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
Pseudo-random generators under uniform assumptions
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Small-bias probability spaces: efficient constructions and applications
SIAM Journal on Computing
On the existence of pseudorandom generators
SIAM Journal on Computing
Pseudorandomness for network algorithms
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Journal of Computer and System Sciences
Security-preserving hardness-amplification for any regular one-way function
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
Foundations of Cryptography: Basic Tools
Foundations of Cryptography: Basic Tools
Pubic Randomness in Cryptography
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
On Security Preserving Reductions - Revised Terminology
On Security Preserving Reductions - Revised Terminology
Key agreement from weak bit agreement
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
SIAM Journal on 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
One-way functions are essential for complexity based cryptography
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
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
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
Efficient pseudorandom generators from exponentially hard one-way functions
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
On the power of the randomized iterate
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Pseudorandom generators from one-way functions: a simple construction for any hardness
TCC'06 Proceedings of the Third conference on Theory of Cryptography
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We consider two of the most fundamental theorems in cryptography. The first, due to Håstad et al. [SIAM J. Comput., 28 (1999), pp. 1364-1396] is that pseudorandom generators can be constructed from any one-way function. The second, due to Yao [Proceedings of the $23$rd Annual Symposium on Foundations of Computer Science (FOCS), 1982, pp. 80-91], states that the existence of weak one-way functions implies the existence of full-fledged one-way functions. These powerful plausibility results shape our understanding of hardness and randomness in cryptography, but unfortunately their proofs are not as tight (i.e., security preserving) as one may desire. This work revisits a technique that we call the randomized iterate, introduced by Goldreich, Krawczyk, and Luby [SIAM J. Comput., 22 (1993), pp. 1163-1175]. This technique was used by Goldreich, Krawczyk, and Luby [SIAM J. Comput., 22 (1993), pp. 1163-1175] to give a construction of pseudorandom generators from regular one-way functions. We simplify and strengthen this technique in order to obtain a similar construction, where the seed length of the resulting generators is as short as $\Theta(n \log n)$ (rather than $\Theta(n^3)$ achieved by Goldreich, Krawczyk, and Luby [SIAM J. Comput., 22 (1993), pp. 1163-1175]). Our technique has the potential of implying seed length $\Theta(n)$, and the only bottleneck for such a result are the parameters of current generators against bounded-space computations. We give a construction with similar parameters for security amplification of regular one-way functions. This improves upon the construction of Goldreich et al. [Proceedings of the $31$st Annual Symposium on Foundations of Computer Science, (FOCS), 1990, pp. 318-326] in that the construction does not need to “know" the regularity parameter of the functions (in terms of security, the two reductions are incomparable). In addition, we use the randomized iterate to show a construction of a pseudorandom generator based on an exponentially hard one-way function that has a seed length of only $\Theta(n^2)$. This improves a recent result of Holenstein [Proceedings of the Theory of Cryptography, Third Theory of Cryptography Conference (TCC), 2006] that shows a construction with seed length $\Theta(n^5)$ based on such one-way functions. Finally, we show that the randomized iterate may even be useful in the general context of Håstad et al. [SIAM J. Comput., 28 (1999), pp. 1364-1396]. In particular, we use the randomized iterate to replace the basic building block of the Håstad et al. [SIAM J. Comput., 28 (1999), pp. 1364-1396] construction. Interestingly, this modification improves efficiency by an $\Theta(n^2)$ factor and reduces the seed length to $\Theta(n^7)$ (which also implies improvement in the security of the construction).