NP is as easy as detecting unique solutions
Theoretical Computer Science
Privacy amplification by public discussion
SIAM Journal on Computing - Special issue on cryptography
Pseudo-random generation from one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Conditionally-perfect secrecy and a provably-secure randomized cipher
Journal of Cryptology - Eurocrypt '90
The computational complexity of universal hashing
Theoretical Computer Science - Special issue on structure in complexity theory
On recycling the randomness of states in space bounded computation
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
A Pseudorandom Generator from any One-way Function
SIAM Journal on Computing
Randomness conductors and constant-degree lossless expanders
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Hardness amplification within NP
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Encryption against Storage-Bounded Adversaries from On-Line Strong Extractors
Journal of Cryptology
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
The complexity of constructing pseudorandom generators from hard functions
Computational Complexity
Cryptography with constant computational overhead
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Extractors Using Hardness Amplification
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Efficiency improvements in constructing pseudorandom generators from one-way functions
Proceedings of the forty-second ACM symposium on Theory of computing
Input locality and hardness amplification
TCC'11 Proceedings of the 8th conference on Theory of cryptography
On pseudorandom generators with linear stretch in NC0
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
IEEE Transactions on Information Theory - Part 1
| Hi-index | 0.00 |
We consider the problem of extracting entropy by sparse transformations, namely functions with a small number of overall input-output dependencies. In contrast to previous works, we seek extractors for essentially all the entropy without any assumption on the underlying distribution beyond a min-entropy requirement. We give two simple constructions of sparse extractor families. These are collections of sparse functions such that for any distribution X on inputs of sufficiently high min-entropy, the output of most functions from the collection on input X is statistically close to uniform. For strong extractor families (i.e., functions in the family do not take additional randomness) we give upper and lower bounds on the sparsity that are tight up to a constant factor for a wide range of min-entropies. We then prove that for some min-entropies weak extractor families can achieve better sparsity. We show how this construction can be used towards more efficient parallel transformation of (non-uniform) one-way functions into pseudorandom generators. More generally, sparse extractor families can be used instead of pairwise independence in various randomized or nonuniform settings where sparsity or preserving locality (i.e., parallelism) is of interest.