42 research outputs found
Multisequences with high joint nonlinear complexity
We introduce the new concept of joint nonlinear complexity for multisequences
over finite fields and we analyze the joint nonlinear complexity of two
families of explicit inversive multisequences. We also establish a
probabilistic result on the behavior of the joint nonlinear complexity of
random multisequences over a fixed finite field
Full Orbit Sequences in Affine Spaces via Fractional Jumps and Pseudorandom Number Generation
Let be a positive integer. In this paper we provide a general theory to
produce full orbit sequences in the affine -dimensional space over a finite
field. For our construction covers the case of the Inversive Congruential
Generators (ICG). In addition, for we show that the sequences produced
using our construction are easier to compute than ICG sequences. Furthermore,
we prove that they have the same discrepancy bounds as the ones constructed
using the ICG.Comment: To appear in Mathematics of Computatio
On the Degree Growth in Some Polynomial Dynamical Systems and Nonlinear Pseudorandom Number Generators
In this paper we study a class of dynamical systems generated by iterations
of multivariate polynomials and estimate the degreegrowth of these iterations.
We use these estimates to bound exponential sums along the orbits of these
dynamical systems and show that they admit much stronger estimates than in the
general case and thus can be of use for pseudorandom number generation.Comment: Mathematics of Computation (to appear
On the Distribution of the Power Generator over a Residue Ring for Parts of the Period
This paper studies the distribution of the power generator of pseudorandom numbers over a residue ring for parts of the period. These results compliment some recently obtained distribution bounds of the power generator modulo an arbitrary number for the entire period. Also, the arbitrary modulus case may have some cryptography related applications and could be of interest in other settings which require quality pseudorandom numbers.This paper studies the distribution of the power generator of pseudorandom numbers over a residue ring for parts of the period. These results compliment some recently obtained distribution bounds of the power generator modulo an arbitrary number for the entire period. Also, the arbitrary modulus case may have some cryptography related applications and could be of interest in other settings which require quality pseudorandom numbers
On lattice profile of the elliptic curve linear congruential generators
Lattice tests are quality measures for assessing the intrinsic structure of pseudorandom number generators. Recently a new lattice test has been introduced by Niederreiter and Winterhof. In this paper, we present a general inequality that is satisfied by any periodic sequence. Then, we analyze the behavior of the linear congruential generators on elliptic curves (EC-LCG) under this new lattice test and prove that the EC-LCG passes it up to very high dimensions. We also use a result of Brandstätter and Winterhof on the linear complexity profile related to the correlation measure of order k to present lower bounds on the linear complexity profile of some binary sequences derived from the EC-LCG