RSA Key Generation for Encryption and Decryption Using MATLAB

RSA key generation using MATLAB programming is a fundamental cryptographic technique. The RSA algorithm leverages properties of large prime numbers to create public and private key pairs for secure information encryption and decryption. The implementation typically involves generating two large prime numbers (p and q), computing their product n (modulus), and calculating Euler's totient function φ(n). The public key consists of modulus n and encryption exponent e (typically 65537), while the private key includes decryption exponent d computed using the modular multiplicative inverse of e mod φ(n).

In MATLAB implementation, key functions like isprime() verify primality, gcd() ensures coprimality, and modular arithmetic operations handle key calculations. The security of RSA relies on the computational difficulty of factoring large integers into their prime components, making ciphertext decryption without the private key extremely challenging. This mathematical foundation establishes RSA as a cornerstone in modern secure communication and information protection systems.

The encryption process uses modular exponentiation (mod(power(message, e), n)) while decryption applies similar operation with private exponent d. MATLAB's symbolic math toolbox or custom functions can efficiently handle these large-number computations required for practical RSA implementations.