This course provides an introduction to modern Cryptography and related mathematical problems.
The purpose of the course is to provide a knowledge of the main concepts and tools of cryptography.
The aim of the course is to provide mathematical tools employed by modern Cryptography which are fundamental to pursue further studies in this field. In particular, we will focus on public-key Cryptography.
More precisely, at the end of the course students will be able to:
• recognise the main modern cryptosystems and digital signatures; • master factoring algorithms and primality tests; • spot weaknesses of a cryptosystem; • recognise the main attacks to the Discrete Logarithm Problem; • master algebraic and geometric constructions which are fundamental in Cryptography such as algebraic curves, finite groups, polynomials and lattices.
The following mathematical prerequisites are mandatory: modular arithmetic, linear algebra, groups, fields. It is recommended to have passed one linear algebra course (e.g. ALGA) and one abstract algebra course (e.g. Algebra 1+2).
Lectures.
- Classic Cryptosystems (substitution, Hill, Vigenère) - Shannon’s Theory, Perfect Secrecy, and the One-Time Pad - Public Key Cryptography (RSA cryptosystem and Diffie-Hellman key exchange) - Primality tests (Legendre, Solovay-Strassen, Miller-Rabin) - Factoring Algorithms (Pollard p-1, quadratic sieve) - Discrete Logarithm Problem and related attacks (Baby Step Giant Step, Pollard rho, Pohlig-Hellman, Index Calculus) - Elliptic Curve Cryptography - An introduction to post-quantum Cryptography
- Stinson, Paterson - "Cryptography. Theory and Practice" - Galbraith - "Mathematics of Public Key Cryptography" - Silverman, Pipher, Hoffstein - "An Introduction to Mathematical Cryptography"
Ricevimento: By appointment.
ALESSIO CAMINATA (President)
ANNA MARIA BIGATTI
EMANUELA DE NEGRI (President Substitute)
FRANCESCO STRAZZANTI (Substitute)
IRENE VILLA (Substitute)
The class will start according to the academic calendar.
Oral exam.
Students with DSA certification ("specific learning disabilities"), disability or other special educational needs are advised to contact the teacher at the beginning of the course to agree on teaching and examination methods that, in compliance with the teaching objectives, take account of individual learning arrangements and provide appropriate compensatory tools.
Questions of the oral exam will concern the main topics presented during the lectures. The aim is to establish not only whether students will have reached an appropriate level of knowledge, but also whether they can analize and approach problems related to Cryptography.
Attendance is recommended.
