Efficient parallel exponentiation in GF(2n) using normal basis representations

Authors:
Mun-Kyu Lee;Yoonjeong Kim;Kunsoo Park;Yookun Cho
Affiliations:
School of Computer Science and Engineering, Seoul National University, Seoul 151-742, Korea;N'ser Community Inc., ChangGang Building, 22 DoWhaDong, Mapo-Gu, Seoul 121-040, Korea;School of Computer Science and Engineering, Seoul National University, Seoul 151-742, Korea;School of Computer Science and Engineering, Seoul National University, Seoul 151-742, Korea
Venue:
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
Year:
2001

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Abstract

Vonzur 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(2 n ) which improves upon von zur Gathen's algorithm. We also show that exponentiation in GF(2 n ) can be done in &Ogr;(log n) time using n/(log n)2 processors. Hence we get processor x time bound &Ogr;(n/log n), which is optimal. Finally, we present an on-line processor assignment scheme which was missing in von zur Gathen's algorithm, and show that its time complexity is negligible.