How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
How to construct random functions
Journal of the ACM (JACM)
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
Hard-core distributions for somewhat hard problems
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Pairwise Independence and Derandomization
Pairwise Independence and Derandomization
On obfuscating point functions
Proceedings of the thirty-seventh 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
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
On the randomness complexity of efficient sampling
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Weak Pseudorandom Functions in Minicrypt
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
The uniform hardcore lemma via approximate Bregman projections
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
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
TCC'11 Proceedings of the 8th conference on Theory of cryptography
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
TCC'10 Proceedings of the 7th 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
A new pseudorandom generator from collision-resistant hash functions
CT-RSA'12 Proceedings of the 12th conference on Topics in Cryptology
Characterizing pseudoentropy and simplifying pseudorandom generator constructions
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
On the Power of the Randomized Iterate
SIAM Journal on Computing
Public-Key cryptography from new multivariate quadratic assumptions
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
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In a seminal paper, Håstad, Impagliazzo, Levin, and Luby showed that pseudorandom generators exist if and only if one-way functions exist. The construction they propose to obtain a pseudorandom generator from an n-bit one-way function uses $\mathcal{O}(n^8)$ random bits in the input (which is the most important complexity measure of such a construction). In this work we study how much this can be reduced if the one-way function satisfies a stronger security requirement. For example, we show how to obtain a pseudorandom generator which satisfies a standard notion of security using only $\mathcal{O}(n^4log^2(n))$ bits of randomness if a one-way function with exponential security is given, i.e., a one-way function for which no polynomial time algorithm has probability higher than 2−cn in inverting for some constant c. Using the uniform variant of Impagliazzo's hard-core lemma given in [7] our constructions and proofs are self-contained within this paper, and as a special case of our main theorem, we give the first explicit description of the most efficient construction from [6].