中文摘要：

为提高超椭圆曲线上标量乘计算效率，将椭圆曲线上的斜-Frobenius映射推广到超椭圆曲线上，在亏格为4的超椭圆曲线上构造斜-Frobenius映射，通过对亏格为2，3，4的超椭圆曲线上的斜-Frobenius映射，提出超椭圆曲线上斜-Frobenius映射的一般形式。基于超椭圆曲线上的斜-Frobenius映射的一般形式构造新的标量乘算法，提高计算超椭圆曲线上标量乘的效率。实验结果表明，提出的基于超椭圆曲线上的斜一Frobenius映射标量乘效率比基于二进制标量乘算法提高了39％。

英文摘要：

In order to improve the computing efficiency of scalar multiplication on hyperelliptic curves, the skew- Frobenius mapping on the elliptic curve is extended to hyperelliptic curves,and a skew-Frobenius mapping is constructed on the hyperelliptic curve with a genus of 4, through the skew-Frobenius mapping on the hyperelliptic curve which is defined on genus 2,3 and 4. The general form of skew-Frobenius mapping on the hyperelliptic curve is proposed. A new scalar multiplication algorithm is constructed based on the genetal form of skew-Frobenius mapping on hyperelliptic curves, which improve the efficiency of scalar multiplication on hyperelliptic curves. Experimental results show the scalar multiplication of the skew-Frobenius mapping on the hyperelliptic curve is about 39% faster than that of the binary scalar multiplication algorithm.