RSA Encryption and Decryption Implementation in MATLAB

RSA encryption and decryption represents a fundamental public-key cryptographic algorithm extensively employed for secure data transmission. The MATLAB implementation, as demonstrated by Thunyawat Rajatasereekul and Voranon Kiettrsalpipop, harnesses MATLAB's powerful computational engine to perform the complex mathematical operations central to RSA cryptography. The core security of RSA relies on the computational difficulty of factoring large prime numbers. The algorithm comprises three main stages: key generation, encryption, and decryption. Key generation begins with selecting two sufficiently large prime numbers (typically using MATLAB's primes() function or probabilistic testing methods), multiplying them to create the modulus n, and subsequently deriving the public and private keys using Euler's totient function and modular arithmetic properties. The public key (e, n) is distributed for encryption purposes, while the private key (d, n) remains confidential for decryption. In MATLAB, this process can be efficiently implemented using built-in functions for modular exponentiation (powermod()) and prime number generation. The encryption process computes ciphertext c = mod(m^e, n), where m represents the plaintext message. Decryption reverses this operation using m = mod(c^d, n) with the private key. MATLAB's optimized numerical algorithms ensure computational feasibility even when handling large-number arithmetic essential for cryptographic security. This implementation demonstrates how MATLAB's numerical computing strengths make it particularly suitable for cryptographic applications, offering both algorithmic transparency for educational purposes and computational efficiency for practical deployments. The RSA example serves as an excellent practical introduction to secure communication protocols in digital systems, showcasing key programming concepts including modular arithmetic, prime number handling, and efficient exponentiation techniques.