【摘要】 本文给出了素数域上亏格为3的超椭圆曲线退化除子加法和倍点运算的确定性公式,这些公式在有固定基点的超椭圆曲线密码算法,如ElGamal型加密算法、Diffie-Hellman协议的发送方及HECDSA的标量乘算法中都有应用。与标准除子标量乘算法相比,给出的1次和2次退化除子标量乘算法可分别获得33.4%和16.7%的加速,同时基点的表示长度可压缩至标准除子表示长度的1/3或2/3。更多还原

【Abstract】 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.更多还原