MATLAB Implementation of RSA Algorithm with Code Description

The RSA algorithm is a widely used asymmetric encryption method proposed by Ron Rivest, Adi Shamir, and Leonard Adleman in 1977. Its core principle relies on the computational difficulty of factoring large integers, utilizing a public-private key pair for encryption and decryption. Implementing RSA in MATLAB helps understand its mathematical foundation and programming logic. ### Overview of RSA Algorithm Steps Select two distinct prime numbers: Large primes are typically required for security, but smaller primes like p=11 and q=13 can be used for experimental purposes. Calculate n and Euler's totient function φ(n): n = p × q, φ(n) = (p-1)(q-1). Choose public key e: e must satisfy 1 < e < φ(n) and be coprime with φ(n). Compute private key d: d is the modular multiplicative inverse of e modulo φ(n), satisfying e × d ≡ 1 mod φ(n). Encryption and decryption: Ciphertext = Plaintext^e mod n, Plaintext = Ciphertext^d mod n. ### MATLAB Implementation Approach Prime selection: Manually input small primes p and q to avoid complex prime generation algorithms. Modular arithmetic: MATLAB's built-in `mod` function can directly handle modular operations (while `powermod` requires manual implementation or Symbolic Math Toolbox). Extended Euclidean algorithm: Implemented through iterative methods to calculate modular inverse d. ### Important Considerations Security: Practical applications require extremely large primes (e.g., 1024-bit or larger), while small primes are suitable only for educational demonstrations. Efficiency optimization: Large-number operations require MATLAB's high-precision arithmetic or third-party libraries to avoid direct computation of超大整数幂. This implementation provides deep understanding of RSA's mathematical essence and asymmetric encryption workflow, establishing foundation for more complex cryptographic applications.