The existence of public key cryptography was first postulated in print in the fall of 1975 by Whitfield Diffie and Martin Hellman. The two researchers, then at Stanford University, wrote a paper in which they presupposed the existence of an encryption technique in which information encrypted with one key (the public key) could be decrypted by a second, apparently unrelated key (the private key). Robert Merkle, then a graduate student at Berkeley, had similar ideas at the same time, but because of the vagaries of the academic publication process, Merkle’s papers were not published until the underlying principles and mathematics of the Diffie-Hellman algorithm were widely known.
Since that time, a variety of public key encryption systems have been developed. Unfortunately, there have been significantly fewer developments in public key algorithms than in symmetric key algorithms. The reason has to do with how these algorithms are created. Good symmetric key algorithms simply scramble their input depending on the input key; developing a new symmetric key algorithm requires coming up with new ways for performing that scrambling reliably. Public key algorithms tend to be based on number theory. Developing new public key algorithms requires identifying new mathematical equations with particular properties.
The following list summarizes the public key systems in common use today:
A system for exchanging cryptographic keys between active parties. ...