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BE4M01MKR	Mathematical Cryptography
Roles:	PO	Extent of teaching:	4P+2S
Department:	13101	Language of teaching:	EN
Guarantors:		Completion:	Z,ZK
Lecturers:		Credits:	6
Tutors:		Semester:	L

Web page:

http://math.feld.cvut.cz/gollova/mkr.html

Anotation:

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

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Page updated 18.1.2026 12:51:41, semester: Z,L/2026-7, L/2025-6, Z/2027-8, Z/2025-6, Send comments about the content to the Administrators of the Academic Programs

Proposal and Realization: I. Halaška (K336), J. Novák (K336)