Fast Arithmetics Using Chinese Remaindering
George Davida, Bruce Litow, Guangwu Xu
TL;DR
This paper discusses issues in Chinese remaindering representation, introduces new conversion methods including a probabilistic algorithm, and refines an existing division algorithm to improve efficiency in modular arithmetic computations.
Contribution
It presents novel conversion techniques and an optimized division algorithm that reduce complexity and improve performance in Chinese remaindering-based arithmetic.
Findings
New probabilistic conversion algorithm based on recent theoretical results
Reduction of the number of moduli in division algorithm by a factor of log n
Enhanced efficiency in Chinese remaindering computations
Abstract
In this paper, some issues concerning the Chinese remaindering representation are discussed. Some new converting methods, including an efficient probabilistic algorithm based on a recent result of von zur Gathen and Shparlinski \cite{Gathen-Shparlinski}, are described. An efficient refinement of the NC division algorithm of Chiu, Davida and Litow \cite{Chiu-Davida-Litow} is given, where the number of moduli is reduced by a factor of .
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Taxonomy
TopicsCoding theory and cryptography · Cryptography and Residue Arithmetic · semigroups and automata theory