A Modified Low Complexity Digit-Level Gaussian Normal Basis Multiplier

Abstract

AbstractGaussian normal bases have been included in a number of standards, such as [1] and NIST [2] for elliptic curve digital signature algorithm (ECDSA). Among different finite field operations used in this algorithm, multiplication is the main operation. In this paper, we consider type T Gaussian normal basis (GNB) multipliers over GF(2m), where m is odd. Such fields include five binary fields recommended by NIST for ECDSA. A modified digit-level GNB multiplier over GF(2m) is proposed in this paper. For T > 2, a complexity reduction algorithm is proposed to reduce the number of XOR gates without increasing the gate delay of the digit-level multiplier. The original and modified digit-level GNB multipliers are implemented on the Xilinx® Virtex5TM FPGA family for different digit sizes. It is shown that the modified digit-level GNB multiplier requires lower space complexity with almost the same delay as compared to the original type T, T > 2, GNB multiplier. Moreover, the bit-parallel GNB multiplier obtained from the proposed modified digit-level multiplier has the least space and time complexities among the existing fast bit-parallel type T GNB multipliers for T > 2.KeywordsFinite fieldGaussian normal basisdigit-serial multipliercomplexity reduction