How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
How to construct random functions
Journal of the ACM (JACM)
A simple unpredictable pseudo random number generator
SIAM Journal on Computing
A simple parallel algorithm for the maximal independent set problem
SIAM Journal on Computing
The bit security of modular squaring given partial factorization of the modulos
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
One-way functions and Pseudorandom generators
Combinatorica - Theory of Computing
RSA and Rabin functions: certain parts are as hard as the whole
SIAM Journal on Computing - Special issue on cryptography
How to construct pseudorandom permutations from pseudorandom functions
SIAM Journal on Computing - Special issue on cryptography
On the power of two-point based sampling
Journal of Complexity
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 generation of cryptographically strong pseudorandom sequences
ACM Transactions on Computer Systems (TOCS)
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Graph Algorithms
DIGITALIZED SIGNATURES AND PUBLIC-KEY FUNCTIONS AS INTRACTABLE AS FACTORIZATION
DIGITALIZED SIGNATURES AND PUBLIC-KEY FUNCTIONS AS INTRACTABLE AS FACTORIZATION
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
Homogeneous measures and polynomial time invariants
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
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Pseudorandom generators (suggested and developed by Blum and Micali and Yao) are efficient deterministic programs that expand a randomly selected k -bit seed into a much longer pseudorandom bit sequence which is indistinguishable in polynomial time from an (equally long) sequence of unbiased coin tosses. Pseudorandom generators are known to exist assuming the existence of functions that cannot be efficiently inverted on the distributions induced by applying the function iteratively polynomially many times. This sufficient condition is also a necessary one, but it seems difficult to check whether particular functions, assumed to be one-way, are also one-way on their iterates. This raises the fundamental question whether the mere existence of one-way functions suffices for the construction of pseudorandom generators.In this paper we present progress towards resolving this question. We consider regular functions, in which every image of a k-bit string has the same number of preimages of length k. We show that if a regular function is one-way then pseudorandom generators do exist. In particular, assuming the intractability of general factoring, we can now prove that pseudorandom generators do exist. Other applications are the construction of pseudorandom generators based on the conjectured intractability of decoding random linear codes, and on the assumed average case difficulty of combinatorial problems as subset-sum.