Abstract

This paper presents a new private key cryptosystem utilizing the Chinese Remainder Theorem (CRT) for encryption and decryption. The system generates keys by selecting a specified number of distinct primes and a random integer `$a$', which is chosen as a random number greater than all the selected primes and coprime to them, ensuring security without revealing the modulus. Encryption and decryption operations are performed within the modulus of each prime, enhancing data protection. The system's security relies solely on the integrity of prime numbers and the randomness of `$a$', offering a promising solution for secure symmetric key cryptography.

Keywords and Phrases

Private key Cryptosystem, Modular arithmetic, Chinese remainder theorem and confidentiality.

A.M.S. subject classification

11T71, 94A60.

.....