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Pseudorandomness and the Minimum Circuit Size Problem

2020
*
Innovations in Theoretical Computer Science
*

(Non-Black-Box Results) We show that for weak circuit classes C against which there are natural

doi:10.4230/lipics.itcs.2020.68
dblp:conf/innovations/Santhanam20
fatcat:pgatorc5k5hlrknytijhfgjufy
*proofs*[44] ,*pseudorandom*functions secure against poly-size circuits*in*C imply superpolynomial lower bounds ... These results are shown using non-black-box techniques, and*in*the first case we show that there is no black-box*proof*of the result under standard crypto assumptions. ... over the uniform distribution, and the role of*pseudorandomness**in**proof**complexity*, among others. ...##
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Pseudorandom permutations with the fast forward property
[article]

2003
*
arXiv
*
pre-print

This paper has been withdrawn by the author(s), due to the existence of a much better paper

arXiv:cs/0112016v2
fatcat:am4c4a5iyjgqhi2fwfgqpyadri
*in*http://arxiv.org/abs/cs.CR/0207027 ...*In*order to shift to the*pseudorandom*case, we need to have some*pseudorandom*number*generator*to*generate*the random choices of the s i 's*in*the CCL process. ...*Proof*. This is an immediate consequence of Theorem 1.3 and*Proposition*1.2. ...##
###
Pseudorandom Generators
[chapter]

1999
*
Modern Cryptography, Probabilistic Proofs and Pseudorandomness
*

Suppose that for all m there exists an (m, 1/8)

doi:10.1007/978-3-662-12521-2_3
fatcat:d44aduuufjgijhehp4toyijjz4
*pseudorandom**generator*G :*Proof*. ...*In*the previous sections, we have seen a number of interesting derandomization results: Note that even when we define the*pseudorandomness*property of the*generator*with respect to nonuniform algorithms ...*Proof*. Suppose G is not a (t, ε)*pseudorandom**generator*. ...##
###
Page 1666 of Mathematical Reviews Vol. , Issue 2004b
[page]

2004
*
Mathematical Reviews
*

The applications of

*pseudorandom*functions range from cryp- tography to computational*complexity*analysis. ... This im- provement is achieved combining the NR functions with the BBS*pseudorandom*number*generator*. ...##
###
Pseudorandom Generators
[chapter]

1986
*
Primality and Cryptography
*

Suppose that for all m there exists an (m, 1/8)

doi:10.1007/978-3-322-96647-6_4
fatcat:6febgpanvrfpbbihvvwqsn77zq
*pseudorandom**generator*G :*Proof*. ...*In*the previous sections, we have seen a number of interesting derandomization results: Note that even when we define the*pseudorandomness*property of the*generator*with respect to nonuniform algorithms ...*Proof*. Suppose G is not a (t, ε)*pseudorandom**generator*. ...##
###
The Power of Negations in Cryptography
[chapter]

2015
*
Lecture Notes in Computer Science
*

The study of monotonicity and negation

doi:10.1007/978-3-662-46494-6_3
fatcat:e6fea6drprg2hh6n4lukojdz2a
*complexity*for Boolean functions has been prevalent*in**complexity*theory as well as*in*computational learning theory, but little attention has been given to it*in*...*generator*cannot. ... Acknowledgements We would like to thank Ilan Orlov for helpful conversations during an early stage of this work, Rocco Servedio for suggesting an initial construction*in**Proposition*5.3, and Andrej Bogdanov ...##
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Some consequences of the existence of pseudorandom generators

1987
*
Proceedings of the nineteenth annual ACM conference on Theory of computing - STOC '87
*

This paper introduces a type of

doi:10.1145/28395.28412
dblp:conf/stoc/Allender87
fatcat:g2b5rruelfeodgf4e7spzxcsau
*generalized*Kolmogorov*complexity*and uses it as a tool to explore the consequences of several assumptions about the existence of secure*pseudorandom**generators*. ... One goal of the investigation begun here is to show that many important questions*in**complexity*theory may be viewed as questions about the Kolmogorov*complexity*of sets*in*P. 0 ...*PSEUDORANDOMNESS*AND KOLMOGOROV*COMPLEXITY**In*this section, we investigate hypotheses about the security of*pseudorandom**generators*and derive necessary conditions,*in*terms of*generalized*Kolmogorov*complexity*...##
###
Some consequences of the existence of pseudorandom generators

