Search result: Catalogue data in Spring Semester 2023
Mathematics Master  | |||||||||||||||||||||||||||
 ElectivesFor the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields. | |||||||||||||||||||||||||||
| Electives: Applied Mathematics and Further Application-Oriented Fields ¬ | |||||||||||||||||||||||||||
| Selection: Theoretical Computer Science, Discrete Mathematics In the Master's programme in Mathematics 401-3052-05L Graph Theory is eligible as an elective course, but only if 401-3052-10L Graph Theory isn't recognised for credits (neither in the Bachelor's nor in the Master's programme). For the category assignment take contact with the Study Administration Office (www.math.ethz.ch/studiensekretariat) after having received the credits. | |||||||||||||||||||||||||||
| Number | Title | Type | ECTS | Hours | Lecturers | ||||||||||||||||||||||
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| 263-4400-00L | Advanced Graph Algorithms and Optimization | W | 10 credits | 3V + 3U + 3A | R. Kyng, M. Probst | ||||||||||||||||||||||
| Abstract | This course will cover a number of advanced topics in optimization and graph algorithms. | ||||||||||||||||||||||||||
| Learning objective | The course will take students on a deep dive into modern approaches to graph algorithms using convex optimization techniques. By studying convex optimization through the lens of graph algorithms, students should develop a deeper understanding of fundamental phenomena in optimization. The course will cover some traditional discrete approaches to various graph problems, especially flow problems, and then contrast these approaches with modern, asymptotically faster methods based on combining convex optimization with spectral and combinatorial graph theory. | ||||||||||||||||||||||||||
| Content | Students should leave the course understanding key concepts in optimization such as first and second-order optimization, convex duality, multiplicative weights and dual-based methods, acceleration, preconditioning, and non-Euclidean optimization. Students will also be familiarized with central techniques in the development of graph algorithms in the past 15 years, including graph decomposition techniques, sparsification, oblivious routing, and spectral and combinatorial preconditioning. | ||||||||||||||||||||||||||
| Prerequisites / Notice | This course is targeted toward masters and doctoral students with an interest in theoretical computer science. Students should be comfortable with design and analysis of algorithms, probability, and linear algebra. Having passed the course Algorithms, Probability, and Computing (APC) is highly recommended, but not formally required. If you are not sure whether you're ready for this class or not, please consult the instructor. | ||||||||||||||||||||||||||
| 252-0408-00L | Cryptographic Protocols | W | 6 credits | 2V + 2U + 1A | M. Hirt | ||||||||||||||||||||||
| Abstract | In a cryptographic protocol, a set of parties wants to achieve some common goal, while some of the parties are dishonest. Most prominent example of a cryptographic protocol is multi-party computation, where the parties compute an arbitrary (but fixed) function of their inputs, while maintaining the secrecy of the inputs and the correctness of the outputs even if some of the parties try to cheat. | ||||||||||||||||||||||||||
| Learning objective | To know and understand a selection of cryptographic protocols and to be able to analyze and prove their security and efficiency. | ||||||||||||||||||||||||||
| Content | The selection of considered protocols varies. Currently, we consider multi-party computation, secret-sharing, broadcast and Byzantine agreement. We look at both the synchronous and the asynchronous communication model, and focus on simple protocols as well as on highly-efficient protocols. | ||||||||||||||||||||||||||
| Lecture notes | We provide handouts of the slides. For some of the topics, we also provide papers and/or lecture notes. | ||||||||||||||||||||||||||
| Prerequisites / Notice | A basic understanding of fundamental cryptographic concepts (as taught for example in the course Information Security) is useful, but not required. | ||||||||||||||||||||||||||
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| 263-4660-00L | Applied Cryptography  | W | 8 credits | 3V + 2U + 2P | K. Paterson, F. Günther | ||||||||||||||||||||||
| Abstract | This course will introduce the basic primitives of cryptography, using rigorous syntax and game-based security definitions. The course will show how these primitives can be combined to build cryptographic protocols and systems. | ||||||||||||||||||||||||||
| Learning objective | The goal of the course is to put students' understanding of cryptography on sound foundations, to enable them to start to build well-designed cryptographic systems, and to expose them to some of the pitfalls that arise when doing so. | ||||||||||||||||||||||||||
| Content | Basic symmetric primitives (block ciphers, modes, hash functions); generic composition; AEAD; basic secure channels; basic public key primitives (encryption,signature, DH key exchange); ECC; randomness; applications. | ||||||||||||||||||||||||||
| Literature | Textbook: Boneh and Shoup, “A Graduate Course in Applied Cryptography”, http://toc.cryptobook.us/book.pdf. | ||||||||||||||||||||||||||
| Prerequisites / Notice | Students should have taken the D-INFK Bachelor's course “Information Security" (252-0211-00) or an alternative first course covering cryptography at a similar level. / In this course, we will use Moodle for content delivery: https://moodle-app2.let.ethz.ch/course/view.php?id=19644. | ||||||||||||||||||||||||||
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| 263-4656-00L | Digital Signatures | W | 5 credits | 2V + 2A | D. Hofheinz | ||||||||||||||||||||||
| Abstract | Digital signatures as one central cryptographic building block. Different security goals and security definitions for digital signatures, followed by a variety of popular and fundamental signature schemes with their security analyses. | ||||||||||||||||||||||||||
| Learning objective | The student knows a variety of techniques to construct and analyze the security of digital signature schemes. This includes modularity as a central tool of constructing secure schemes, and reductions as a central tool to proving the security of schemes. | ||||||||||||||||||||||||||
| Content | We will start with several definitions of security for signature schemes, and investigate the relations among them. We will proceed to generic (but inefficient) constructions of secure signatures, and then move on to a number of efficient schemes based on concrete computational hardness assumptions. On the way, we will get to know paradigms such as hash-then-sign, one-time signatures, and chameleon hashing as central tools to construct secure signatures. | ||||||||||||||||||||||||||
| Literature | Jonathan Katz, "Digital Signatures." | ||||||||||||||||||||||||||
| Prerequisites / Notice | Ideally, students will have taken the D-INFK Bachelors course "Information Security" or an equivalent course at Bachelors level. | ||||||||||||||||||||||||||
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