How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
A hard-core predicate for all one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
On the existence of pseudorandom generators
SIAM Journal on Computing
Journal of Computer and System Sciences
P = BPP if E requires exponential circuits: derandomizing the XOR lemma
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A Pseudorandom Generator from any One-way Function
SIAM Journal on Computing
List decoding: algorithms and applications
ACM SIGACT News
Learning Polynomials with Queries: The Highly Noisy Case
SIAM Journal on Discrete Mathematics
Extractors and pseudorandom generators
Journal of the ACM (JACM)
Derandomization That Is Rarely Wrong from Short Advice That Is Typically Good
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
Randomization and Derandomization in Space-Bounded Computation
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
Extracting Randomness: How and Why - A survey
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
Randomness vs. Time: De-Randomization under a Uniform Assumption
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Lower bounds on the efficiency of generic cryptographic constructions
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Fast Monte-Carlo Algorithms for Approximate Matrix Multiplication
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Exposure-resilient cryptography
Exposure-resilient cryptography
Deterministic Extractors for Bit-Fixing Sources and Exposure-Resilient Cryptography
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Encryption against Storage-Bounded Adversaries from On-Line Strong Extractors
Journal of Cryptology
Deterministic Extractors for Bit-Fixing Sources by Obtaining an Independent Seed
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
On obfuscating point functions
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Derandomizing polynomial identity tests means proving circuit lower bounds
Computational Complexity
Computational Complexity: A Quantitative Perspective (North-Holland Mathematical Studies)
Computational Complexity: A Quantitative Perspective (North-Holland Mathematical Studies)
Approximating the Weight of the Euclidean Minimum Spanning Tree in Sublinear Time
SIAM Journal on Computing
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Simple extractors via constructions of cryptographic pseudo-random generators
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Deterministic extractors for independent-symbol sources
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
On the Security Loss in Cryptographic Reductions
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
Pseudorandom Generators and Typically-Correct Derandomization
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Typically-correct derandomization
ACM SIGACT News
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There exists a positive constant 驴 T(n) 驴 n 驴 and for any problem L 驴 BPTIME(T(n)), there exists a deterministic algorithm running in poly(T(n)) time which decides L, except for at most a 2驴驴(T(n) logT(n)) fraction of inputs of length n.The proof uses a novel derandomization technique based on a new type of randomness extractors, called exposure-resilient extractors. An exposure-resilient extractor is an efficient procedure that, from a random variable with imperfect randomness, produces randomness that passes all statistical tests including those that have bounded access to the random variable, with adaptive queries that can depend on the string being tested. More precisely, EXT : {0, 1} n 脳 {0, 1} d 驴 {0, 1} m is a (k, 驴)-exposure-resilient extractor resistant to q queries if, when the minentropy of the random variable x is at least k and the random variable y is uniformly distributed, EXT(x, y) looks 驴-random to all statistical tests modeled by oracle circuits of unbounded size that can query q bits of x. Besides the extractor that is needed for the proof of the main result (whose parameters are tailored for this application), we construct, for any 驴 k, 驴)-exposure-resilient extractor with query resistance n 驴, k = n 驴 n 驴(1), 驴 = n 驴驴(1), m = n 驴(1) and d = O(log n).