Abstract

Von zur Gathen proposed an ecient parallel exponentiation algorithm in nite elds using normal basis representations. In this paper we present a processor-ecient parallel exponentiation ) which improves upon von zur Gathen's algorithm. We also show that exponentiation ) can be done in O(log n) time using n=(log n) processors. Hence we get processor time bound O(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.

Citations