Mathematics of Cryptology


September 26 - October 2, 2003



Historically, cryptology focused on the design and cryptanalysis of encryption schemes. But, nowadays, cryptology offers much more: signature schemes, provable security, secret sharing, multi-party computation, zero knowledge protocols, electronic payment schemes, electronic voting schemes, to name a few. At the same time, the mathematics that is involved has become quite sophisticated: integer factorization using number fields, lattices, discrete logarithms on elliptic curves or on Jacobians of curves of higher genus, cohomological tools for point counting, pairings, among others.


The aim of the workshop was to help further strengthening and extending the ties between the cryptology community and that part of the mathematics community with an interest in cryptology, especially from algebra, number theory and geometry.


Leading experts from these communities were invited to give key-note lectures:

         Jacques Stern: When provable security meets number theory;

         Hendrik Lenstra: Recent developments in primality testing;

         Rene Schoof: Construction of Weil and Tate pairings;

         Alan Lauder: Computing zeta functions of hyperelliptic curves via deformations;

         Ueli Maurer: Probability Theory in Cryptography;

         Gerhard Frey: Applications of pairings in cryptography;

         Hans Dobbertin: Some Mathematics Behind the Design of Block Ciphers;

         Frederik Vercauteren: p-adic algorithms for counting points on elliptic curves;

         Arjen Lenstra: Integer factorization and cryptology;

         Phong Nguyen: New results on lattice-based cryptography;

         Ronald Cramer: Secure encryption from hard subgroup membership problems;

         Berry Schoenmakers: Homomorphic cryptosystems and applications;

         Peter Stevenhagen: Constructing elliptic curves with a given number of points;

         Igor Shparlinski: Playing 'Hide-and-Seek' in Finite Fields: Hidden Number Problem and Its Applications;

         Bas Edixhoven: A possible generalisation of Schoof's algorithm.


There were about 60 registered participants. One third came from the Netherlands, and two thirds from Australia, Belgium, Denmark, U.K., Germany, Finland, France, Italy, Poland, Spain, Switzerland, Turkey, and the U.S.A. Among the Dutch participants, three came from the Ministry of Defense, and one from industry (Cistron).


The workshop was financed by: NWO, Lenstra (Spinoza grant), EIDMA, the Thomas Stieltjes Institute for Mathematics, STW, and the Lorentz Center.


Our impression is that the workshop was a big success. The lectures were of very high quality, but the atmosphere remained quite informal. There was much interaction between the participants. The facilities and staff of the Lorentz Center were very much appreciated by both organizers and participants.


S.J. Edixhoven (University Leiden, The Netherlands)

B. Schoenmakers (University Eindhoven, The Netherlands)

R. Cramer (Brics Aarhus, Denmark)