How to construct random functions
Journal of the ACM (JACM)
One-way functions and Pseudorandom generators
Combinatorica - Theory of Computing
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
Pseudorandomness for network algorithms
STOC '94 Proceedings of the twenty-sixth 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
A Practice-Oriented Treatment of Pseudorandom Number Generators
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
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
On the existence of pseudorandom generators
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
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
A new pseudorandom generator from collision-resistant hash functions
CT-RSA'12 Proceedings of the 12th conference on Topics in Cryptology
A new pseudorandom generator from collision-resistant hash functions
CT-RSA'12 Proceedings of the 12th conference on Topics in Cryptology
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We present a new hash-function-based pseudorandom generator (PRG). Our PRG is reminiscent of the classical constructions iterating a function on a random seed and extracting Goldreich-Levin hardcore bits at each iteration step. The latest PRG of this type that relies on reasonable assumptions (regularity and one-wayness) is due to Haitner et al. In addition to a regular one-way function, each iteration in their "randomized iterate" scheme uses a new pairwise-independent function, whose descriptions are part of the seed of the PRG. Our construction does not use pairwise-independent functions and is thus more efficient, requiring less computation and a significantly shorter seed. Our scheme's security relies on the standard notions of collision-resistance and regularity of the underlying hash function, where the collision-resistance is required to be exponential. In particular, any polynomial-time adversary should have less than 2−n/2 probability of finding collisions, where n is the output size of the hash function. We later show how to relax the regularity assumption by introducing a new notion that we call worst-case regularity, which lower bounds the size of primages of different elements from the range (while the common regularity assumption requires all such sets to be of equal size). Unlike previous results, we provide a concrete security statement.