MATLAB Implementation of RSA Encryption Algorithm

RSA encryption is a widely used public-key cryptographic algorithm with significant applications in data security and digital signatures. Implementing RSA encryption in MATLAB typically involves three core steps: key generation, encryption, and decryption.

Key Generation The core of RSA lies in generating public and private key pairs. The implementation starts by selecting two sufficiently large prime numbers and calculating their product as the modulus. Then computes Euler's totient function value and selects an integer coprime with this value as the public key exponent. Finally, the private key exponent is obtained through modular inverse computation using MATLAB's extended Euclidean algorithm implementation.

Encryption Process Data encryption uses the recipient's public key. In MATLAB, this is achieved through modular exponentiation operations where plaintext data is converted to integers and encrypted using the public key exponent and modulus. In practical applications, data is typically processed in blocks to ensure each block's value doesn't exceed the modulus size.

Decryption Process The recipient uses the private key for decryption, employing similar modular exponentiation operations. The correct private key can restore the ciphertext to the original plaintext data through inverse mathematical operations.

MATLAB Implementation Key Points Large Number Operations: MATLAB's built-in big integer support (such as the vpi toolbox) can handle the large number calculations required by RSA Efficiency Optimization: For practical applications, fast power algorithm should be implemented to optimize modular exponentiation operations Data Preprocessing: Before encryption, data typically requires padding (such as OAEP) to enhance security through MATLAB's cryptographic functions

The MATLAB implementation of RSA demonstrates the mathematical foundation of public-key encryption algorithms while showcasing the programming language's flexibility in cryptographic applications. Note that in practical usage, key length should be sufficiently long (recommended 2048 bits or more) to ensure security through proper parameter selection in the code.