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 O(log n) time using n/(log n)2 processors. Hence we get processor x 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.
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