# Subject description - B4M01MKR

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B4M01MKR Mathematical Cryptography
Roles:PO Extent of teaching:4P+2S
Department:13101 Language of teaching:CS
Guarantors:  Completion:Z,ZK
Lecturers:Gollová A. Credits:6
Tutors:Gollová A. Semester:L

Anotation:

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:

  V.Shoup, A Computational introduction to number theory and algebra, Cambridge University Press, 2008, http://shoup.net/ntb/  D.Boneh, Twenty Years of Attacks on the RSA Cryptosystem. https://crypto.stanford.edu/~dabo/papers/RSA-survey.pdf  D.Hankerson, A.J.Menezes, S.Vanstone, Guide to elliptic curve cryptography, Springer, 2004.

Requirements:

Webpage:

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

Subject is included into these academic programs:

 Program Branch Role Recommended semester MPOI2_2016 Cyber Security PO 2 MPOI2_2018 Cyber Security PO 2

 Page updated 10.8.2020 12:51:48, semester: Z,L/2020-1, L/2019-20, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)