ElGamal Encryption With The Ristretto255 Group

I think if John Napier were alive today he would wonder at how discrete logarithms have been used to secure our world. And, I am also sure he would strike up an immediate bond with Taher Elgamal and who, in 1985, published this classic paper [here]:

Within the paper, he proposed the ElGamal discrete logarithm encryption system and also the ElGamal signature scheme (and which became the core of the DSA signature method). In 2009, Elgamal was awarded the RSA Conference 2009 Lifetime Achievement Award, and where he was dubbed the “father of SSL”.

At the core of the ElGamal public key methods is the Discrete Logarithm Problem, and where we have:

Y= g^x (mod p)

and where it is difficult to determine x, even if we have Y, g and p (as long as p is a large enough prime number). And so it is used in the Diffie-Hellman method for key exchange. We also use it to sign a message, and where we create a key pair (a public key and a private key). The private key is used to encrypt something (such as the hash of the message), and then the public key is used to prove the signing.