Divisor Class Halving Algorithms for Genus Three Hyperelliptic Curves  

作　　者：YOU Lin YANG Yilin GAO Shuhong 

机构地区：[1]School of Cyberspace Security,Hangzhou Dianzi University,Hangzhou 310013,China [2]School of Mathematical and Statistical Sciences,Clemson University,Clemson SC 29634-0975,USA

出　　处：《Chinese Journal of Electronics》2020年第1期97-105,共9页电子学报（英文版）

基　　金：supported by the Key Program of the Nature Science Foundation of Zhejiang Province of China(No.LZ17F020002);the National Natural Science Foundation of China(No.61772166)

摘　　要：In an(hyper)elliptic curve cryp to sys tem,the most important operation or the most time-consuming operation is the divisor scalar multiplication which consists of a sequence of doubling(of divisor)and addition(of two divisors).Point halving algorithms for elliptic curve cryptosystem and divisor halving algorithms for genus-2 hyperelliptic curve cryptosystem had been successively put forward to take the place of doubling algorithms for speeding up(hyper)elliptic curve cryptosystem.We present an outline for an algorithm for divisor halving on genus-3 hyperelliptic curves over the binary field and give some explicit formulae for a class of genus-3 curves.Our algorithm improves previously known best doubling algorithms in most cases.A halve-and-add binary method for divisor scalar multiplications is presented.In an(hyper)elliptic curve cryptosystem,the most important operation or the most time-consuming operation is the divisor scalar multiplication which consists of a sequence of doubling(of divisor) and addition(of two divisors). Point halving algorithms for elliptic curve cryptosystem and divisor halving algorithms for genus-2 hyperelliptic curve cryptosystem had been successively put forward to take the place of doubling algorithms for speeding up(hyper)elliptic curve cryptosystem. We present an outline for an algorithm for divisor halving on genus-3 hyperelliptic curves over the binary field and give some explicit formulae for a class of genus-3 curves.Our algorithm improves previously known best doubling algorithms in most cases. A halve-and-add binary method for divisor scalar multiplications is presented.

关 键 词：Genus-3 hyperelliptic curve cryptosys tem Divisor scalar multiplication Divisor doubling Divisor halving. 

分 类 号：O186.11[理学—数学]