Journal of Computer and System Sciences
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
Graph nonisomorphism has subexponential size proofs unless the polynomial-time hierarchy collapses
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Reductions in circuit complexity: an isomorphism theorem and a gap theorem
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
Extractors and pseudo-random generators with optimal seed length
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Pseudorandom generators without the XOR lemma
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
Hardness amplification within NP
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Hard-core distributions for somewhat hard problems
FOCS '95 Proceedings of the 36th Annual 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
On Worst-Case to Average-Case Reductions for NP Problems
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Pseudo-random generators for all hardnesses
Journal of Computer and System Sciences - STOC 2002
Using nondeterminism to amplify hardness
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
The complexity of constructing pseudorandom generators from hard functions
Computational Complexity
On Constructing Parallel Pseudorandom Generators from One-Way Functions
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
On the Complexity of Hardness Amplification
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
How to generate cryptographically strong sequences of pseudo random bits
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
No better ways to generate hard NP instances than picking uniformly at random
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
On hardness amplification of one-way functions
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
Hardness amplification proofs require majority
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Hardness Amplification Proofs Require Majority
SIAM Journal on Computing
| Hi-index | 0.00 |
We study the task of hardness amplification which transforms a hard function into a harder one. It is known that in a high complexity class such as exponential time, one can convert worst-case hardness into average-case hardness. However, in a lower complexity class such as NP or sub-exponential time, the existence of such an amplification procedure remains unclear. We consider a class of hardness amplifications called weakly black-box hardness amplification, in which the initial hard function is only used as a black box to construct the harder function. We show that if an amplification procedure in TIME(t) can amplify hardness beyond an O(t) factor, then it must basically embed in itself a hard function computable in TIME(t). As a result, it is impossible to have such a hardness amplification with hardness measured against TIME(t). Furthermore, we show that, for any k ∈ N, if an amplification procedure in ΣkP can amplify hardness beyond a polynomial factor, then it must basically embed a hard function in ΣkP. This in turn implies the impossibility of having such hardness amplification with hardness measured against ΣkP/poly.