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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2021/2022

Mathematical Cryptography

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Code Completion Credits Range Language
B4M01MKR Z,ZK 6 4P+2S Czech
Lecturer:
Alena Gollová
Tutor:
Alena Gollová
Supervisor:
Department of Mathematics
Synopsis:

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.

Requirements:
Syllabus of lectures:

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.

Syllabus of tutorials:
Study Objective:
Study materials:

[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.

Note:
Further information:
http://math.feld.cvut.cz/gollova/mkr.html
Time-table for winter semester 2021/2022:
Time-table is not available yet
Time-table for summer semester 2021/2022:
06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue
Wed
roomT2:C3-51
Gollová A.
12:45–14:15
(lecture parallel1)
Dejvice
T2:C3-51
Thu
roomT2:C3-51
Gollová A.
09:15–10:45
(lecture parallel1)
Dejvice
T2:C3-51
roomT2:C3-51
Gollová A.
11:00–12:30
(lecture parallel1
parallel nr.101)

Dejvice
T2:C3-51
Fri
The course is a part of the following study plans:
Data valid to 2022-08-13
For updated information see http://bilakniha.cvut.cz/en/predmet4695306.html