How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
A fast and simple randomized parallel algorithm for the maximal independent set problem
Journal of Algorithms
Optimization, approximation, and complexity classes
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Small-bias probability spaces: efficient constructions and applications
SIAM Journal on Computing
On the existence of pseudorandom generators
SIAM Journal on Computing
Computerized patient information system in a psychiatric unit: five-year experience
Journal of Medical Systems
Cryptographic primitives based on hard learning problems
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
Tiny families of functions with random properties: a quality-size trade-off for hashing
Proceedings of the workshop on Randomized algorithms and computation
A Pseudorandom Generator from any One-way Function
SIAM Journal on Computing
Loss-less condensers, unbalanced expanders, and extractors
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Relations between average case complexity and approximation complexity
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Randomness conductors and constant-degree lossless expanders
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Foundations of Cryptography: Basic Tools
Foundations of Cryptography: Basic Tools
A complete problem for statistical zero knowledge
Journal of the ACM (JACM)
Tight bounds for depth-two superconcentrators
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
More on Average Case vs Approximation Complexity
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Number-theoretic constructions of efficient pseudo-random functions
Journal of the ACM (JACM)
Foundations of Cryptography: Volume 2, Basic Applications
Foundations of Cryptography: Volume 2, Basic Applications
Correcting errors without leaking partial information
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
On Constructing Parallel Pseudorandom Generators from One-Way Functions
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Constructions of Low-Degree and Error-Correcting \in-Biased Generators
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
SIAM Journal on Computing
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
On the round complexity of covert computation
Proceedings of the forty-second ACM symposium on Theory of computing
Limits on the stretch of non-adaptive constructions of pseudo-random generators
TCC'11 Proceedings of the 8th conference on Theory of cryptography
Verifying proofs in constant depth
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Extractors and Lower Bounds for Locally Samplable Sources
ACM Transactions on Computation Theory (TOCT)
Pseudorandom generators with long stretch and low locality from random local one-way functions
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
A dichotomy for local small-bias generators
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Survey: Innovative approaches for security of small artefacts
Computer Science Review
The Complexity of Distributions
SIAM Journal on Computing
Verifying proofs in constant depth
ACM Transactions on Computation Theory (TOCT)
Robust pseudorandom generators
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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We consider the question of constructing cryptographic pseudorandom generators (PRGs) in NC0, namely ones in which each bit of the output depends on just a constant number of input bits. Previous constructions of such PRGs were limited to stretching a seed of n bits to n +驴o(n) bits. This leaves open the existence of a PRG with a linear (let alone superlinear) stretch in NC0. In this work we study this question and obtain the following main results: We show that the existence of a linear-stretch PRG in NC0驴implies non-trivial hardness of approximation results without relying on PCP machinery. In particular, it implies that Max3SAT is hard to approximate to within some multiplicative constant. We construct a linear-stretch PRG in NC0驴under a specific intractability assumption related to the hardness of decoding "sparsely generated" linear codes. Such an assumption was previously conjectured by Alekhnovich (FOCS 2003).