22IT051-CRT-CRNS.pptx abhnmcjdfniervfdfc

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1. CHINESE REMAINDER THEOREM ID: 22IT051 SUB: CRNS (IT348) Lab Faculty: Madhav Ajwalia Sir 1 22IT051(CRNS-CRT)

2. Introduction of CRT The Chinese Remainder Theorem (CRT) is a fundamental concept in number theory that deals with solving systems of simultaneous linear congruences. It was first documented in ancient China, around the 3rd century AD, by the mathematician Sun Zi. CRT provides a way to reconstruct an integer xxx when given its remainders with respect to pairwise coprime moduli. Why is CRT Important? It simplifies solving multiple modular arithmetic equations into one. Enables efficient computation in many fields, especially when dealing with large numbers. 2 22IT051(CRNS-CRT)

3. Formulas for Solving CRT Problems 3 22IT051(CRNS-CRT)

4. Formulas for Solving CRT Problems(Continue) 4 22IT051(CRNS-CRT)

5. Formulas for Solving CRT Problems(Continue) 5 22IT051(CRNS-CRT)

6. Solution: 6 22IT051(CRNS-CRT)

7. Real Life Application Computer Arithmetic and Parallel Computing: Efficient large-number computations. Distributed systems. Large-scale matrix operations. Optimization algorithms. E-Commerce and Payment Systems Secure payment gateways. Cryptography: RSA algorithm optimization. Homomorphic encryption. 7 22IT051(CRNS-CRT)

8. References Geeksforgeeks: https://www.geeksforgeeks.org/introduction-to-chinese-remainder-theorem/ https://www.geeksforgeeks.org/chinese-remainder-theorem/ 8 22IT051(CRNS-CRT)

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