Please use this identifier to cite or link to this item:
|Title||Chinese Remainder Theorem and It’s Applications|
|Title in Arabic||نظرية البواقي الصينية و تطبيقاتها|
The Chinese Reminder Theorem is an ancient but important calculation algorithm in modular arithmetic. The Chinese Remainder Theorem enables one to solve simultaneous equations with respect to different moduli in considerable generality. In this thesis I introduce an overview of the history of the Chinese Remainder Theorem, state the theorem in different algebraic structures and explain different uses for the theorem in managing large numbers, speed up calculation, and finding out some division criterion. The tenor of the thesis revolves around how to calculate residues modulo composite number and consequently introducing divisibility criteria of those number and applying this in the binary system. Also, I present criteria for calculating residues modulo all integers less than 100. As well as I explain how to use the Chinese Remainder Theorem in integer factorization and managing large integers. Also we use Chinese Remainder Theorem to obtain self-dual codes over Rings and to obtain the RSA cryptography.
|Publisher||الجامعة الإسلامية - غزة|
|Files in this item|