Open AccessDivisor Class Halving Algorithms for Genus Three Hyperelliptic Curves
Author(s) -
YOU Lin,
YANG Yilin,
GAO Shuhong
Publication year - 2020
Publication title -
chinese journal of electronics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.267
H-Index - 25
eISSN - 2075-5597
pISSN - 1022-4653
DOI - 10.1049/cje.2019.10.005
Subject(s) - divisor (algebraic geometry) , genus , hyperelliptic curve , class (philosophy) , mathematics , algorithm , hyperelliptic curve cryptography , combinatorics , computer science , artificial intelligence , botany , biology , finite field , public key cryptography , elliptic curve cryptography , operating system , encryption
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.