RSA Encryption Algorithm: Principles, Implementation, and Applications

The RSA encryption algorithm is a widely-used asymmetric encryption technique proposed by Ron Rivest, Adi Shamir, and Leonard Adleman in 1977. It relies on the mathematical difficulty of factoring large integers to ensure data security. The core principle of RSA involves using a key pair: a public key for data encryption and a private key for decryption. The RSA workflow consists of several critical steps. First is key generation, which involves selecting two large prime numbers, computing their product as the modulus, and then generating the public and private keys. In code implementation, this typically uses probabilistic prime testing algorithms like Miller-Rabin to generate large primes securely. During encryption, the sender uses the recipient's public key to encrypt data, and only the recipient can decrypt it using the corresponding private key. Beyond encryption, RSA can also be used for digital signatures to verify data integrity and authenticity. RSA's advantages include high security and broad applicability, making it suitable for secure communications, digital certificates, and e-commerce scenarios. However, RSA has significant computational overhead, particularly with longer key lengths where encryption and decryption speeds decrease substantially. Therefore, in practical applications, RSA is often combined with symmetric encryption algorithms to balance efficiency and security through hybrid cryptosystems. It's important to note that RSA's security depends on the difficulty of factoring large numbers. As computational power advances, shorter keys may become vulnerable. Thus, using sufficiently long keys (such as 2048 bits or longer) is recommended to ensure long-term security. Modern implementations often include optimizations like Chinese Remainder Theorem (CRT) to speed up private key operations and padding schemes like OAEP to prevent cryptographic attacks.