Title :
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
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;
Conference_Titel :
Wireless Communications, Networking and Mobile Computing (WiCOM), 2012 8th International Conference on
Conference_Location :
Shanghai
Print_ISBN :
978-1-61284-684-2
DOI :
10.1109/WiCOM.2012.6478713
