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Course Catalog 2013-2014
MAT-63256 Mathematical Cryptology, 7 cr |
Additional information
The course is lectured biennially.
Suitable for postgraduate studies
Person responsible
Keijo Ruohonen, Stephane Foldes
Lessons
| Study type | P1 | P2 | P3 | P4 | Summer | Implementations | Lecture times and places |
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Requirements
Closed-book written exam.
Completion parts must belong to the same implementation
Learning Outcomes
After completing the course the student is familiar with the mostly used cryptosystems in modern cryptography, and their basic properties. The student also masters the required prerequisites in number theory and algebra. In particular, the student identifies the division of algorithms into intractable and tractable, so essential in cryptography. Completing the course the student is able to identify common cryptosystems, and evaluate their advantages and disadvantages, and the underlying mathematical paradigms, and for cryptographic protocols, too, to an extent (this is however mostly left to the relevant courses in information technology). Despite modern cryptology being the result of relatively recent research, it has progressed far and wide, and therefore it is simply not possible to include outcomes for it all within a single course. Completing the course the student nevertheless should be able the generalize and extend the skills.
Content
| Content | Core content | Complementary knowledge | Specialist knowledge |
| 1. | Elements and basic algorithms of number theory and algebra. Simple examples. | Applications to analysis of more complex cases. Alternative algorithms. | |
| 2. | The AES cryptosystem, its goals and algebraic background. | Further analysis of the AES cryptosystem. | |
| 3. | Computational complexity and its relation to cryptographic concerns, in particular to public-key systems. | ||
| 4. | The RSA cryptosystem, its goals, analyses and number-theoretic background. | Further analysis of RSA, its variants and special uses. | |
| 5. | Cryptosystems based on group-theoretic concepts: ELGAMAL, DIFFIE-HELLMAN, ECC. | Further analyses of these systems, their variants and special uses. | |
| 6. | Overview of the NTRU cryptosystem. | Further analysis and structure of NTRU. | |
| 7. | Quantum encryption, its background and systems. |
Instructions for students on how to achieve the learning outcomes
Final grade is determined from tutorial activity and the final closed-book exam. Passing the course requires passing the final exam, and for this at most half of the maximum points are required. Bonus points obtained by tutorial activity may be used to add the exam points according to a given scheme. A thorough mastering of the core content should be sufficient for passing the course with grade 3. To get the degree 4 at least some complementary knowledge is usually required, getting the grade 5 then requires a more thorough mastering of this knowledge.
Assessment scale:
Numerical evaluation scale (1-5) will be used on the course
Partial passing:
Study material
| Type | Name | Author | ISBN | URL | Edition, availability, ... | Examination material | Language |
| Book | An Introduction to Cryptography | Mollin, R.A. | 1-58488-127-5 | No | English | ||
| Book | An Introduction to Mathematical Cryptography | Hoffstein, J., Pipher, J., Silverman, J.H. | 978-0-387-77993-5 | No | English | ||
| Other online content | Homepage | No | English | ||||
| Summary of lectures | Mathematical Cryptology | Ruohonen, K. | Yes | English |
Prerequisites
| Course | Mandatory/Advisable | Description |
| MAT-60050 Algebra | Advisable | 1 |
| MAT-60056 Algebra | Advisable | 1 |
| MAT-02650 Algoritmimatematiikka | Advisable |
1 . The courses are interchangable.
Prerequisite relations (Requires logging in to POP)
Correspondence of content
| Course | Corresponds course | Description |
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More precise information per implementation
| Implementation | Description | Methods of instruction | Implementation |
| Lectures and tutorials of Mathematical Cryptology. |
Contact teaching: 0 % Distance learning: 0 % Self-directed learning: 0 % |