Portale di Ateneo - En.Unibs.it

An introduction to cryptography.
What is cryptography? Modern cryptography and protocols.
Attack models and security definitions; symmetric and public key cryptography.
Shannon's theorem on cryptography

Elements of group theory
Finite groups; subgroups; laterals and transversals; normal subgroups and homomorphisms; cyclic groups; Lagrange's theorem; DLOG

DLOG-based cryptography
Diffie-Hellman and basic cryptoanalysis. Authentication and signatures. The STS protocol.
ElGamal encryption; its properties and its cryptoanalysis.

Modular integers and a little number theory
The Euclidean algorithm and its extended variant. Congruences and modular arithmetic; Fermat's little theorem; Jacobi's symbol and Euler's function. Primality testing.

RSA and its variants
Some basic properties of RSA; the Chinese remainder theorem; some attacks.
Semantic security and IND-CPA; variants of RSA; OAEP

Euclidean domains and finite fields.
The extended Euclidean algorithm revisited; Euclidean domains; polynomial rings; finite fields.

From DES to AES
Feistel's architecture; DES and 3-DES; design criteria; linear and differential cryptoanalysis.
AES: construction and implementation; properties and analysis.

Elliptic curve cryptography.
Elliptic curves over finite fields; the group law and its implementation.
EC-based protocols and their realisation.

Bilinear pairing and key escrow.
Bilinear pairing between groups; applications and attacks; ID-based encryption; key-escrow

Zero knowledge and anonimity
What does zero knowledge mean? Protocols and applications.
Anonimity in a digital world; re-encryption, mixnets and onions. The e-voting problem.

Homomorphic encryption

Linear error correcting codes
A mathematical theory of communication and Shannon's theorem (on coding theory).
Error correcting codes; block codes; Hamming distance; linear codes; bounds and syndrome decoding.

Cyclic codes
Construction; encoding and decoding.

Reed-Solomon and BCH codes.
Construction; bounds; Welch-Berlekamp's algorithm. The Discrete Fourier Transform and its applications.

LDPC and turbo codes

A short introduction to Network coding