YOU Lin, YANG Yilin, GAO Shuhong. Divisor Class Halving Algorithms for Genus Three Hyperelliptic Curves[J]. Chinese Journal of Electronics, 2020, 29(1): 97-105. doi: 10.1049/cje.2019.10.005
Citation: YOU Lin, YANG Yilin, GAO Shuhong. Divisor Class Halving Algorithms for Genus Three Hyperelliptic Curves[J]. Chinese Journal of Electronics, 2020, 29(1): 97-105. doi: 10.1049/cje.2019.10.005

Divisor Class Halving Algorithms for Genus Three Hyperelliptic Curves

doi: 10.1049/cje.2019.10.005
Funds:  This work is supported by the Key Program of the Nature Science Foundation of Zhejiang Province of China (No.LZ17F020002) and the National Natural Science Foundation of China (No.61772166).
  • Received Date: 2016-05-10
  • Rev Recd Date: 2019-03-13
  • Publish Date: 2020-01-10
  • 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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