The Finite Field Arithmetic and FPGA Simulation Based on ONB

Author

Ping Zhang ; Hui Wu ; Yujun Gao ; Xiaoming Wen

Author_Institution

Dept. of Commun. & Autom., Electr. Power Co. of Zhengzhou, Zhengzhou, China

fYear

2012

fDate

21-23 Sept. 2012

Firstpage

1

Lastpage

3

Abstract

Limited domain multiplication is the most basic computing in the elliptic curve cryptosystem(ECC), so it is very important to design fast time-multiplier to improve the speed of encryption and decryption. In this paper, Multiplication matrix was given on the analysis of the multiplication tables of optimal normal basis(ONB) in the finite fields, which can be used by type I and type II. The matrix not only can be got the value of different M in finite field operations, but also can achieve the best balance between resources occupation and speed adjustment. In particular, a hardware implementation of the normal basis multiplier in GF(2 ¹⁶²) was shown as an example using FPGA.

Keywords

field programmable gate arrays; public key cryptography; ECC; FPGA simulation; decryption speed; elliptic curve cryptosystem; encryption speed; fast time-multiplier design; finite field arithmetic; finite field operations; given; hardware implementation; limited domain multiplication; multiplication matrix; multiplication tables; normal basis multiplier; optimal normal basis; resource occupation; speed adjustment; Algorithm design and analysis; Elliptic curve cryptography; Field programmable gate arrays; Finite element methods; Galois fields; Radiation detectors; Registers;

fLanguage

English

Publisher

ieee

Conference_Titel

Wireless Communications, Networking and Mobile Computing (WiCOM), 2012 8th International Conference on

Conference_Location

Shanghai

ISSN

2161-9646

Print_ISBN

978-1-61284-684-2

Type

conf

DOI

10.1109/WiCOM.2012.6478713

Filename

6478713