Subject description - B4M01MKR
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Explanatory Notes
Instructions
| B4M01MKR | Mathematical Cryptography | ||
|---|---|---|---|
| Roles: | PO | Extent of teaching: | 4P+2S |
| Department: | 13101 | Language of teaching: | CS |
| 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 sets mathematical foundations of modern cryptography (RSA, El-Gamal, elliptic curve cryptography). Related algorithms for primality testing, number factorisation and discrete logarithm are treated as well.Course outlines:
| 1. | Introduction into cryptography. Basic notions of number theory. | |
| 2. | Counting modulo n. Complexity of operations in Z_n. | |
| 3. | RSA cryptosystem and attacks on it. | |
| 4. | Abelian groups. | |
| 5. | Element order in a group, cyclic groups. | |
| 6. | Structure of Z_n^* groups. | |
| 7. | Discrete logarithm, Diffie-Hellman protocol. | |
| 8. | Elliptic curves, discrete logarithm on an elliptic curve. | |
| 9. | Generating of random primes, probability algoritms. | |
| 10. | Primality tests, Carmichael numbers. | |
| 11. | Factorisation using the Euler function. | |
| 12. | Subexponential algorithms for discrete logarithm. | |
| 13. | Subexponential algorithms for factorisation, a quadratic sieve. | |
| 13. | Quantum computing and satefy of cryptosystems. |
Exercises outline:
Literature:
| [1] | V.Shoup, A Computational introduction to number theory and algebra, Cambridge University Press, 2008, http://shoup.net/ntb/ | |
| [2] | D.Boneh, Twenty Years of Attacks on the RSA Cryptosystem. https://crypto.stanford.edu/~dabo/papers/RSA-survey.pdf | |
| [3] | D.Hankerson, A.J.Menezes, S.Vanstone, Guide to elliptic curve cryptography, Springer, 2004. |
Requirements:
Subject is included into these academic programs:| Program | Branch | Role | Recommended semester |
| MPOI2_2018 | Cyber Security | PO | 2 |
| Page updated 14.10.2024 17:51:34, semester: Z/2025-6, Z,L/2024-5, L/2023-4, Send comments about the content to the Administrators of the Academic Programs | Proposal and Realization: I. Halaška (K336), J. Novák (K336) |