Unit CRYPTOGRAPHY AND APPLICATIONS
- Course
- Informatics
- Study-unit Code
- A002090
- Curriculum
- Cybersecurity
- Teacher
- Massimo Giulietti
- CFU
- 12
- Course Regulation
- Coorte 2021
- Offered
- 2022/23
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa integrata
CRYPTOGRAPHY AND APPLICATIONS: MOD. 1
| Code | A002091 |
|---|---|
| CFU | 6 |
| Teacher | Daniele Bartoli |
| Teachers |
|
| Hours |
|
| Learning activities | Affine/integrativa |
| Area | Attività formative affini o integrative |
| Academic discipline | MAT/03 |
| Type of study-unit | Obbligatorio (Required) |
| Language of instruction | English |
| Contents | Basics on Coding Theory |
| Reference texts | S. Ball A Course in Algebraic Error-Correcting Codes Springer |
| Educational objectives | To introduce basic concepts of Coding Theory. |
| Prerequisites | Linear Algebra |
| Teaching methods | Frontal lessons |
| Other information | For further information, please contact the teacher daniele.bartoli@unipg.it |
| Learning verification modality | The valuation consists of a written part (basic definitions and numerical exercises) and a theoretical oral part |
| Extended program | Finite fields Codes and block codes Linear Codes Equivalence of codes Projective codes and spaces Griesmer Bound McWilliams dual codes and identities Cyclic codes Evaluation Codes MDS and NMDS codes Algebraic-Geometric Codes (outline) |
CRYPTOGRAPHY AND APPLICATIONS: MOD. 2
| Code | A002092 |
|---|---|
| CFU | 6 |
| Teacher | Massimo Giulietti |
| Teachers |
|
| Hours |
|
| Learning activities | Affine/integrativa |
| Area | Attività formative affini o integrative |
| Academic discipline | MAT/03 |
| Type of study-unit | Obbligatorio (Required) |
| 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. Advanced Signature Schemes. Post quantum Crypto. Homomorphich Crypto. |
| 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 course also aims to refine the abstraction skills and, on the other hand, show how a good theoretical knowledge allows the development of significant application tools. 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 Making judgments: -being able to construct and develop logical arguments with a clear identification of assumptions and conclusions; -be able to recognize correct proofs, and to identify fallacious reasoning. -be able to produce proposals capable of correctly interpreting complex problems in the field of cryptography and its applications. -being able to autonomously formulate pertinent judgments on the applicability of cryptographic models to theoretical and / or concrete situations. Communication skills: -Ability to present arguments, problems, ideas and solutions, both one's own and others, in mathematical terms and their conclusions, with clarity and accuracy and in ways appropriate to the listeners to whom one is addressing, both in form oral and in written form. -Ability to clearly motivate the choice of strategies, methods and contents, as well as the computational tools adopted. Learning skills: Read and deepen a topic of cryptographic literature. To deal autonomously with the systematic study of cryptographic topics not previously explored. |
| 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 | |
| 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. For information on support services for students with disabilities and / or SLD, visit the page http://www.unipg.it/disabilita-e-dsa |
| 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. Edwards curves and EdDSA. Secret sharing. Post-quantum crypto. Homomorphic encryption. |