Efficient subquadratic parallel multiplier based on modified SPB of GF(2m)

Toeplitz matrix-vector product (TMVP) approach is a special case of Karatsuba algorithm to design subquadratic multiplier in GF(2
^m
). In binary extension fields, shifted polynomial basis (SPB) is a variable basis representation, and is widely studied. SPB multiplication using coordinate transformation technique can transform TMVP formulas, however, this approach is only applied for the field constructed by all trinomials or special class of pentanomials. For this reason, we present a new modified SPB multiplication for an arbitrary irreducible pentanomial, and the proposed multiplication scheme has formed a TMVP formula.