Encryption with ElGamal
Almost every working day, I have the privilege to work in a place that once hosted one the greats: John Napier. It was John who discovered logarithms, and showed that g^a times g^b is g^(a+b), and that g^a divided by g^b is g^(a-b). In our modern world, we use this type of method so often in our cryptography implementation, and it often provides the core around privacy-enhancing methods (such as with Zero-Knowledge Proof and Anonymisation). As our numbers become very large, though, we often define them within a finite field (Z_p), and where we select a large prime number (p), and then perform all our operations with the magic of the (mod p) operation.
I think if John Napier were alive today he would wonder at how discrete logarithms have been used to secure our world. I am also sure he would strike-up an immediate bond with Taher Elgamal and who, in 1985, published this classic paper [here]:
