Cryptography (Reprinted from IBM Journal of Research and Development, vol 31, 1987)

This paper is concerned with two aspects of cryptography in which the autho r has been working. One is the Data Encryption Standard (DES), developed at IBM and now in wide use for commercial cryptographic applications. This is a "private key" system; the communicants share a secret key, and the eaves dropper will succeed if he can guess this key among its quadrillions of pos sibilities. The other is the Diffie-Hellman key exchange protocol, a typica l "public key" cryptographic system. Its security is based on the difficult y of taking "discrete logarithms" (reversing the process of exponentiation in a finite field). We describe the system and some analytic attacks agains t it.