George B. Purdy

George Barry Purdy is a mathematician and computer scientist who specializes in cryptography, combinatorial geometry and number theory. Purdy received his Ph.D. from the University of Illinois at Urbana–Champaign in 1972, officially under the supervision of Paul T. Bateman, but his de facto adviser was Paul Erdős. He was on the faculty in the mathematics department at Texas A&M University for 11 years, and was appointed the Geier Professor of computer science at the University of Cincinnati in 1986.

Purdy has Erdős number one and coauthored many papers with Paul Erdős, who regarded him as his own student. He is the "P" in G.W. Peck, a pseudonym for the group of mathematicians that also included Ronald Graham, Douglas West, Paul Erdős, Fan Chung, and Daniel Kleitman.

In 1971, Purdy was asked by Larry Roberts, the head of DARPA, to develop a secure hash function to protect passwords on ARPANET. Purdy developed the so-called Purdy polynomial, which was a polynomial of degree 2²⁴ + 17 computed modulo the 64-bit prime p = 2⁶⁴ - 59. The terms of the polynomial could be computed using modular exponentiation. DARPA was satisfied with the hash function, and also allowed Purdy to publish it in Communications of the ACM. It was well received around the world, and DEC eventually used it in their OpenVMS operating system. A DEC report said they chose it because it was very secure, and also because the existing standard DES could not be exported, which meant that an alternative was needed. OpenVMS uses a 64-bit version, based on a 64-bit prime, the same size as the one in the paper. Computer hacker Kevin Mitnick mentions the Purdy polynomial in his autobiography and says that it caused him to be found out.