Date of Award
2016
Publication Type
Master Thesis
Degree Name
M.A.Sc.
Department
Electrical and Computer Engineering
Keywords
Cantor Algorithm, Elliptic Curve, Explicit Formulae, Hyper Elliptic Curve, Jacobian Curve, Mumford Representation
Supervisor
Wu, Huapeng
Rights
info:eu-repo/semantics/openAccess
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Abstract
In this thesis we have proposed explicit formulae for group operation such as addition and doubling on the Jacobians of Hyper Elliptic Curves genus 2, 3 and 4. The Cantor Algorithm generally involves to perform arithmetic operations in the polynomial ring . The explicit method performs the arithmetic operation in the integer ring of ��. Significant improvement has been made in the explicit formulae algorithm proposed here. Other explicit formulae used Montgomery trick to derive efficient formulae for faster group computation. The method used in this thesis to develop an efficient explicit formula was inspired by the geometric properties in the hyper elliptic curves of genus and by keeping the Jacobian variety curve constant. This formulae take Mumford coordinates as input. The explicit formulae here performs the computation in affine space of genus 2, 3 and 4 of Hyper Elliptic Curves in general form, which can be used to develop Hyper Elliptic Curve Cryptosystem.
Recommended Citation
Asif, Raqib Ahmed, "Efficient Computation For Hyper Elliptic Curve Based Cryptography" (2016). Electronic Theses and Dissertations. 5719.
https://scholar.uwindsor.ca/etd/5719