Subject description - BE4M01MKR
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| BE4M01MKR | Mathematical Cryptography | ||
|---|---|---|---|
| Roles: | PO | Extent of teaching: | 4P+2S |
| Department: | 13101 | Language of teaching: | EN |
| Guarantors: | Velebil J. | Completion: | Z,ZK |
| Lecturers: | Gollová A. | Credits: | 6 |
| Tutors: | Gollová A. | Semester: | L |
Web page:
http://math.feld.cvut.cz/gollova/mkr.htmlAnotation:
The lecture will set mathematical foundations of modern cryptography (RSA, El-Gamal, elliptic curve cryptography, hashing). Also, the related algorithms for primality testing (numbers sieves) and discrete logarithms will be treated.Course outlines:
| 1. | Basic notions of number theory, generators of random numbers and random primes. | |
| 2. | A review of basic cryptosystems (RSA, El-Gamal). | |
| 3. | Rabin-Miller test for generating random primes. | |
| 4. | Using Euler's totient function for factorisation, generator of Z_m^*. | |
| 5. | Hashing and message authentication. | |
| 6. | Subexponential algorithms for factorisation and discrete logarithm. | |
| 7. | Basic ideas of quadratic sieve. | |
| 8. | Basic ideas of deterministic primality test. | |
| 9. | Elliptic curves and their Abelian group. | |
| 10. | Discrete logarithm on an elliptic curve. Generators of random elliptic curves. | |
| 11. | Attacks on RSA cryptosytem and its implementation. | |
| 12. | Quantum computing and satefy of cryptosystems. | |
| 13. | Stockpile. |
Exercises outline:
Literature:
| [1] | D.Hankerson, A.J.Menezes, S.Vanstone, Guide to elliptic curve cryptography, Springer, 2004. | |
| [2] | V.Shoup, A Computational introduction to number theory and algebra, Cambridge University Press, 2008, http://shoup.net/ntb/ |
Requirements:
Subject is included into these academic programs:
| Program | Branch | Role | Recommended semester |
| MEOI2_2018 | Cyber Security | PO | 2 |
| Page updated 14.3.2025 12:51:33, semester: L/2024-5, L/2025-6, Z/2024-5, Z/2025-6, Send comments about the content to the Administrators of the Academic Programs | Proposal and Realization: I. Halaška (K336), J. Novák (K336) |