Exponentiation in finite fields using dual basis multiplier
Implementing finite fields arithmetic is very important, when realizing error control systems and cryptosystems. Recenty several algorithms for implementing multiplication in GF(2 m ) have been proposed. When using the polynomial (or standard) basis representation, it is also important that efficient squaring algorithm is improved.
In this paper we present an efficient bit-serial squarer in polynomial basis representation for GF(2 m ). First, we give an interesting relation between exponentiation and maximum length feedback shift register sequences(m-sequences) in GF(q m ). Secondly, we present an efficient sequarer in GF(2 m ) based upon Berlekamp's bit-serial multiplier (also called dual basis multiplier) architecture. The squarer has very simple structure and can compute the square in [m/2] steps.
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