Title: Efficient Doubling On Jacobian of Genus 2 hyperelliptic Curve over prime fields.

Abstract:
Hyperelliptic curve cryptosystems (HECC) are becoming popular as an alternative to RSA and elliptic curves based systems for public key based security applications. Most time consuming operation on HECC is the scalar multiplication. That is computation kP for a positive integer k and P an element of Jacobian group of hyperelliptic curve. Traditionally scalar multiplication is done by double-and-add method using binary representations of scalars. Hence an efficient doubling will improve the performance of any HECC. An element of Jacobian of hyperelliptic curve can be represented as a pair of polynomials (U, V). We introduce a trick of representing V in a weighted form. This saves the one of the inversion of the two inversions needed for computation of doubling. Overall we save two multiplications on the cost of doubling. We have implemented our formula and tested it.