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

Reminiscences and Reflections of a Codebreaker.- FISH and I.- Sturgeon, The FISH BP Never Really Caught.- ENIGMA and PURPLE: How the Allies Broke German and Japanese Codes During the War.- The Geheimschreiber Secret.- The RSA Public Key Cryptosystem.- Number Theory and Cryptography (using Maple).- A Talk on Quantum Cryptography or How Alice Outwits Eve.- The Rigidity Theorems of Hamada and Ohmori, Revisited.- Counting Prime Divisors on Elliptic Curves and Multiplication in Finite Fields.- On Cyclic MDS-Codes.- Computing Roots of Polynomials over Function Fields of Curves.- Remarks on codes from modular curves: MAPLE applications.

These are the proceedings of the Conference on Coding Theory, Cryptography, and Number Theory held at the U. S. Naval Academy during October 25-26, 1998. This book concerns elementary and advanced aspects of coding theory and cryptography. The coding theory contributions deal mostly with algebraic coding theory. Some of these papers are expository, whereas others are the result of original research. The emphasis is on geometric Goppa codes (Shokrollahi, Shokranian-Joyner), but there is also a paper on codes arising from combinatorial constructions (Michael). There are both, historical and mathematical papers on cryptography. Several of the contributions on cryptography describe the work done by the British and their allies during World War II to crack the German and Japanese ciphers (Hamer, Hilton, Tutte, Weierud, Urling). Some mathematical aspects of the Enigma rotor machine (Sherman) and more recent research on quantum cryptography (Lomonoco) are described. There are two papers concerned with the RSA cryptosystem and related number-theoretic issues (Wardlaw, Cosgrave).

The book covers up-to-date research in the form of surveys in an extremely hot field. Includes supplementary material: sn.pub/extras