How to construct random functions
Journal of the ACM (JACM)
One-way functions and Pseudorandom generators
Combinatorica - Theory of Computing
How to construct pseudorandom permutations from pseudorandom functions
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
A hard-core predicate for all one-way functions
STOC '89 Proceedings of the twenty-first 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
Universal classes of hash functions (Extended Abstract)
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
Key agreement from weak bit agreement
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
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
Pseudorandom generators from one-way functions: a simple construction for any hardness
TCC'06 Proceedings of the Third conference on Theory of Cryptography
Weak Pseudorandom Functions in Minicrypt
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Basing weak public-key cryptography on strong one-way functions
TCC'08 Proceedings of the 5th conference on Theory of cryptography
Saving private randomness in one-way functions and pseudorandom generators
TCC'08 Proceedings of the 5th conference on Theory of cryptography
Efficiency improvements in constructing pseudorandom generators from one-way functions
Proceedings of the forty-second ACM symposium on Theory of computing
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
On the power of the randomized iterate
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
A new pseudorandom generator from collision-resistant hash functions
CT-RSA'12 Proceedings of the 12th conference on Topics in Cryptology
On the Power of the Randomized Iterate
SIAM Journal on Computing
Resource-based corruptions and the combinatorics of hidden diversity
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
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In their seminal paper [HILL99], Håstad, Impagliazzo, Levin and Luby show that a pseudorandom generator can be constructed from any one-way function. This plausibility result is one of the most fundamental theorems in cryptography and helps shape our understanding of hardness and randomness in the field. Unfortunately, the reduction of [HILL99] is not nearly as efficient nor as security preserving as one may desire. The main reason for the security deterioration is the blowup to the size of the input. In particular, given one-way functions on n bits one obtains by [HILL99] pseudorandom generators with seed length $\cal{O}$(n8). Alternative constructions that are far more efficient exist when assuming the one-way function is of a certain restricted structure (e.g. a permutations or a regular function). Recently, Holenstein [Hol06] addressed a different type of restriction. It is demonstrated in [Hol06] that the blowup in the construction may be reduced when considering one-way functions that have exponential hardness. This result generalizes the original construction of [HILL99] and obtains a generator from any exponentially hard one-way function with a blowup of $\cal{O}$(n5), and even $\cal{O}$(n4 log2n) if the security of the resulting pseudorandom generator is allowed to have weaker (yet super-polynomial) security In this work we show a construction of a pseudorandom generator from any exponentially hard one-way function with a blowup of only $\cal{O}$(n2) and respectively, only $\cal{O}$(n log2n) if the security of the resulting pseudorandom generator is allowed to have only super-polynomial security. Our technique does not take the path of the original [HILL99] methodology, but rather follows by using the tools recently presented in [HHR05] (for the setting of regular one-way functions) and further developing them