New viewpoint of bit-serial/parallel normal basis multipliers using irreducible all-one polynomial

Recently, normal bases have been an appealing technique for hardware implementation in many applications, especially when finite fields are very large, such as the public key cryptosystems. In this article, a new viewpoint is introduced for performing the multiplication in the normal basis representation over binary field where the field defining irreducible polynomial is an all-one polynomial. The proposed multipliers carry out the normal basis multiplication by using extended polynomial basis multiplier to construct two architectures. These two classes of architectures are in bit-serial and bit-parallel which reduce the cost of space and time respectively.