In this paper, we propose an efficient AB2 multiplication algorithm using SPB(shifted polynomial basis) over finite fields. Using the feature of the SPB, we split the equation for AB2 multiplication into two parts. The two partitioned equations are executable at the same time, and we derive an algorithm that processes them in parallel. Then we propose an efficient semi-systolic AB2 multiplier based on the proposed algorithm. The proposed multiplier has less area-time (AT) complexity than related multipliers. In detail, the proposed AB2 multiplier saves about 94%, 87%, 86% and 83% of the AT complexity of the multipliers of Wei, Wang-Guo, Kim-Lee, Choi-Lee, respectively. Therefore, the proposed multiplier is suitable for VLSI implementation and can be easily adopted as the basic building block for various applications.

Finite fields, Multiplication, Shifted polynomial basis, Semi-systolic array, Cryptography