Modular Inverses and Chinese Remainder Algorithm
W. H. Ko
TL;DR
This paper introduces new forms of modular inverses, proves their reciprocity, and develops a generalized algorithm applicable to solving simultaneous congruences for both coprime and non-coprime moduli.
Contribution
The paper presents novel reciprocity formulas for modular inverses and a unified algorithm for the Chinese Remainder problem applicable to various moduli.
Findings
New reciprocity formulas for modular inverses
A generalized algorithm for Chinese Remainder problem
Algorithm applicable to both coprime and non-coprime moduli
Abstract
This paper introduces two forms of modular inverses and proves their reciprocity formulas respectively. These formulas are then applied to formulate new and generalized algorithm for computing these modular inverses. The same algorithm is also shown to be applicable for the Chinese Remainder problem, i.e., simultaneous linear congruence equations, for co-prime moduli as well as non-co-prime moduli.
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Taxonomy
TopicsCryptography and Residue Arithmetic · Cryptography and Data Security · Coding theory and cryptography