Divisor Class Halving Algorithms for Genus Three Hyperelliptic Curves | Zendy

YOU Lin | Zendy; YANG Yilin | Zendy; GAO Shuhong | Zendy

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Divisor 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) , scalar multiplication , hyperelliptic curve , mathematics , hyperelliptic curve cryptography , elliptic curve , cryptosystem , algorithm , hessian form of an elliptic curve , genus , jacobian curve , finite field , arithmetic , discrete mathematics , schoof's algorithm , elliptic curve cryptography , pure mathematics , computer science , cryptography , public key cryptography , encryption , quarter period , botany , biology , operating system

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.

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