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 2 n ) 2 / log q n ) time using n / ( log 2 n ) 2 processors. Hence we get a processor-time bound of O ( n / log q n ) , 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.
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