Polynomial basis 방식의 3배속 직렬 유한체 곱셈기

Efficient finite field operation in the elliptic curve (EC) public key cryptography algorithm, which attracts much of latest issues in the applications in information security, is very important. Traditional serial finite multipliers root from Mastrovito's serial multiplication architecture. In this paper, we adopt the polynomial basis and propose a new finite field multiplier, inducing numerical expressions which can be applied to exhibit 3 times as much performance as the Mastrovito's. We described the proposed multiplier with HDL to verify and evaluate as a proper hardware IP. HDL-implemented serial GF (Galois field) multiplier showed 3 times as fast speed as the traditional serial multiplier's adding only partial-sum block in the hardware. So far, there have been grossly 3 types of studies on GF(2m) multiplier architecture, such as serial multiplication, array multiplication, and hybrid multiplication. In this paper, we propose a novel approach on developing serial multiplier architecture based on Mastrovito's, by modifying the numerical formula of the polynomial-basis serial multiplication. The proposed multiplier architecture was described and implemented in HDL so that the novel architecture was simulated and verified in the level of hardware as well as software.