Implementation of Finite Field Arithmetic Operations for Polynomial and Normal Basis Representations

DOI

10.2991/iccst-15.2015.25How to use a DOI?

Keywords

Basis conversion, cryptography, elliptic curve cryptography, finite field, normal basis, optimal normal basis

Abstract

Elliptic Curve Cryptography is generally are implemented over prime fields or binary fields. Arithmetic in binary elds can be classified according to the basis representation being used. Two of the most common basis used in binary elds are polynomial basis and normal basis. The optimal normal basis is especially known to be more efficient than polynomial basis because the inversion can be achieved by performing repeated multiplication using the method of Itoh and Tsujii, and squaring can be executed by performing only one cyclic shift operation. In previous research we have built algorithms and implementations on basis conversion between polynomial basis and normal basis. In this paper we will present implementation of arithmetic operation algorithms on both polynomial basis and optimal normal basis representation and the conversion method between them. We will also give comparison of time and space between implementation by using optimal basis representation with conversion and without conversion.

Copyright

© 2015, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Download article (PDF)

TY  - CONF
AU  - Mirza Maulana
AU  - Wenny Franciska Senjaya
AU  - Budi Rahardjo
AU  - Intan Muchtadi-Alamsyah
AU  - Marisa W. Paryasto
PY  - 2015/01
DA  - 2015/01
TI  - Implementation of Finite Field Arithmetic Operations for Polynomial and Normal Basis Representations
BT  - Proceedings of the 3rd International Conference on Computation for Science and Technology
PB  - Atlantis Press
SP  - 129
EP  - 134
SN  - 2352-538X
UR  - https://doi.org/10.2991/iccst-15.2015.25
DO  - 10.2991/iccst-15.2015.25
ID  - Maulana2015/01
ER  -