# Chapter 11

Diffie-Hellman

For our discussion of public-key cryptography, we're going to follow the historical path. Public-key cryptography was really started by Whitfield Diffie and Martin Hellman when they published their article “New Directions in Cryptography” in 1976 [33].

So far in this book, we've only talked about encryption and authentication with shared secret keys. But where do we get those shared secret keys from? If you have 10 friends you want to communicate with, you can meet them all and exchange a secret key with each of these friends for future use. But like all keys, these keys should be refreshed regularly, so at some point you will have to meet and exchange keys all over again. A total of 45 keys are needed for a group of 10 friends. But as the group gets larger, the number of keys grows quadratically. For 100 people all communicating with each other, you need 4950 keys. Specifically, in a group of *N* people, we would need *N*(*N* − 1)/2...