MATLAB Implementation of RSA Algorithm with Encryption and Decryption Functions

This document addresses the requirement for implementing the RSA algorithm using MATLAB, specifically focusing on encryption and decryption functionalities. Before implementing these functions, it's essential to understand the underlying principles and mathematical foundations of the RSA algorithm. RSA is an asymmetric encryption algorithm whose security relies on the computational difficulty of factoring large prime numbers. Therefore, when implementing the algorithm, mathematical libraries are required to handle operations with large integers, including addition, subtraction, multiplication, division, and modular arithmetic. The implementation typically involves using MATLAB's Symbolic Math Toolbox or custom functions for big integer operations, with key functions including modular exponentiation (using powermod), Euclidean algorithm for GCD calculation, and extended Euclidean algorithm for modular inverses.

When programming the solution, considerations must be given to both algorithm efficiency and security aspects, such as protecting private key security and preventing digital signature tampering. The implementation should include corresponding security measures, such as using cryptographic hash functions (like SHA-256 through MATLAB's DataHash function) to ensure data integrity, or employing public key encryption techniques to safeguard private key security. The code structure typically involves separate functions for key generation (selecting large primes p and q, computing n=p*q, Euler's totient function φ(n), choosing public exponent e, and calculating private exponent d), encryption (c = m^e mod n), and decryption (m = c^d mod n). Performance optimization techniques may include using Chinese Remainder Theorem for faster decryption and implementing efficient prime number generation algorithms.

Proper error handling should be implemented for edge cases such as message values exceeding the modulus n, and the program should include validation checks for cryptographic parameters. The implementation should follow MATLAB best practices for function modularization and code documentation to ensure maintainability and educational value for users studying cryptographic algorithm implementations.