BICI-INDAM 2005 International PhD School on Mathematical Aspects of Modern Cryptography

BICI-INDAM 2005 International PhD School on Mathematical Aspects of Modern Cryptography 4-9 September, 2005 University of Bologna Residential Center Bertinoro (Forlì), Italy

[ What the School is About
| Schedule
| Registration
| Important Dates
| Location
| How to Reach Bertinoro
| Participants
| Organization and Sponsorship
| Local Weather Forecast]

What the School is About

The modern discipline of Cryptography is a prime example of the usefullness of sophisticated mathematical ideas applied to important practical problems. Ironically, among the various branches of Mathematics it is Number Theory that has perhaps contributed the most to modern Cryptography. That is, the very discipline that Gauss and Hardy, in his famous apology, had described as the most sublime because of its complete lack of practical utility. Recent important developments in the field of Cryptography, notably the development of a polynomial-time primality test announced a couple of years ago, have strengthened even further this connection.

The school is made possible by the financial support of INDAM, the Italian Institute of Higher Mathematics. Courses will be taught by well-known experts and will touch on the following aspects:

Computational-Complexity based Cryptography, a module taught by Rafail Ostrovsky, UCLA
This module introduces students to complexity-based approach to cryptography and cryptographic protocol design. Topics include notions of hardness, one-way functions, hard-core bits, pseudo-random generators, pseudo-random functions, public-key and private-key encryption, semantic security and CCA2-security, message authentication, digital signatures, interactive proofs, zero-knowledge proofs, collision-resistant hash functions, oblivious transfer, private information retrieval, commitment protocols, key-agreement, and two-party secure computation.
Information-Theory based Cryptography, a module taught by Ueli Maurer, ETH Zürich
A perspective on the role of information theory in cryptography is presented, demonstrating that information-theoretic thinking arises in many diverse contexts in cryptography. In a broad sense, if one considers also uncertainty measures other than Shannon entropy, many cryptographic definitions, constructions, and security proofs are information-theoretic in nature. Information-theoretic arguments arise not only in the context of security against computationally unbounded adversaries, with both impossibility proofs and constructive results, but also computational (intractability) aspects are sometimes intricately intertwined with purely information-theoretic arguments. The presented topics include the classical information-theoretic analysis of encryption and authentication, randomness extraction and privacy amplification, secret-key agreement by public discussion, the bounded storage model, random systems and their indistinguishability, the random oracle model, and information-theoretic aspects of computational cryptographic security proofs .
Lecture notes: [1] [2]
Infrastructure and Arakelov divisors, a module taught by René Schoof, Università di Roma Tor Vergata
Nowadays, the Number Field Sieve is the most powerful algorithm for factoring integers. A related algorithm is Buchmann's method for computing class groups and unit groups of number fields. Buchmann's algorithm has been implemented in several computer algebra packages (Kant, Pari, Lidia, Magma). It exploits the so-called "infrastructure" of a number field. In this course we present the mathematical theory of the Number Field Sieve and of Buchmann's algorithm from the point of view of Arakelov theory. This module is coupled with the next one. You can find useful material here and here.
Lattices in Computational Number Theory, a module taught by Hendrik Lenstra, Universiteit Leiden
Lattice basis reduction methods form the workhorse for many number-theoretic algorithms, including algorithms that are of importance in cryptography. After a brief explanation of what lattices are and how basis reduction methods work, the course will emphasize applications, taken from the following list: algebraic number theory; integer programming; diophantine approximation; factoring polynomials; linear algebra over the integers; finding restricted divisors.
You can find here lecture notes and a useful paper.

How to participate:

You can register here.

Fellowships: A certain number of student grants will be available. If you are eligible, you can apply right now for a BICI-UNESCO (ROSTE) grant.

Other fellowships are graciously made available by contributions of INDAM and Romagna Acque. If you are a student you can apply using this application form.

For any inquiries contact the School Director.

Schedule

08.00-09.00	arrivals	breakfast
	Sat	Sun	Mon	Tue	Wed	Thu	Fri
09.30-10.30		Lenstra	Schoof	Lenstra	Sightseeing	Lenstra	Schoof
10.30-11.00		Coffee				Coffee
11.00-12.00		Schoof	Lenstra	Lenstra		Maurer	Schoof
12.30-13.30		Lunch				Lunch
15.00-16.00		Maurer	Ostrovsky	Maurer		Ostrovsky	Ostrovsky
16.15-17.15		Ostrovsky	Maurer	Maurer		Schoof	Ostrovsky

Important Dates

Arrival: Saturday 3, September 2005

Departure: Friday 9 - Saturday 10, September 2005

Arrival:	Saturday 3, September 2005
Departure:	Friday 9 - Saturday 10, September 2005

Location

The meeting will be held in the small medieval hilltop town of Bertinoro. This town is in Emilia Romagna about 50km east of Bologna at an elevation of about 230m. Here is a map putting it in context. It is easily reached by train and taxi from Bologna and is close to many splendid Italian locations such as Ravenna, a treasure trove of byzantine art and history, and the Republic of San Marino (all within 35km) as well as some less well-known locations like the thermal springs of Fratta Terme and the castle and monastic gardens of Monte Maggio. Bertinoro can also be a base for visiting some of the better-known Italian locations such as Padua, Ferrara, Vicenza, Venice, Florence and Siena.

Bertinoro itself is picturesque, with many narrow streets and walkways winding around the central peak. The meeting will be held in a redoubtable ex-Episcopal fortress that has been converted by the University of Bologna into a modern conference center with computing facilities and Internet access. From the fortress you can enjoy a beautiful the vista that stretches from the Tuscan Apennines to the Adriatic coast.

How to Reach Bertinoro

List of participants

Alessio Davide, Università degli studi di Padova
Chmielewski Lukasz, Warsaw University
Fitzpatrick Noel, University Dublin City, DCU
Garcia Flavio, Radbout University Nijmegen
Isaksson Marcus, Chalmers University
Kamara Seny, Johns Hopkins University
Kaminska Aleksandra, Warsaw University
Kulesza Kamil, Polish Academy of Science
Lenstra Hendrik, University of Leiden
Maffei Marco, Alcatel Alenia Spazio
Maurer Ueli, ETH Zürich
Moci Luca, Università "La Sapienza" Roma
Morra Anna, Università degli studi di Padova
Orciari Stefano, Università degli studi di Milano
Orlandi Claudio, Università degli studi di Firenze
Ostrovsky Rafail, UCLA
Panconesi Alessandro, Università "La Sapienza" Roma
Persiano Pino, Università di Salerno
Piccioni Maria Luce, Università di Tor Vergata, Roma
Raub Dominik, ETH Zürich
Schoof Rene, Università di Tor Vergata, Roma
Ventre Carmine, Università di Salerno
Visconti Ivan, Università di Salerno
Zhang Qing, Royal Holloway, University of London

Organization and Sponsorship

School Directors
School Directors	Alessandro Panconesi, University La Sapienza of Rome, and Pino Persiano, University of Salerno
Local Organization
Local Organization	Andrea Bandini, Elena Della Godenza, Centro Congressi di Bertinoro
Sponsored by	BICI Bertinoro International Center for Informatics
	INDAM Istituto Nazionale di Alta Matematica
	Romagna Acque

[ What the School is About | Schedule | Registration | Important Dates | Location | How to Reach Bertinoro | Participants | Organization and Sponsorship | Local Weather Forecast]