Efficient Exponentiation for a Class of Finite Fields GF(2 n ) Determined by Gauss Periods [chapter]

Soonhak Kwon, Chang Hoon Kim, Chun Pyo Hong
2003 Lecture Notes in Computer Science  
We present a fast and compact hardware architecture of exponentiation in a finite field GF (2 n ) determined by a Gauss period of type (n, k) with k ≥ 2. Our construction is based on the ideas of Gao et al. and on the computational evidence that a Gauss period of type (n, k) over GF (2) is very often primitive when k ≥ 2. Also in the case of a Gauss period of type (n, 1), i.e. a type I optimal normal element, we find a primitive element in GF (2 n ) which is a sparse polynomial of a type I
more » ... al normal element and we propose a fast exponentiation algorithm which is applicable for both software and hardware purposes. We give an explicit hardware design using the algorithm.
doi:10.1007/978-3-540-45238-6_19 fatcat:drsd2r5nyzbzxjfse7gevbextm