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The mathematics of secrets
Tuesday January 20th, 2009, h.20,30Keeping a secret can be difficult, but it is even more difficult to communicate it to another distant person without anyone else being able to understand it. Cryptography appeared in past times when messengers on horses were bringing encrypted messages from one city to another in order to communicate the position of the enemy or the name of the traitor amongst the king's trustees. Nowadays, we are all constantly sending encrypted messages around the world, for example when we use our credit card. The most advanced cryptographic methods are based on the theory of numbers, a branch of mathematics that at first it was considered to lack applications but today it has become necessary for the coordination of world commerce and the society of information. Prime numbers are of crucial importance in the process of encrypting a message. But have we really been able to invent an encrypting method that is impregnable? How does it work? Is it theoretically possible to find a way to violate secrets? What would happen if this was to take place nowadays?
Alberto Berretti
Graduated in Physics in 1981 at the University of Rome "La Sapienza", he then moved for studies and work in France, New York and Lausanne. Nowadays, he is teaching Analysis in the Engineering Department at the University of Rome "Tor Vergata". He has a great number of scientific publications in important international magazines in the field of Statistical Mechanics, Montecarlo methods and Hamiltonian Dynamic Systems. Over the last years he has also been interested in electronic communications from both the technical and the social point of view. He is the autor, together with Vittorio Zambardino, of the book "Internet - Avviso ai Naviganti" published by Donzelli, that has sold more than seven thousand copies.He is giving seminars about this topic at the chair of "Sociology of Communication" at the University of Rome "La Sapienza" and the Italian Institute of Philosophical Studies at the University of Naples. He has also collaborated for the supplement of "La Reppublica" entitled Information Technology.
Francesco Pappalardi
After graduating in Mathematics at the University of Rome "La Sapienza", he has obtained his PhD in Mathematics in Montréal at the "McGill University" in 1993. In the same year he became assistant professor at the "Concordia University" of Montréal and the next year he moved to Paris, where he worked at the University of Paris Sud. Since 1995 he is a researcher in Rome and since 2002 he is associate professor of Algebra in the Mathematics Department at the University of Rome "Roma Tre". His research is focused on the analytical theory of numbers with particular interest in the problems regarding the distribution of the primitive roots. He is also interested in the analytical applications of the Theory of Elliptical Curves and the Analytical Theory of the classical arithmetic functions. He has scientific collaborations with various countries amongst which Australia, India and Canada.