Most people tend to view number theory as the very paradigm of pure mathematics. With the advent of computers, however, number theory has been finding an increasing number of applications in practical settings, such as in cryptography, random number generation, coding theory, and even concert hall acoustics. Yet other applications are still emerging - providing number theorists with some major new areas of opportunity. The 1996 IMA summer program on Emerging Applications of Number Theory was aimed at stimulating further work with some of these newest (and most attractive) applications. Concentration was on number theory's recent links with: (a) wave phenomena in quantum mechanics (more specifically, quantum chaos); and (b) graph theory (especially expander graphs and related spectral theory). This volume contains the contributed papers from that meeting and will be of interest to anyone intrigued by novel applications of modern number-theoretical techniques.

Most people tend to view number theory as the very paradigm of pure mathematics. With the advent of computers, however, number theory has been finding an increasing number of applications in practical settings, such as in cryptography, random number generation, coding theory, and even concert hall acoustics. Yet other applications are still emerging - providing number theorists with some major new areas of opportunity. The 1996 IMA summer program on Emerging Applications of Number Theory was aimed at stimulating further work with some of these newest (and most attractive) applications. Concentration was on number theory's recent links with: (a) wave phenomena in quantum mechanics (more specifically, quantum chaos); and (b) graph theory (especially expander graphs and related spectral theory). This volume contains the contributed papers from that meeting and will be of interest to anyone intrigued by novel applications of modern number-theoretical techniques.

This book is the proceedings of CRYPTO 86, one in a series of annual conferences devoted to cryptologic research. They have all been held at the University of California at Santa Barbara. The first conference in this series, CRYPTO 81, organized by A. Gersho, did not have a formal proceedings. The proceedings of the following four conferences in this series have been published as: Advances in Cryptology: Proceedings of Crypto 82, D. Chaum, R. L. Rivest, and A. T. Sherman, eds., Plenum, 1983. Advances in Cryptology: Proceedings of Crypto 83, D. Chaum, ed., Plenum, 1984. Advances in Cryptology: Proceedings of CRYPTO 84, G. R. Blakley and D. Chaum, eds., Lecture Notes in Computer Science #196, Springer, 1985. Advances in Cryptology - CRYPTO '85 Proceedings, H. C. Williams, ed., Lecture Notes in Computer Science #218, Springer, 1986. A parallel series of conferences is held annually in Europe. The first of these had its proceedings published as Cryptography: Proceedings, Burg Feuerstein 1982, T. Beth, ed., Lecture Notes in Computer Science #149, Springer, 1983.