The Quadratic Extension Extractor for (Hyper)Elliptic Curves in Odd Characteristic

We propose a simple and efficient deterministic extractor for the (hyper)elliptic curve C, defined over Fq2 , where q is some power of an odd prime. Our extractor, for a given point P on C, outputs the first Fq-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 Fq.

• Type: Conference
• Year: 2007
• Where: WAIFI
• Authors: Reza Rezaeian Farashahi, Ruud Pellikaan
• Keywords: Efficient Deterministic Extractor, Hyper)elliptic Curve C, Mathematics, Odd Prime, WAIFI 2007