On Some Algebraic Properties of the Chinese Remainder Theorem with Applications to Real Life

Abstract

The study sought to establish some algebraic properties of the Chinese Remainder Theorem. The Chinese Remainder Theorem is an ancient but important mathematical theorem that enables one to solve simultaneous equations with respect to different modulo and makes it possible to reconstruct integers in a certain range from their residues modulo to the pairwise relatively prime modulo and also construct libraries for manipulations on very large integers. The study seeks to find out some real life applications of the Chinese Remainder Theorem in our everyday life activities especially in trading and in information security and retrieval avoiding any leakages to invaders or intruders. The study presented proofs of some theorems vital in the real life applications of the Chinese Remainder Theorem. In the study, we identified that in the statement of the Principal Ideal Domain and that of Rings can be classified as some algebraic properties of the Chinese Remainder Theorem.

Construction of a model of steganographic embedding of the UAV identifier into ADS-B data

“…-Chinese remainder theorem (system С 1 ); -theorem on a finite integral ring (system С 2 ). It is known from works [13,14] that the Chinese remainder theorem allows solving systems of linear equations modulo. If:…”

“…The procedure for determining the vector of the studied characteristics f 1 1 − ( ) is carried out using the Chinese remainder theorem [13,14].…”