Speeding up point multiplication on hyperelliptic curves with efficiently-computable endomorphisms

Abstract

As Koblitz curves were generalized to hyperelliptic Koblitz curves for faster point multiplication by Güunter, et al. [10] we extend the recent work of Gallant, et al. [8] to hyperelliptic curves. So the extended method for speeding point multiplication applies to a much larger family of hyperelliptic curves over finite fields that have efficiently-computable endomorphisms. For this special family of curves, a speedup of up to 55 (59) % can be achieved over the best general methods for a 160-bit point multiplication in case of genus g =2 (3).