How to construct random functions
Journal of the ACM (JACM)
One-way functions and Pseudorandom generators
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How to construct pseudorandom permutations from pseudorandom functions
SIAM Journal on Computing - Special issue on cryptography
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
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
Pubic Randomness in Cryptography
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
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How to generate cryptographically strong sequences of pseudo random bits
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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
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Security preserving amplification of hardness
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
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
Pseudorandom generators from one-way functions: a simple construction for any hardness
TCC'06 Proceedings of the Third conference on Theory of Cryptography
Oblivious-Transfer Amplification
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
Efficient pseudorandom generators based on the DDH assumption
PKC'07 Proceedings of the 10th international conference on Practice and theory in public-key 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
S-T connectivity on digraphs with a known stationary distribution
ACM Transactions on Algorithms (TALG)
Input locality and hardness amplification
TCC'11 Proceedings of the 8th conference on Theory of cryptography
General hardness amplification of predicates and puzzles
TCC'11 Proceedings of the 8th conference on Theory of cryptography
Pseudorandom generators for combinatorial shapes
Proceedings of the forty-third annual ACM symposium on Theory of computing
TCC'10 Proceedings of the 7th international conference on Theory of Cryptography
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
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
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We consider two of the most fundamental theorems in Cryptography. The first, due to Håstad et al. [HILL99], is that pseudorandom generators can be constructed from any one-way function. The second due to Yao [Yao82] states that the existence of weak one-way functions (i.e. functions on which every efficient algorithm fails to invert with some noticeable probability) implies the existence of full fledged one-way functions. These powerful plausibility results shape our understanding of hardness and randomness in Cryptography. Unfortunately, the reductions given in [HILL99, Yao82] are not as security preserving as one may desire. The main reason for the security deterioration is the input blow up in both of these constructions. For example, given one-way functions on n bits one obtains by [HILL99] pseudorandom generators with seed length Ω(n8). This paper revisits a technique that we call the Randomized Iterate, introduced by Goldreich, et. al.[GKL93]. This technique was used in to give a construction of pseudorandom generators from regular one-way functions. We simplify and strengthen this technique in order to obtain a similar reduction where the seed length of the resulting generators is as short as ${\cal{O}}(n \log n)$ rather than Ω(n3) in [GKL93]. Our technique has the potential of implying seed-length ${\cal{O}}(n)$, and the only bottleneck for such a result is the parameters of current generators against space bounded computations. We give a reduction with similar parameters for security amplification of regular one-way functions. This improves upon the reduction of Goldreich et al. [GIL+90] in that the reduction does not need to know the regularity parameter of the functions (in terms of security, the two reductions are incomparable). Finally, we show that the randomized iterate may even be useful in the general context of [HILL99]. In Particular, we use the randomized iterate to replace the basic building block of the [HILL99] construction. Interestingly, this modification improves efficiency by an n3 factor and reduces the seed length to ${\cal{O}}(n^7)$ (which also implies improvement in the security of the construction).