2010•Unpublished venueRequires access

Co-Z Divisor Addition Formulae in Jacobian of Genus 2 Hyperelliptic Curves over Prime Fields.

Vladyslav Kovtun, Irina Sagir

Abstract

Abstract—in this paper we proposed a new approach to divisor scalar multiplication in Jacobian of genus 2 hyperelliptic curves over fields with odd characteristic, without field inversion. It is based on improved addition formulae of the weight 2 divisors in projective divisor representation in most frequent case that suit very well to scalar multiplication algorithms based on Euclidean addition chains. Keywords-hyperelliptic curve, divisor, Jacobian, addition formulae, exponentiation, projective representation

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Key concepts: Hyperelliptic curve, Hyperelliptic curve cryptography, Scalar multiplication, Mathematics, Jacobian matrix and determinant, Divisor (algebraic geometry), Finite field, Exponentiation