10th Joint Conf. on Math. and Comp. Sci., May 22–25, 2014, Cluj, Romania
1
Pseudorandomness of binary threshold sequences derived
from multiplicative inverse
László Mérai
Department of Computer Algebra, Eötvös Loránd University, Budapest, Hungary
merai@cs.elte.hu
Let p be a prime and c1 , c2 , . . . , ch ∈ Zp be fixed elements. For initial values x1 , . . . , xh ∈ Zp
consider the sequence (xn ) defined by the linear recursion
xn = c1 xn−1 + . . . + ch xn−h ,
n > h.
The aim of the talk is to study the pseudorandom properties of the following finite binary
sequence ET = {e1 , e2 , . . . , eT } ∈ {1, −1}T built from the linear recursive sequence (xn ) by the
rule
1 if p - f (xn ) and 0 < f −1 (xn ) < p/2
en =
-1 otherwise,
where f −1 (xn ) is the multiplicative inverse of f (xn ) modulo p.