Communications of the
Korean Mathematical Society CKMS

In this paper, we show how to construct an optimal normal basis over finite field of high degree and compare two methods for fast operations in some finite field $GF(2^n)$. The first method is to use an optimal normal basis of $GF(2^n)$ over $GF(2)$. In case of $n = st$ where $s$ and $t$ are relatively primes, the second method which regards the finite field $GF(2^n)$ as an extension field of $GF(2^s)$ and $GF(2^t) $ is to use an optimal normal basis of $GF(2^t)$ over $GF(2)$. In section 4, we tabulate implementation result of two methods.

Keywords: finite fields, normal bases, complexity

MSC numbers: Primary : 12Y05