1989
*
Journal of computer and system sciences (Print)
*

This paper introduces a type of

doi:10.1016/0022-0000(89)90021-4
fatcat:hqvwyaq7unh35phl6cuwcnyuca
*generalized*Kolmogorov*complexity*and uses it as a tool to explore the consequences of several assumptions about the existence of secure*pseudorandom**generators*. ... One goal of the investigation begun here is to show that many important questions*in**complexity*theory may be viewed as questions about the Kolmogorov*complexity*of sets*in*P. 0 ...*PSEUDORANDOMNESS*AND KOLMOGOROV*COMPLEXITY**In*this section, we investigate hypotheses about the security of*pseudorandom**generators*and derive necessary conditions,*in*terms of*generalized*Kolmogorov*complexity*...##
###
On transformation of interactive proofs that preserve the prover's complexity

2000
*
Proceedings of the thirty-second annual ACM symposium on Theory of computing - STOC '00
*

On transformations of interactive

doi:10.1145/335305.335330
dblp:conf/stoc/Vadhan00
fatcat:37wn3ym4zrdbnddwgv6lb5cmey
*proofs*that preserve the prover's*complexity*. ... We also examine a similar deficiency*in*a transformation of Fürer et al. [FGM · 89] from interactive*proofs*to ones with perfect completeness. ... I thank Shafi Goldwasser, who sparked my interest*in*the prover's*complexity*, and suggested the issues addressed*in*this paper as research problems. ...##
###
On systems of complexity one in the primes
[article]

2014
*
arXiv
*
pre-print

Consider a translation-invariant system of linear equations V x = 0 of

arXiv:1403.7040v2
fatcat:to7cmkfpgvhy3nqzedinq2czuq
*complexity*one, where V is an integer r × t matrix. ... This extends a quantitative result of Helfgott and de Roton for three-term arithmetic progressions, while the qualitative result is known to hold for all systems of equations of finite*complexity*by the ...*general*for systems of*complexity*one. ...##
###
Pseudorandom Functions: Three Decades Later
[chapter]

2017
*
Tutorials on the Foundations of Cryptography
*

*In*this tutorial we survey various incarnations of

*pseudorandom*functions, giving self-contained

*proofs*of key results from the literature. ...

*In*1984, Goldreich, Goldwasser and Micali formalized the concept of

*pseudorandom*functions and proposed a construction based on any length-doubling

*pseudorandom*

*generator*. ... Acknowledgements This survey is dedicated to Oded Goldreich, a towering and charismatic figure, who has inspired

*generations*of researchers through his limitless passion and devotion to intellectual inquiry ...

##
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Space Pseudorandom Generators by Communication Complexity Lower Bounds

2014
*
International Workshop on Approximation Algorithms for Combinatorial Optimization
*

*In*1989, Babai, Nisan and Szegedy [2] gave a construction of a

*pseudorandom*

*generator*for logspace, based on lower bounds for multiparty communication

*complexity*. ...

*In*this paper, we show how to use the

*pseudorandom*

*generator*construction of [2] to obtain a third construction of a

*pseudorandom*

*generator*with seed length O(log 2 n), achieving the same parameters as ... The

*pseudorandom*

*generator*of [2] has seed length 2 Θ( √ log n) . The

*proof*that their construction gives a

*pseudorandom*

*generator*relies on a lower bound for multiparty communication

*complexity*. ...

##
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Immunity and pseudorandomness of context-free languages

2011
*
Theoretical Computer Science
*

, there is no almost 1-1 weakly

doi:10.1016/j.tcs.2011.07.013
fatcat:snlqltddvrdehce22ky5n32mga
*pseudorandom**generator*computable deterministically*in*linear time by a single-tape Turing machine. ... Finally, we prove that (vi) against REG/n, there exists an almost 1-1*pseudorandom**generator*computable*in*nondeterministic pushdown automata equipped with a write-only output tape and (vii) against REG ... From the arbitrariness of B*in*C, we can conclude that G is a*pseudorandom**generator*against C.*In*what follows, we shall describe the*proof*of*Proposition*6.1. ...##
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BPHSPACE(S)⊆DSPACE(S3/2)

1999
*
Journal of computer and system sciences (Print)
*

The algorithm employs Nisan's

doi:10.1006/jcss.1998.1616
fatcat:t22siallszb37ckho4ut7gioqm
*pseudorandom**generator*for space bounded computation, together with some new techniques for reducing the number of random bits needed by an algorithm. Academic Press ... running*in*space O(S 3Â2 ). ... Then the (m, 2)-*generator*G h is =d 2 -*pseudorandom*with respect to Q.*Proof*of Lemma 4.1. ...##
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Pseudorandomness and derandomization

2012
*
XRDS Crossroads The ACM Magazine for Students
*

*In*this lecture we introduce two key constructs

*in*the pursuit of these topics, namely

*pseudorandom*

*generators*and extractors, respectively. ... We also review some background on finite fields that will be needed

*in*future lectures. ... 1

*Pseudorandom*

*Generators*Definition Intuitively, a

*pseudorandom*

*generator*(PRG) is a procedure that

*generates*a

*pseudorandom*distribution. ...

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