Low-Complexity Digit-Level Systolic Gaussian Normal Basis Multiplier

Abstract

Normal basis multiplication over $GF(2^{m})$ is widely used in various applications such as elliptic curve cryptography. As a special class of normal basis with low complexity, Gaussian normal basis (GNB) has received considerable attention recently. In this paper, we propose a novel decomposition algorithm to develop a digit-level (DL) low-complexity systolic structure for GNB multiplication over $GF(2^{m})$ . First, we propose two algorithms separately to achieve a systolic GNB multiplier with low critical path delay and low register complexity. Next, we present the corresponding structure according to the proposed algorithm (combination of previous two proposed algorithms). Compared with the existing systolic DL GNB multipliers (through both the theoretical and application-specific integrated circuit comparison), the proposed multiplier achieves significantly less area-delay product (ADP), e.g., for a systolic structure of digit size of 8 for $GF(2^{409})$ , the proposed structure has 12.3% less ADP compared to the best of the existing designs, for the same digit size.