Pseudo-randomness of discrete-log sequences from elliptic curves

Abstract

We investigate an upper bound on the discrepancy and a lower bound on the linear complexity of a class of sequences, derived from elliptic curves by using discrete logarithm in this paper. The results indicate that these sequences may have 'nice' pseudo-random properties. The important tool in the proof is certain character sums estimate along elliptic curves. In addition, we apply linear recurrence relation over elliptic curves to output binary sequences with very interesting pseudo-random behavior. © 2008 Springer-Verlag Berlin Heidelberg.