The Finite Field Arithmetic and FPGA Simulation Based on ONB

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.