Preface: geometry, combinatorial designs and cryptology

Preface: geometry, combinatorial designs and cryptology

This issue of the journal is devoted to the themes of Geometry, Combinatorial Designs and Cryptology. The guest editors selected sixteen contributions covering various areas within these themes, ranging from public-key cryptography to matters related to key distribution and authentication, from problems in graph theory to resolvability issues in designs, from finite projective planes to higher-...

Divisible Designs , Laguerre Geometry , and Beyond Summer School on Combinatorial Geometry and Optimisation 2004

Final version, layout for two-sided printing using A4 paper (December 2004). Preface These notes are based upon a series of lectures given at the Summer School on Combina-torial Geometry and Optimisation 2004 " Giuseppe Tallini ". It took place at the Catholic University of Brescia, Italy, from June 4th until June 10th, 2004, within the MIUR COFIN 2004 research project Strutture Geometriche, Co...

The Geometry of Numbers in Cryptology

Combinatorial Designs and Availability

We consider a variation of Design Theory, in which the elements of the base set may be “available” or not. The random variable of interest is the number of subsets in the design which contain some available element. We are particularly interested in the variance of this variable, and we look for arrangements which minimize this value. We provide the solution to some instances of this problem; w...

Combinatorial Geometry

Combinatorial geometry is the study of combinatorial properties of fundamental geometric objects, whose origins go back to antiquity. It has come into maturity in the last century through the seminal works of O. Helly, K. Borsuk, P. Erdős, H. Hadwidger, L. Fejes Tóth, B. Grübaum and many other excellent mathematicians who initiated new combinatorial approaches to classical questions studied by ...