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	For Angling may be said to be so much like the Mathematicks, that it can ne'er be fully learnt; at least not so fully, but that there will still be more new experiments left for the tryal of other men that succeed us. Izaak Walton
	Dipartimento di Matematica Facoltà di Ingegneria Università degli studi di Brescia Via Valotti 9 25133 Brescia Tel. +39 030 3715739/5776 Fax. +39 030 3715745 ResearcherID: F-4066-2010

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Luca Giuzzi, DPhil (Sussex)

Back.

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Teaching

Algebra for coding theory and cryptography

I am currently giving a course on Algebra for Coding Theory and cryptography, aimed ad both undergraduate and graduate students. The aim of this course is to introduce the necessary mathematical tools for the construction of encryption schemes and protocols and their cryptanalysis. Among the topics presented there are:

1. Elements of group theory
2. Public-key protocols based on the discrete log problem: Diffie-Hellman, ElGamal, STS and their variants
3. Pairing based cryptography: ID-based encryption and key escrow
4. Elements of number theory
5. RSA: implementation and cryptanalysis; OAEP and some security models
6. Primality testing
7. Finite fields
8. The construction of AES
9. Cryptanalysis of a symmetric cryptosystem
10. Elements of the theory of Elliptic Curves

More details and an extensive bibliography are available (in italian) on the following pages: 2010, 2011.

Combinatorial Geometry

I am also currently giving a course on Combinatorial Geometry at Università Cattolica. The aim of this course is to introduce some of the most important techniques and results in Combinatorial Geometry. In particular, among the topics discussed there will be:

1. Introduction to linear spaces and designs; the De Brujin-Erdős theorem and some of its consequences
2. Parameters of a design and bounds on the parameters of a symmetric 2-design
3. Hadamard 2-designs and Hadamard matrices: properties and some constructions; extension of a design and Hadamard 3-designs
4. The Bruck-Ryser-Chowla theorem and its consequences
5. Finite projective spaces and finite projective planes
6. Arcs and ovals in a Finite projective plane: the theorem of Segre and the existence of hyperovals in even characteristic
7. Blocking sets, Baer subplanes and Unitals
8. Applications to coding theory.

The main page for the course is here.

Topics in Algebra and Geometry

During the 2008/09 and 2009/10 academic years, I gave a course on ``Topics in Algebra and Geometry'', offered to 4th year students in Civil Engineering at Università degli Studi di Brescia. Main topics of this course are matrix theory and applications and an introduction to curves and surfaces in projective spaces. A bibliography and some lecture notes are available here.

Algebra and Geometry

In the 2006/07 and 2007/08 academic years, I taught course on Algebra and Geometry for first year undergraduate students of Mechanical Engineering at Politecnico di Bari. All relevant information is available (in italian) here.

Coding theory

In 2004/05 I gave a one semester course on Coding Theory at Università Cattolica. The book Codici correttori - un'introduzione arose from this experience.

Miscellanea

1. Notes on Discrete Maths (in Italian).
2. Some introductory notes on Classical Cryptography with A. Sonnino, as presented during the 2005 Summer school "G. Tallini" (Potenza, in Italian).
3. Notes of the lectures on An introduction to algebraic decoding of cyclic codes, 29-05-2006 and 31-05-2006, Facoltà di Ingegreria (Brescia).

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Teaching seminars

1. 09-07-2004, Geometry in Cryptography, talk on Elliptic Curves Cryptography, delivered at the 2004 Summer School "G. Tallini (Brescia).
2. 01-12-2004, Cryptography, security and anonimity, Facoltà di Ingengeria (Brescia)