The series is aimed specifically at publishing peer-reviewed reviews and contributions presented at conferences, workshops, and international seminars as well as edited volumes commemorating and honoring significant achievements by mathematicians. This content covers various topics within pure and applied mathematics and provides up-to-date coverage of new developments, methods, and applications.

The Proceedings contain twenty selected, refereed contributions arising from the International Conference on Public-Key Cryptography and Computational Number Theory held in Warsaw, Poland, on September 11-15, 2000.

The conference, attended by eightyfive mathematicians from eleven countries, was organized by the Stefan Banach International Mathematical Center.

This volume contains articles from leading experts in the world on cryptography and computational number theory, providing an account of the state of research in a wide variety of topics related to the conference theme. It is dedicated to the memory of the Polish mathematicians Marian Rejewski (1905-1980), Jerzy Róøycki (1909-1942) and Henryk Zygalski (1907-1978), who deciphered the military version of the famous Enigma in December 1932 January 1933. A noteworthy feature of the volume is a foreword written by Andrew Odlyzko on the progress in cryptography from Enigma time until now.

Inhalt

Contents:

Andrew Odlyzko: Mathematics, cryptology, and technology · Johannes Buchmann, Safuat Hamdy: A survey on IQ cryptography · Jean-Marc Couveignes: Algebraic groups and discrete logarithm · Karl Dilcher: Fermat numbers, Wieferich and Wilson primes: computations and generalizations· Andreas Enge: How to distinguish hyperelliptic curves in even characteristic · Steven D. Galbraith: Limitations of constructive Weil descent · Otokar GroSek, Spyros S. Magliveras, Wandi Wei: On the security of a public-key cryptosystem · Jeffrey Hoffstein, Joseph Silverman: Optimizations for NTRU · Michael John Jacobson, Jr., Renate Scheidler, Hugh C. Williams: The efficiency and security of a real quadratic field based key exchange protocol · Przemyslaw Kubiak: Extending the binary gcd algorithms · Daniel Kucner, Miroslaw Kutylowski: Stochastic kleptography detection · Arjen K. Lenstra, Eric R. Verheul: An overview of the XTR public key system · Siguna Müller: A survey of IND-CCA secure public-key encryption schemes relative to factoring · Volker Müller: Efficient point multiplication for elliptic curves over special optimal extension fields · Harald Niederreiter: Error-correcting codes and cryptography · Secret public key schemes · Attila Pethö: Index form surfaces and construction of elliptic curves over large finite fields · Herman te Riele: On the size of solutions of the inequality (ax+b)< (ax) · Claus Peter Schnorr: Security of DL-encryption and signatures against generic attacks - a survey · Edlyn Teske: Square-root algorithms for the discrete logarithm problem (a survey) · Horst G. Zimmer: Height functions on elliptic curves.