Unit CRYPTOGRAPHY AND APPLICATIONS - MODULE 1
- Course
- Informatics
- Study-unit Code
- A002692
- Curriculum
- Artificial intelligence
- Teacher
- Massimo Giulietti
- Teachers
-
- Massimo Giulietti
- Hours
- 42 ore - Massimo Giulietti
- CFU
- 6
- Course Regulation
- Coorte 2022
- Offered
- 2023/24
- Learning activities
- Affine/integrativa
- Area
- Attività formative affini o integrative
- Academic discipline
- MAT/03
- Type of study-unit
- Opzionale (Optional)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- English
- Contents
- Classical Cryptography. Perfect Secrecy. Product Cryptosystems. DES and AES.
Linear and Differential Cryptanalysis. Introduction to Public-key Cryptography The RSA Cryptosystem. Factoring Algorithms.
The ElGamal Cryptosystem and Discrete Logs. Galois Fields.Elliptic Curves. Signature Schemes. Hash Functions - Reference texts
- D.R. Stinson, Cryptography - Theory and Practice - Chapman & Hall/CRC
Mathematics of Public Key Cryptography. Version 2.0. S.D. Gailbraith, 2018 - Educational objectives
- Cryptography and applications is the course of the Master of Science devoted to the mathematical foundations of network security. The main goal of the course is to provide students with the theoretical / mathematical basis to address concrete problems related to the security of communications. The main knowledge gained will be: -Familiarity with modular arithmetic and finite fields -Familiarity with the basics of algorithmic theory of numbers. -Familiarity with the notions of cryptosystem, public key encryption, digital signature, authentication, symmetric encryption. The main skills will be: - Assessing the safety of a symmetric cryptosystem - Evaluating the safety of an asymmetric cryptosystem - Assessing the difficulty of computational problems in number theory - Defining the parameters of a safe infrastructure of public key cryptography
- Prerequisites
- In order to understand and know how to apply most of the techniques described in the course, the student must have successfully passed the exams of Discrete Mathematics and Mathematical Analysis of the first degree
- Teaching methods
- The course consists of classroom lectures on all topics of the course. In each lesson about half of the time will be devoted to solving problems and exercises
- Other information
- For further information, please contact the teacher
massimo.giulietti@unipg.it - Learning verification modality
- The exam consists of an oral exam. Three questions relating to three separate parts of the program will be submitted to the student. The test lasts about 30-40 minutes and is designed to ensure the level of knowledge and ability of understanding reached by the student on the theoretical and methodological implications listed in the program (modular arithmetic and finite fields, public key encryption, symmetric encryption, hash and digital signature, The oral test will also allow to verify communication skills, appropriateness of language and autonomous organization of the exposure
- Extended program
- Classical Cryptography. The Shift Cipher. The Substitution Cipher. The Affine Cipher. The Vigenere Cipher
The Hill Cipher. The Permutation Cipher. Stream Ciphers.
Perfect Secrecy. Product Cryptosystems. Block ciphers: substitution-permutation networs. DES and AES.
Linear and Differential Cryptanalysis. Hash functions in cryptography. Iterated hash functions. Merkle-Damgard construction, SHA algorithms. Message authentication codes and universal hash families.
Introduction to Public-key Cryptography Elementary number theory: euclidean division, the chinese remainder theorem. The RSA Cryptosystem. Primality tests. Factoring Algorithms.
The ElGamal Cryptosystem and Discrete Logs. Algorithms for Discrete Logs. Galois Fields. Elliptic Curves. Signature Schemes. DSA and elliptic DSA.