New table look-up methods for faster Frobenius map based scalar multiplication over GF(pn)

Abstract

We describe a new scalar multiplication algorithm for elliptic and hyperelliptic curve cryptosystems. The algorithm is obtained by combining Koblitz's idea of using Frobenius automorphism along with a very special kind of look-up table. In the case where the base point is unknown, we present an efficient algorithm to compute the look-up table online. Our algorithm applies to prime power fields GF(pn). One important subclass of such fields are Optimal Extension Fields (OEF's) which are believed to be ideal for efficient implementation of cryptographic primitives. Over prime power fields, our algorithm compares favourably to other known algorithms for scalar multiplication. © Springer-Verlag Berlin Heidelberg 2004.