Introduction: Squarer is an important circuit building block in squareand-multiply-based exponentiation and inversion circuits. When GF (2n) elements are represented in a normal basis, squaring is simply a circular shift operation. Therefore, most previous works on squarers focused on other representations of GF (2n) elements. For practical applications where values of n are often in the range ...

The efficient design of digit-serial multipliers for special binary composite fields, F2nm where gcd(n, m) 1⁄4 1, is presented. These composite fields can be constructed via an irreducible pentanomial of degree nm but not an irreducible trinomial of degree nm. The conventional construction method for such digit-serial multipliers is to exploit the simplicity of pentanomials to obtain efficent l...