One-way functions and pseudorandom generators
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
On the existence of pseudorandom generators
SIAM Journal on Computing
A Pseudorandom Generator from any One-way Function
SIAM Journal on Computing
Pseudorandom generators without the XOR lemma
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
Relations between average case complexity and approximation complexity
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Foundations of Cryptography: Basic Tools
Foundations of Cryptography: Basic Tools
On Pseudorandom Generators in NC
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Pubic Randomness in Cryptography
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
More on Average Case vs Approximation Complexity
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Number-theoretic constructions of efficient pseudo-random functions
Journal of the ACM (JACM)
Ruling Out PTAS for Graph Min-Bisection, Densest Subgraph and Bipartite Clique
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Exponential Lower Bounds for the Running Time of DPLL Algorithms on Satisfiable Formulas
Journal of Automated Reasoning
SIAM Journal on Computing
Cryptography with constant computational overhead
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
On Pseudorandom Generators with Linear Stretch in NC0
Computational Complexity
The influence of variables on Boolean functions
SFCS '88 Proceedings of the 29th 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
An improved pseudorandom generator based on hardness of factoring
SCN'02 Proceedings of the 3rd international conference on Security in communication networks
Public-key cryptography from different assumptions
Proceedings of the forty-second ACM symposium on Theory of computing
Detecting high log-densities: an O(n¼) approximation for densest k-subgraph
Proceedings of the forty-second ACM symposium on Theory of computing
Efficiency improvements in constructing pseudorandom generators from one-way functions
Proceedings of the forty-second ACM symposium on Theory of computing
Computational complexity and information asymmetry in financial products
Communications of the ACM
Input locality and hardness amplification
TCC'11 Proceedings of the 8th conference on Theory of cryptography
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
A dichotomy for local small-bias generators
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Answering n{2+o(1)} counting queries with differential privacy is hard
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Robust pseudorandom generators
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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We continue the study of locally-computable pseudorandom generators (PRG) G:{0,1}n - {0,1}m that each of their outputs depend on a small number of d input bits. While it is known that such generators are likely to exist for the case of small sub-linear stretch m=n+n1-δ, it is less clear whether achieving larger stretch such as m=n+Ω(n), or even m=n1+δ is possible. The existence of such PRGs, which was posed as an open question in previous works, has recently gained an additional motivation due to several interesting applications. We make progress towards resolving this question by obtaining several local constructions based on the one-wayness of "random" local functions -- a variant of an assumption made by Goldreich (ECCC 2000). Specifically, we construct collections of PRGs with the following parameters: 1. Linear stretch m=n+Ω(n) and constant locality d=O(1). 2. Polynomial stretch m=n1+δ and any (arbitrarily slowly growing) super-constant locality d=ω(1), e.g., log*n. 3. Polynomial stretch m=n1+δ, constant locality d=O(1), and inverse polynomial distinguishing advantage (as opposed to the standard case of n-ω(1)). As an additional contribution, we show that our constructions give rise to strong inapproximability results for the densest-subgraph problem in d-uniform hypergraphs for constant d. This allows us to improve the previous bounds of Feige (STOC 2002) and Khot (FOCS 2004) from constant inapproximability factor to nε-inapproximability, at the expense of relying on stronger assumptions.