## Abstract

The aim of this paper is to reduce the number of operations in Cantor's algorithm for the Jacobian group of hyperelliptic curves for genus 4 in projective coordinates. Specifically, we developed explicit doubling and addition formulas for genus 4 hyperelliptic curves over binary fields with h(x) = 1. For these curves, we can perform a divisor doubling in 63M + 19S, while the explicit adding formula requires 203M + 18S, and the mixed coordinates addition (in which one point is given in affine coordinates) is performed in 165M + 15S. These formulas can be useful for public key encryption in some environments where computing the inverse of a field element has a high computational cost (either in time, power consumption or hardware price), in particular with embedded microprocessors.

Original language | English |
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Pages (from-to) | 115-139 |

Number of pages | 25 |

Journal | Advances in Mathematics of Communications |

Volume | 4 |

Issue number | 2 |

DOIs | |

State | Published - May 2010 |

Externally published | Yes |

## Keywords

- Binary field
- Explicit formulas
- Genus 4
- Hyperelliptic curves
- Projective coordinates

## ASJC Scopus subject areas

- Algebra and Number Theory
- Computer Networks and Communications
- Discrete Mathematics and Combinatorics
- Applied Mathematics