Encryption security technology

RSA (Rivest-Shamir-Adleman) is an asymmetric encryption algorithm whose principle is based on number theory. The RSA algorithm uses two keys, one is the public key and the other is the private key. The public key is used to encrypt data and the private key is used to decrypt data.

The key authentication principle of RSA is as follows:

1. Key generation: First, generate two different prime numbers, denoted as p and q. Computes n = p * q, where n is the product of two prime numbers. Then, calculate the Euler function φ(n) = (p-1) * (q-1). Choose an integer e, where 1 < e < φ(n), and e and φ(n) are relatively prime. Finally, calculate d = e^(-1) mod φ(n), where d is the multiplicative inverse of e mod φ(n). The public key is (n, e) and the private key is (n, d).

2. Encryption: For a plaintext message M to be sent, convert it to an integer m. Then, use the public key (n, e) to encrypt m and calculate the ciphertext c = m^e mod n. The ciphertext c is the encrypted message.

3. Decryption: The receiver uses the private key (n, d) to decrypt the received ciphertext c and calculate the plaintext message m = c^d mod n. The obtained plaintext m is the original message.

The key to the principle of key authentication is to use the public key to encrypt the message, and only the corresponding private key can decrypt it. Since prime factorization is difficult, cracking the RSA algorithm requires a large amount of calculations, making it one of the most commonly used encryption algorithms today.