Efficient parallel exponentiation in GF(qn) using normal basis representations

Authors:
Mun-Kyu Lee;Yoonjeong Kim;Kunsoo Park;Yookun Cho
Affiliations:
Electronics and Telecommunications Research Institute, 161 Gajeong-dong, Yuseong-gu, Daejeon 305-350, South Korea;Division of Information and Communication Engineering, Seoul Women's University, Seoul 139-774, South Korea;School of Computer Science and Engineering, Seoul National University, Seoul 151-742, South Korea;School of Computer Science and Engineering, Seoul National University, Seoul 151-742, South Korea
Venue:
Journal of Algorithms
Year:
2005

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Abstract

Von zur Gathen proposed an efficient parallel exponentiation algorithm in finite fields using normal basis representations. In this paper we present a processor-efficient parallel exponentiation algorithm in GF(q^n) which improves upon von zur Gathen's algorithm. We also show that exponentiation in GF(q^n) can be done in O((log"2n)^2/log"qn) time using n/(log"2n)^2 processors. Hence we get a processor-time bound of O(n/log"qn), which matches the best known sequential algorithm. Finally, we present an efficient on-line processor assignment scheme which was missing in von zur Gathen's algorithm.