Elliptic curve pseudorandom sequence generators

Abstract

In this paper, we introduce a new approach to the genera-tion of binary sequences by applying trace functions to elliptic curvesover GF(2m). We call these sequences elliptic curve pseudorandom se-quences (EC-sequence). We determine their periods, distribution of zerosand ones, and linear spans for a class of EC-sequences generated fromsupersingular curves. We exhibit a class of EC-sequences which has halfperiod as a lower bound for their linear spans. EC-sequences can beconstructed algebraically and can be generated eficiently in softwareor hardware by the same methods that are used for implementation ofelliptic curve public-key cryptosystems.