RSAalgoritmiin

RSAalgoritmiin is a cryptographic algorithm used for secure data transmission. It is an asymmetric algorithm, meaning it uses two different keys for encryption and decryption: a public key and a private key. The public key can be shared with anyone, while the private key must be kept secret.

The RSA algorithm's security relies on the difficulty of factoring large prime numbers. To generate the keys, two large prime numbers, p and q, are chosen. Their product, n = p * q, forms the modulus for both keys. The public key consists of the modulus n and an exponent e, chosen such that e is coprime to (p-1)(q-1). The private key consists of the modulus n and a private exponent d, which is the modular multiplicative inverse of e modulo (p-1)(q-1).

Encryption is performed using the public key. A message m is encrypted to a ciphertext c using the formula c = m^e mod n. Decryption is performed using the private key. The original message m can be recovered from the ciphertext c using the formula m = c^d mod n.

RSA is widely used for secure communication over the internet, particularly in protocols like SSL/TLS for securing web traffic. It is also used for digital signatures, which verify the authenticity and integrity of a message. The strength of RSA depends on the size of the prime numbers used. Larger primes make factoring more computationally expensive, thus increasing security.