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 fast and simple randomized parallel algorithm for the maximal independent set problem
Journal of Algorithms
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
RSA and Rabin functions: certain parts are as hard as the whole
SIAM Journal on Computing - Special issue on cryptography
On the construction of a random number generator and random function generators
Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
Pseudorandom generators for space-bounded computations
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Small-bias probability spaces: efficient constructions and applications
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Perfect Local Randomness in Pseudo-Random Sequences
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Simple construction of almost k-wise independent random variables
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
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We call a distribution on n-bit strings (Ɛ, e)-locally random, if for every choice of e ≤ n positions the induced distribution on e-bit strings is in the L1-norm at most Ɛ away from the uniform distribution on e-bit strings. We establish local randomness in polynomial random number generators (RNG) that are candidate one-way functions. Let N be a squarefree integer and let f1, ..., fl be polynomials with coefficients in ZN = Z/NZ. We study the RNG that stretches a random x Ɛ ZN into the sequence of least significant bits of f1(x), ..., fl(x). We show that this RNG provides local randomness if for every prime divisor p of N the polynomials f1,...,fl are linearly independent modulo the subspace of polynomials of degree ≤ 1 in Zp[x]. We also establish local randomness in polynomial random function generators. This yields candidates for cryptographic hash functions. The concept of local randomness in families of functions extends the concept of universal families of hash functions by CARTER and WEGMAN (1979). The proofs of our results rely on upper bounds for exponential sums.