Low Latency $GF(2^{m})$ Polynomial Basis Multiplier
José Luis Imaña · IEEE Transactions on Circuits and Systems I Regular Papers · 2010
Finite fieldGF(2m) arithmetic is becoming increasingly important for a variety of different applications including cryptography, coding theory and computer algebra. Among finite field arithmetic operations,GF(2m) multiplication is of special interest because it is considered the most important building block. This contribution describes a new low latency parallel-in/parallel-out sequential polynomial basis multiplier overGF(2m). For irreducibleGF(2m) generating polynomialsf(x)=xm+xkt+xkt-1+⋯+xk1+1 withm≥ 2kt-1, the proposed multiplier has a theoretical latency of 2kt+1 cycles . This latency is the lowest one found in the literature forGF(2m) multipliers. Furthermore, the conditionm≥ 2kt-1 is specially important because the five binary irreducible polynomials recommended by NIST for elliptic curve cryptography (ECC) implementation verify this condition.