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Pseudorandomness and the Minimum Circuit Size Problem

Rahul Santhanam, Michael Wagner
2020 Innovations in Theoretical Computer Science  
(Non-Black-Box Results) We show that for weak circuit classes C against which there are natural 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.  ... 
doi:10.4230/lipics.itcs.2020.68 dblp:conf/innovations/Santhanam20 fatcat:pgatorc5k5hlrknytijhfgjufy

Pseudorandom permutations with the fast forward property [article]

Boaz Tsaban
2003 arXiv   pre-print
This paper has been withdrawn by the author(s), due to the existence of a much better paper in http://arxiv.org/abs/cs.CR/0207027  ...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.  ... 
arXiv:cs/0112016v2 fatcat:am4c4a5iyjgqhi2fwfgqpyadri

Pseudorandom Generators [chapter]

Oded Goldreich
1999 Modern Cryptography, Probabilistic Proofs and Pseudorandomness  
Suppose that for all m there exists an (m, 1/8) 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.  ... 
doi:10.1007/978-3-662-12521-2_3 fatcat:d44aduuufjgijhehp4toyijjz4

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]

Evangelos Kranakis
1986 Primality and Cryptography  
Suppose that for all m there exists an (m, 1/8) 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.  ... 
doi:10.1007/978-3-322-96647-6_4 fatcat:6febgpanvrfpbbihvvwqsn77zq

The Power of Negations in Cryptography [chapter]

Siyao Guo, Tal Malkin, Igor C. Oliveira, Alon Rosen
2015 Lecture Notes in Computer Science  
The study of monotonicity and negation 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  ... 
doi:10.1007/978-3-662-46494-6_3 fatcat:e6fea6drprg2hh6n4lukojdz2a

Some consequences of the existence of pseudorandom generators

E. Allender
1987 Proceedings of the nineteenth annual ACM conference on Theory of computing - STOC '87  
This paper introduces a type of 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  ... 
doi:10.1145/28395.28412 dblp:conf/stoc/Allender87 fatcat:g2b5rruelfeodgf4e7spzxcsau

Some consequences of the existence of pseudorandom generators

Eric W. Allender
1989 Journal of computer and system sciences (Print)  
This paper introduces a type of 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  ... 
doi:10.1016/0022-0000(89)90021-4 fatcat:hqvwyaq7unh35phl6cuwcnyuca

On transformation of interactive proofs that preserve the prover's complexity

Salil Vadhan
2000 Proceedings of the thirty-second annual ACM symposium on Theory of computing - STOC '00  
On transformations of interactive 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.  ... 
doi:10.1145/335305.335330 dblp:conf/stoc/Vadhan00 fatcat:37wn3ym4zrdbnddwgv6lb5cmey

On systems of complexity one in the primes [article]

Kevin Henriot
2014 arXiv   pre-print
Consider a translation-invariant system of linear equations V x = 0 of 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.  ... 
arXiv:1403.7040v2 fatcat:to7cmkfpgvhy3nqzedinq2czuq

Pseudorandom Functions: Three Decades Later [chapter]

Andrej Bogdanov, Alon Rosen
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  ... 
doi:10.1007/978-3-319-57048-8_3 fatcat:dwdqcxanardkthw4oon7qn7aia

Space Pseudorandom Generators by Communication Complexity Lower Bounds

Anat Ganor, Ran Raz, Marc Herbstritt
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.  ... 
doi:10.4230/lipics.approx-random.2014.692 dblp:conf/approx/GanorR14 fatcat:zgrsvyodbna2zid3hnktfx3qla

Immunity and pseudorandomness of context-free languages

Tomoyuki Yamakami
2011 Theoretical Computer Science  
, there is no almost 1-1 weakly 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.  ... 
doi:10.1016/j.tcs.2011.07.013 fatcat:snlqltddvrdehce22ky5n32mga

BPHSPACE(S)⊆DSPACE(S3/2)

Michael Saks, Shiyu Zhou
1999 Journal of computer and system sciences (Print)  
The algorithm employs Nisan's 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.  ... 
doi:10.1006/jcss.1998.1616 fatcat:t22siallszb37ckho4ut7gioqm

Pseudorandomness and derandomization

Luca Trevisan
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.  ... 
doi:10.1145/2090276.2090287 fatcat:q6voqoi3abah3omf3di6u6q4qe
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