Fast Arithmetic of Genus 3 Hyperelliptic Curves over Prime Fields

Explicit formulae for addition and doubling on genus 3 hyperelliptic curve over prime fields using degenerate divisors are presented, which can be applied to scalar multiplications of hyperelliptic curve cryptosystems with a fixed base point, e.g., ElGamal-type encryption, the sender of Diffie-Hellman and HECDSA. Compared with scalar multiplications using standard divisors, the proposed scheme using degenerate divisors of degree 1 or 2 can attain a speed-up of approximately 33.4% and 16.7%, respectively. At the same time, the representation of the base point can be compressed to one third or two thirds of standard divisors.