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  On the uniformity of distribution of the Naor-- Reingold pseudo-random function', Finite Fields and Their Appl [6 citations — 6 self]

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by Igor E. Shparlinski
http://www.comp.mq.edu.au/~igor/NR-Gen.ps
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Abstract:

We show that the new pseudo-random number function, introduced recently by M. Naor and O. Reingold, possess one more attractive and useful property. Namely, it is proved that for almost all values of parameters it produces a uniformly distributed sequence. The proof is based on some recent bounds of character sums with exponential functions.

Citations

505 Random Number Generation and QuasiMonte Carlo Methods – Niederreiter - 1992
97 Number-theoretic constructions of efficient pseudo-random functions – Naor, Reingold - 1997
91 Quasi-Monte Carlo methods and pseudo-random – Niederreiter - 1978
49 Ten Lectures on the Interface Between Analytic Number Theory – Montgomery
42 Reingold O., “Number-Theoretic constructions of efficient pseudorandom functions – Naor - 1997
40 Multiplicative number theory – Davenport - 1980
36 Character sums with exponential functions and their applications – Konyagin, Sharplinski - 1999
23 On the distribution of digits in periodic fractions – Korobov - 1972
23 Exponential Sums and their Applications – Korobov - 1992
18 Shifted primes without large prime factors – Baker, Harman - 1998
15 Primzahlverteilung – Prachar - 1957
13 Zero-free regions for Dirichlet L-functions, and the least prime in an arithmetic progression – Heath-Brown - 1992
11 On the linear complexity of the Naor-- Reingold pseudo-random function – Shparlinski, Silverman - 1999
9 New bounds for Gauss sums derived from kth powers, and for Heilbronn’s exponential – Heath-Brown, Konyagin
8 On the Naor--Reingold pseudo-random number function from elliptic curves – Shparlinski - 2000
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