Spectacular Exponents: A semi modular Approach to Fast Exponentiation
Journal Title: JOURNAL OF ADVANCES IN MATHEMATICS - Year 2019, Vol 16, Issue 0
Abstract
This paper introduces a computational scheme for calculating the exponential bw where b and w are positive integers. This two-step method is based on elementary number theory that is used routinely in this and similar contexts, especially the Chinese remainder theorem (CRT), Lagrange’s theorem, and a variation on Garner’s algorithm for inverting the CRT isomorphism. We compare the performance of the new method to the standard fast algorithm and show that for a certain class of exponents it is significantly more efficient as measured by the number of required extended multiplications.
Authors and Affiliations
Robert Valenza
Keywords
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- EP ID EP651904
- DOI 10.24297/jam.v16i0.8301
- Views 166
- Downloads 0
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