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A Survey of Fast Exponentiation Methods
 JOURNAL OF ALGORITHMS
, 1998
"... Publickey cryptographic systems often involve raising elements of some group (e.g. GF(2 n), Z/NZ, or elliptic curves) to large powers. An important question is how fast this exponentiation can be done, which often determines whether a given system is practical. The best method for exponentiation de ..."
Abstract

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Publickey cryptographic systems often involve raising elements of some group (e.g. GF(2 n), Z/NZ, or elliptic curves) to large powers. An important question is how fast this exponentiation can be done, which often determines whether a given system is practical. The best method for exponentiation depends strongly on the group being used, the hardware the system is implemented on, and whether one element is being raised repeatedly to different powers, different elements are raised to a fixed power, or both powers and group elements vary. This problem has received much attention, but the results are scattered through the literature. In this paper we survey the known methods for fast exponentiation, examining their relative strengths and weaknesses.
A Critique of the Mathematical Abilities of CA Systems
 Computer Algebra Systems. A Practical Guide
, 1999
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