RSA Key Generation, Signatures, and Encryption using OpenSSL
Demonstration of using OpenSSL to create RSA public/private key pair, sign and encrypt messages using those keys, and then decrypt and verify the received messages. Commands used: OpenSSL. Created by Steven Gordon on 7 March 2012 at Sirindhorn International Institute of Technology, Thammasat University, Thailand.
Using the RSA algorithm, RSA key generation creates a pair of public and private keys. The public key can be shared with anyone, but the private key must be kept secret.
The RSA algorithm is a public-key cryptography algorithm based on the difficulty of factoring large numbers. The key generation process involves the following steps:
- Choose two large prime numbers, p, and q.
- Calculate n = p * q.
- Calculate φ(n) = (p – 1)(q – 1).
- Choose an encryption exponent e such that 1 < e < φ(n) and e and φ(n) are relatively prime.
- Calculate the decryption exponent d such that d * e ≡ 1 (mod φ(n)).
The public key is the pair (n, e), and the private key is the valued.
The RSA algorithm is secure, but it is not unbreakable. If an attacker can factor n, they can calculate d and decrypt any encrypted message with the public key.
The security of RSA key generation depends on the difficulty of factoring large numbers. Today, the most significant number factored in is 24,862,048,259,933 − 1. This number has 24,862,048 digits, which took 200 years to factor.
The size of the keys generated by RSA key generation is also essential. The larger the keys, the more secure they are. The current standard for RSA keys is 2048 bits, but 4096 bits are recommended for more security.
RSA key generation is a complex process but an essential part of secure communication. The RSA algorithm is fast, and the keys generated by RSA key generation are typically very long. This makes them difficult to crack, even with powerful computers.