Finite field  GF (2 m ) arithmetic is becoming increasingly important for a variety of different applications including cryptography, coding theory and computer algebra. Among finite field arithmetic operations,  GF (2 m ) 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 over  GF (2 m ). For irreducible  GF (2 m ) generating polynomials  f ( x )= xm + xkt + xk  t -1+⋯+ xk  1 +1 with  m  ≥ 2 k  t -1, the proposed multiplier has a theoretical latency of 2 kt +1 cycles . This latency is the lowest one found in the literature for  GF (2 m ) multipliers. Furthermore, the condition  m  ≥ 2 kt -1 is specially important because the five binary irreducible polynomials recommended by NIST for elliptic curve cryptography (ECC) implementation verify this condition.
['José Luis Imaña']
Low Latency $GF(2^{m})$ Polynomial Basis Multiplier