International Association
for Cryptologic Research

In this paper we introduce a new transformation method and a multiplication

algorithm for multiplying the elements of the field GF$(2^k)$

expressed in a normal basis. The number of XOR gates for the proposed

multiplication algorithm is

fewer than that of the optimal normal basis multiplication, not taking into

account the cost of forward and backward transformations. The algorithm is

more suitable for applications in which tens or hundreds of field multiplications

are performed before needing to transform the results back.