Fast operation method in $GF(2^n)$ using a modified optimal normal basis
Commun. Korean Math. Soc. 1997 Vol. 12, No. 3, 531-538
Il-Whan Park, Seok-Won Jung, Hee-Jean Kim, Jong-In Lim Electronics and Telecommunications Research Institute, Korea University, Korea University, Korea University
Abstract : 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