How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
Journal of Computer and System Sciences
Designing programs that check their work
Journal of the ACM (JACM)
BPP has subexponential time simulations unless EXPTIME has publishable proofs
Computational Complexity
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
Extractors and pseudo-random generators with optimal seed length
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
On pseudorandomness and resource-bounded measure
Theoretical Computer Science
Pseudorandom generators without the XOR lemma
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
Modern Cryptography, Probabilistic Proofs, and Pseudorandomness
Modern Cryptography, Probabilistic Proofs, and Pseudorandomness
Graph Nonisomorphism Has Subexponential Size Proofs Unless the Polynomial-Time Hierarchy Collapses
SIAM Journal on Computing
Proceedings of the 7th Annual Symposium on Theoretical Aspects of Computer Science
STACS '90 Proceedings of the 7th Annual Symposium on Theoretical Aspects of Computer Science
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
Easiness Assumptions and Hardness Tests: Trading Time for Zero Error
COCO '00 Proceedings of the 15th Annual IEEE Conference on Computational Complexity
Hard-core distributions for somewhat hard problems
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Randomness vs. Time: De-Randomization under a Uniform Assumption
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Derandomizing Arthur-Merlin Games Using Hitting Sets
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Near-Optimal Conversion of Hardness into Pseudo-Randomness
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
In Search of an Easy Witness: Exponential Time vs. Probabilistic Polynomial Time
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
Pseudorandomness and Average-Case Complexity via Uniform Reductions
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
Extractors from Reed-Muller Codes
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Simple Extractors for All Min-Entropies and a New Pseudo-Random Generator
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Some improvements to total degree tests
ISTCS '95 Proceedings of the 3rd Israel Symposium on the Theory of Computing Systems (ISTCS'95)
Pseudo-random generators for all hardnesses
Journal of Computer and System Sciences - STOC 2002
Encryption against Storage-Bounded Adversaries from On-Line Strong Extractors
Journal of Cryptology
Uniform hardness versus randomness tradeoffs for Arthur-Merlin games
Computational Complexity
Derandomizing polynomial identity tests means proving circuit lower bounds
Computational Complexity
Reconstructive dispersers and hitting set generators
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
A (de)constructive approach to program checking
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
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
Hi-index | 0.00 |
In 1998, Impagliazzo and Wigderson [18] proved a hardnessvs. randomness tradeoff for BPP in the uniform setting,which was subsequently extended to give optimal tradeoffs for thefull range of possible hardness assumptions by Trevisan and Vadhan [29] (in a slightly weaker setting). In 2003, Gutfreund,Shaltiel and Ta-Shma [11] proved a uniform hardness vs. randomness tradeoff for AM, but that result only worked on the "high-end" of possible hardness assumptions. In this work, we give uniform hardness vs. randomness tradeoffsfor AM that are near-optimal for the full range of possiblehardness assumptions. Following [11], we do this by constructing a hitting-set-generator (HSG) for AM with "resilient reconstruction." Our construction is a recursive variant of the Miltersen-Vinodchandran HSG [24], the only known HSG construction with this required property. The main new idea is to have the reconstruction procedure operate implicitly and locally on superpolynomially large objects, using tools from PCPs(low-degree testing, self-correction) together with a novel use ofextractors that are built from Reed-Muller codes [28, 26] for a sort of locally-computable error-reduction. As a consequence we obtain gap theorems for AM (and AM ∩ coAM) that state, roughly, that either AM (or AM ∩ coAM)protocols running in time t(n) can simulate all of EXP("Arthur-Merlin games are powerful"), or else all of AM (or AM ∩ coAM) can be simulated in nondeterministic time s(n) ("Arthur-Merlin games can be derandomized"), for a near-optimal relationship between t(n) and s(n). As in GST, the case of AM ∩ coAM yields a particularly clean theorem that is ofspecial interest due to the wide array of cryptographic and other problems that lie in this class.