Title :
Modular Multiplication and Division Algorithms Based on Continued Fraction Expansion
Author_Institution :
LIP6, UPMC Univ. Paris 06, Paris, France
Abstract :
In this paper, we provide new methods to generate a class of algorithms computing modular multiplication and division. All these algorithms rely on sequences derived from the Euclidean algorithm for a well chosen input. We then use these sequences as number scales of the Ostrowski number system to construct the result of either the modular multiplication or division.
Keywords :
algebra; number theory; Euclidean algorithm; Ostrowski number system; continued fraction expansion; modular division computing algorithm; modular multiplication computing algorithm; Algorithm design and analysis; Approximation algorithms; Approximation methods; Bismuth; Complexity theory; Indium tin oxide; Transforms; Division; Modular arithmetic; Multiplication; Ostrowski number system;
Conference_Titel :
Computer Arithmetic (ARITH), 2015 IEEE 22nd Symposium on
Conference_Location :
Lyon
Print_ISBN :
978-1-4799-8663-7
DOI :
10.1109/ARITH.2015.21
