RSAalgoritmissa

RSAalgoritmissa refers to the RSA algorithm, a widely used public-key cryptosystem. Its security relies on the computational difficulty of factoring large integers. Developed by Ron Rivest, Adi Shamir, and Leonard Adleman in 1977, it was named after their surnames.

The RSA algorithm operates using a pair of keys: a public key and a private key. The public key can be freely distributed and is used for encrypting messages and verifying digital signatures. The private key, however, must be kept secret by its owner and is used for decrypting messages and creating digital signatures.

The process begins with the generation of two large prime numbers, p and q. These primes are kept secret. Their product, n = pq, forms the modulus for both the public and private keys. A public exponent, e, is chosen such that it is coprime to (p-1)(q-1). The public key is then the pair (n, e). The private key's exponent, d, is calculated such that (d * e) mod (p-1)(q-1) = 1. The private key is the pair (n, d).

Encryption involves taking a plaintext message m, treated as an integer, and computing the ciphertext c as c = m^e mod n. Decryption reverses this process, where the original message m is recovered from the ciphertext c using the private key: m = c^d mod n. This mathematical relationship allows secure communication without the need for prior sharing of secret keys. RSA is foundational to many secure communication protocols, including TLS/SSL.