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A Survey of Fast Exponentiation Methods

✍ Scribed by Daniel M. Gordon

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
194 KB
Volume
27
Category
Article
ISSN
0196-6774

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✦ Synopsis

Public-key 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.

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