The quadratic extension extractor for (hyper)elliptic curves in odd characteristic

Abstract

We propose a simple and efficient deterministic extractor for the (hyper)elliptic curve C, defined over double-struck F signq2, where q is some power of an odd prime. Our extractor, for a given point P on C, outputs the first double-struck F signq-coefficient of the abscissa of the point P. We show that if a point P is chosen uniformly at random in C, the element extracted from the point P is indistinguishable from a uniformly random variable in double-struck F signq. © Springer-Verlag Berlin Heidelberg 2007.