Unit CRYPTOGRAPHY AND APPLICATIONS

Course
Mathematics
Study-unit Code
A002090
Curriculum
Matematica per la crittografia
Teacher
Massimo Giulietti
CFU
12
Course Regulation
Coorte 2023
Offered
2023/24
Type of study-unit
Obbligatorio (Required)
Type of learning activities
Attività formativa integrata

CRYPTOGRAPHY AND APPLICATIONS: MOD. 1

Code A002091 6 Massimo Giulietti Massimo Giulietti 42 ore - Massimo Giulietti Caratterizzante Formazione teorica avanzata MAT/03 Obbligatorio (Required) English 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 D.R. Stinson, Cryptography - Theory and Practice - Chapman & Hall/CRCMathematics of Public Key Cryptography. Version 2.0. S.D. Gailbraith, 2018 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 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 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 For further information, please contact the teacher massimo.giulietti@unipg.it 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 Classical Cryptography. The Shift Cipher. The Substitution Cipher. The Affine Cipher. The Vigenere CipherThe 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.

CRYPTOGRAPHY AND APPLICATIONS: MOD. 2

Code A002092 6 Marco Timpanella Marco Timpanella 42 ore - Marco Timpanella Caratterizzante Formazione teorica avanzata MAT/03 Obbligatorio (Required) English Post-Quantum Cryptography: Lattice-based Cryptography, Code-based Cryptography, Multivariate Cryptography, Hash-based Cryptography.Secret Sharing Schemes (SSS): Shamir's Scheme, SSS from geometric structures, SSS from linear codes.Privacy-Preserving Cryptographic Systems: Homomorphic Encryption, Secure Multi-Party Computation, Private Information Retrieval. D.R. Stinson, Cryptography - Theory and Practice - Chapman & Hall/CRCMathematics of Public Key Cryptography. Version 2.0. S.D. Gailbraith, 2018 "Cryptography and Applications - Module II" is a Master's Degree course dedicated to advanced topics in the field of cybersecurity and cryptography.The main objective of the course is to build upon the basic cryptography knowledge acquired in the first module and provide students with theoretical and mathematical foundations to tackle advanced problems related to communication security. The course also aims to refine students' ability to abstract and demonstrate how a solid theoretical understanding enables the development of significant application tools.The main knowledge gained will be: -Awareness of different approaches used in post-quantum cryptography.-Familiarity with cryptographic tools for privacy protection, such as private information retrieval, secure multi-party computation, and homomorphic encryption.-Proficiency in key distribution methods based on Secret Sharing Schemes.The main skills will be: -Assessing the security of a post-quantum encryption system. - Evaluating the security of a post-quantum signature system. - Assessing the difficulty of computational problems in number theory - Evaluating the privacy-preserving capabilities of a system for a user.Making judgments:-being able to construct and develop logical arguments with a clearidentification of assumptions and conclusions;-be able to recognize correct proofs, and to identify fallacious reasoning.-be able to produce proposals capable of correctly interpreting complexproblems in the field of cryptography and its applications.-being able to autonomously formulate pertinent judgments on theapplicability of cryptographic models to theoretical and / or concretesituations.Communication skills:-Ability to present arguments, problems, ideas and solutions, both one'sown and others, in mathematical terms and their conclusions, with clarityand accuracy and in ways appropriate to the listeners to whom one isaddressing, both in form oral and in written form.-Ability to clearly motivate the choice of strategies, methods andcontents, as well as the computational tools adopted.Learning skills:Read and deepen a topic of cryptographic literature. To deal autonomouslywith the systematic study of cryptographic topics not previously explored. 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, Mathematical Analysis of the first degree and of Cryptography and applications mod. I of the master degree. 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 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. 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 / orSLD, visit the page http://www.unipg.it/disabilita-e-dsa Post-Quantum Cryptography:Lattice-based Cryptography: introduction to lattices, lattice problems, NTRU (operation and security).Code-based Cryptography: linear codes, decoding problem, McEliece cryptosystem.Multivariate Cryptography: MQ problem, hidden field equations cryptosystem (operation and security), digital signature scheme (oil and vinegar).Hash-based Cryptography: Lamport's one-time signature scheme (operation and security).Secret Sharing Schemes (SSS): types of SSS and implementations. Shamir's Scheme. SSS from geometric structures. SSS from linear codes.Privacy-Preserving Cryptographic Systems:Homomorphic Encryption: Partially Homomorphic Encryption, Somewhat Homomorphic Encryption, Fully Homomorphic Encryption: examples and applications.Secure Multi-Party Computation and connections with SSS and homomorphic encryption.Private Information Retrieval: PIR protocols and PIR codes (constructions using covering codes, k-partial packings, sets of points in projective spaces over finite fields).
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