplification" (a multivariate polynomial encoding, a first derandomized XOR Lemma, and a second derandomized XOR Lemma) that are composed
Coil sensitivity encoding for fast MRI. In:
 Proceedings of the ISMRM 6th Annual Meeting,
, 1998
"... New theoretical and practical concepts are presented for considerably enhancing the performance of magnetic resonance imaging (MRI) by means of arrays of multiple receiver coils. Sensitivity encoding (SENSE) is based on the fact that receiver sensitivity generally has an encoding effect complementa ..."
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Cited by 193 (3 self)
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configurations and kspace sampling patterns. Special attention is given to the currently most practical case, namely, sampling a common Cartesian grid with reduced density. For this case the feasibility of the proposed methods was verified both in vitro and in vivo. Scan time was reduced to onehalf using a two
Randomness, Pseudorandomness, and its Applications to Cryptography
, 1998
"... Introduction What does it mean for something to be random? What is a random number? Is 2 a random number? If one has a truly random number, and then proceeds to show it to everyone in the world and use it in every application, does it remain a random number? Intuitively, we all have a feel for perf ..."
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Introduction What does it mean for something to be random? What is a random number? Is 2 a random number? If one has a truly random number, and then proceeds to show it to everyone in the world and use it in every application, does it remain a random number? Intuitively, we all have a feel
PSEUDORANDOM NUMBER GENERATOR
, 1977
"... ii A simple and inexpensive pseudorandom number generator has been designed and built using linear feedback shift registers to generate rectangular and gaussian distributed numbers. The device has been interfaced to a Nova computer to provide a high speed source of random numbers. The two distribu ..."
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ii A simple and inexpensive pseudorandom number generator has been designed and built using linear feedback shift registers to generate rectangular and gaussian distributed numbers. The device has been interfaced to a Nova computer to provide a high speed source of random numbers. The two
EMPIRICAL PSEUDORANDOM NUMBER GENERATORS
"... The most common pseudorandom number generator or PRNG, the linear congruential generator or LCG, belongs to a whole class of rational congruential generators. These generators work by multiplicative congruential method for integers, which implements a ”growandcut procedure”. We extend this concept ..."
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The most common pseudorandom number generator or PRNG, the linear congruential generator or LCG, belongs to a whole class of rational congruential generators. These generators work by multiplicative congruential method for integers, which implements a ”growandcut procedure”. We extend
On Stochastic Security of Pseudorandom Sequences
"... Abstract. Cryptographic primitives such as secure hash functions (e.g., SHA1, SHA2, and SHA3) and symmetric key block ciphers (e.g., AES and TDES) have been commonly used to design pseudorandom generators with counter modes (e.g., in NIST SP80090A standards). It is assumed that if these primitives ..."
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Abstract. Cryptographic primitives such as secure hash functions (e.g., SHA1, SHA2, and SHA3) and symmetric key block ciphers (e.g., AES and TDES) have been commonly used to design pseudorandom generators with counter modes (e.g., in NIST SP80090A standards). It is assumed that if these primitives
On the pseudorandom generator ISAAC
"... Abstract. This paper presents some properties of he deterministic random bit generator ISAAC (FSE’96), contradicting several statements of its introducing article. In particular, it characterizes huge subsets of internal states which induce a strongly nonuniform distribution in the 8 192 first bits ..."
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, as a source of nonuniform randomness, weak states might distort simulations, and harm cryptographic applications, and so generators with many such states should not be used. Sections 3 and 4 respectively propose a modification of ISAAC’s algorithm to avoid the design flaws presented, and point out
On the pseudorandom generator ISAAC
"... Abstract. This paper presents some properties of he deterministic random bit generator ISAAC (FSE’96), contradicting several statements of its introducing article. In particular, it characterizes huge subsets of internal states which induce a strongly nonuniform distribution in the 8 192 first bits ..."
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, as a source of nonuniform randomness, weak states might distort simulations, and harm cryptographic applications, and so generators with many such states should not be used. Sections 3 and 4 respectively propose a modification of ISAAC’s algorithm to avoid the design flaws presented, and point out
The Coin Problem, and Pseudorandomness for Branching Programs
"... is given, which lands on head with probability either 1/2+β or 1/2 − β. We are given the outcome of n independent tosses of this coin, and the goal is to guess which way the coin is biased, and to answer correctly with probability ≥ 2/3. When our computational model is unrestricted, the majority fun ..."
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Cited by 16 (0 self)
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that Nisan’s Generator fools widthw readonce regular branching programs, using seed length O(w 4 log n log log n + log n log(1/ε)). For w = ε = Θ(1), this seedlength is O(log n log log n). The coin theorem and its relatives might have other connections to PRGs. This application is related
Results 1  10
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669