Coding Theory and Cryptography: From Enigma and Geheimschreiber to Quantum Theory

The National Security Agency funded a conference on Coding theory, Cryp- tography, and Number Theory (nick-named Cryptoday) at the United States Naval Academy, on October 25-27, 1998. We were very fortunate to have been able to attract talented mathematicians and cryptographers to the meeting. Unfortunately, some people couldn't make it for either scheduling or funding reasons. Some of these have been invited to contribute a paper anyway. In addition, Prof. William Tutte and Frode Weierud have been kind enough to allow the inclusion of some very interesting unpublished papers of theirs. The papers basically fall into three catagories. Historical papers on cryp- tography done during World War II (Hatch, Hilton, Tutte, Ulfving, and Weierud), mathematical papers on more recent methods in cryptography (Cosgrave, Lomonoco, Wardlaw), and mathematical papers in coding theory (Gao, Joyner, Michael, Shokranian, Shokrollahi). A brief biography of the authors follows. - Peter Hilton is a Distinguished Professor of Mathematics Emeritus at the State University of New York at Binghamton. He worked from 1941 to 1945 in the British cryptanalytic headquarters at Bletchley Park. Profes- sor Hilton has done extensive research in algebraic topology and group theory. - William Tutte is a Distinguished Professor Emeritus and an Adjunct Pro- fessor in the Combinatorics and Optimization Department at the Univer- sity of Waterloo. He worked from 1941 to 1945 in the British cryptana- lytic headquarters at Bletchley Park. Professor Tutte has done extensive research in the field of combinatorics.