Pseudo-random generation from one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
The computational complexity of universal hashing
Theoretical Computer Science - Special issue on structure in complexity theory
On the existence of pseudorandom generators
SIAM Journal on Computing
Noise-tolerant learning, the parity problem, and the statistical query model
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
FOCS '04 Proceedings of the 45th Annual IEEE 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
One-way functions are essential for complexity based cryptography
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Security preserving amplification of hardness
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Goldreich's One-Way Function Candidate and Myopic Backtracking Algorithms
TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
On the Security of Goldreich's One-Way Function
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Cryptography with constant input locality
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
Public-key cryptography from different assumptions
Proceedings of the forty-second ACM symposium on Theory of computing
On hardness amplification of one-way functions
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
On the power of the randomized iterate
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
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
Sparse extractor families for all the entropy
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
| Hi-index | 0.00 |
We establish new hardness amplification results for one-way functions in which each input bit influences only a small number of output bits (a.k.a. input-local functions). Our transformations differ from previous ones in that they approximately preserve input locality and at the same time retain the input size of the original function. Let f : {0, 1}n → {0, 1}m be a one-way function with input locality d, and suppose that f cannot be inverted in time exp(Õ(√n ċ d) on an ε-fraction of inputs. Our main results can be summarized as follows: - If f is injective then it is equally hard to invert f on a (1-ε)-fraction of inputs. - If f is regular then there is a function g: {0, 1}n → {0, 1}m+O(n) that is d + O(log3 n) input local and is equally hard to invert on a (1 - ε)-fraction of inputs. A natural candidate for a function with small input locality and for which no sub-exponential time attacks are known is Goldreich's one-way function. To make our results applicable to this function, we prove that when its input locality is set to be d = O(log n) certain variants of the function are (almost) regular with high probability. In some cases, our techniques are applicable even when the input locality is not small. We demonstrate this by extending our first main result to one-way functions of the "parity with noise" type.