On matrix-vector product based sub-quadratic arithmetic complexity schemes for field multiplication
M.A. Hasan · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2007
Using an efficient way to compute the product of a Toeplitz matrix and a vector, a sub-quadratic arithmetic complexity scheme for field multiplication over binary extension fields has recently been proposed by Fan and Hasan. The scheme has been developed using a shifted polynomial basis for the representation of the field elements and has been stated to be applicable to the conventional polynomial basis, although with an increased gate delay for some field defining polynomials. The conventional polynomial basis is widely used in practice and is part of different recommendations and standards for cryptographic applications. In this article, we give additional details of the sub-quadratic complexity algorithm for the case of the polynomial basis by presenting efficient transformation matrices for a class of low weight field defining polynomials, namely trinomials.