# Periodic structure of the exponential pseudorandom number generator

@inproceedings{Kaszian2014PeriodicSO,
title={Periodic structure of the exponential pseudorandom number generator},
author={Jonas Kaszian and Pieter Moree and Igor E. Shparlinski},
booktitle={Applied Algebra and Number Theory},
year={2014}
}
• Published in
Applied Algebra and Number…
4 December 2013
• Computer Science, Mathematics
We investigate the periodic structure of the exponential pseudorandom number generator obtained from the map $x\mapsto g^x\pmod p$ that acts on the set $\{1, \ldots, p-1\}$.
1 Citations

## References

SHOWING 1-10 OF 40 REFERENCES
An Improved Pseudo-Random Generator Based on the Discrete Logarithm Problem
• R. Gennaro
• Computer Science, Mathematics
Journal of Cryptology
• 2004
A new pseudo-random bit generator is constructed that outputs n – c – 1 bits per exponentiation with a c-bit exponent and is among the fastest generators based on hard number-theoretic problems.
Short cycles in repeated exponentiation modulo a prime
• Mathematics, Computer Science
Des. Codes Cryptogr.
• 2010
This work obtains nontrivial upper bounds on the number of fixed points and short cycles in the above dynamical system generated by repeated exponentiations modulo p.
Cycles in Repeated Exponentiation Modulo pn
The number of cycles of the defined dynamical system generated by repeated exponentiations modulo a number is considered for $r=p^n$.
On the distribution of the power generator
• Mathematics, Computer Science
Math. Comput.
• 2001
The uniform distribution of the RSA generator and the Blum-Blum-Shub generator is proved, provided that the period t > m 3/4+δ with fixed δ > 0 and, under the same condition, the uniform distributed of a positive proportion of the leftmost and rightmost bits.
Efficient Pseudorandom Generators Based on the DDH Assumption
• Computer Science, Mathematics
Public Key Cryptography
• 2007
A family of pseudorandom generators based on the decisional Diffie-Hellman assumption is proposed, which can be based on any group of prime order provided that an additional requirement is met (i.e., there exists an efficiently computable function that enumerates the elements of the group).
Fixed Points for Discrete Logarithms
• Mathematics
ANTS
• 2010
We establish a conjecture of Brizolis that for every prime p > 3 there is a primitive root g and an integer x in the interval [1,p − 1] with log g x = x. Here, log g is the discrete logarithm
On the Security of Modular Exponentiation with Application to the Construction of Pseudorandom Generators
• Computer Science, Mathematics
Journal of Cryptology
• 2003
It is shown that the output of the exponentiation modulo a composite function fN,g(x)=gx mod N (where N=P⋅ Q ) is pseudorandom, even when its input is restricted to being half the size (i.e. x< $\sqrt N$).
An Efficient Discrete Log Pseudo Random Generator
• Computer Science, Mathematics
CRYPTO
• 1998
It is shown that discrete exponentiation modulo a prime p can hide n − Ω(log n) bits and be used to discover the discrete log of g s mod p where s has Ω('log n') bits.
Concentration of points on curves in finite fields
• Mathematics, Computer Science
• 2013
We obtain analogues of several recent bounds on the number of solutions of polynomial congruences modulo a prime with variables in short intervals in the case of polynomial equations in high degree
COUNTING FIXED POINTS, TWO-CYCLES, AND COLLISIONS OF THE DISCRETE EXPONENTIAL FUNCTION USING p-ADIC METHODS
• Mathematics
Journal of the Australian Mathematical Society
• 2012
P-adic methods are used, primarily Hensel’s lemma and p-adic interpolation, to count fixed points, two-cycles, collisions, and solutions to related equations modulo powers of a prime p.