Fast Scalar Multiplications on the Curve v2 = up-au-b over the Finite Field of Characteristic p

摘要: Hyperelliptic curves have been widely researched for cryptographic applications, and some special hyperelliptic are often considered practical applications. For efficient implementation of curve cryptosystems, it is crucial to scalar multiplication in the Jacobian groups. Cq: v2 = up-au-b over field $\Fopf_{q}$ with q a power an odd prime p, Duursma Sakurai 2000 presented algorithm 1 b ∈ $\Fopf_{p}$. In this paper, by introducing concept simple divisors, we prove that general divisor can be decomposed into sum divisors. Based on fact, present formula p-scalar multiplications any reduced divisor, then give two algorithms speed up parameters extension Compared signed binary method, computations our cost 55% 76% less.