An Efficient Algorithm for Computing Multiplicative Inverses in GF($2^m$) Using Optimal Normal Bases

최적 정규기저를 이용한 효율적인 역수연산 알고리즘에 관한 연구

This paper proposes a new multiplicative inverse algorithm for the Galois field GF (2/sup m/) whose elements are represented by optimal normal basis type Ⅱ. One advantage of the normal basis is that the squaring of an element is computed by a cyclic shift of the binary representation. A normal basis element is always possible to rewrite canonical basis form. The proposed algorithm combines normal basis and canonical basis. The new algorithm is more suitable for implementation than conventional algorithm.