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Number Theory and RSA - NMMB206

Title:	Teorie čísel a RSA
Guaranteed by:	Department of Algebra (32-KA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2016 to 2016
Semester:	summer
E-Credits:	5
Hours per week, examination:	summer s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	doc. Mgr. et Mgr. Jan Žemlička, Ph.D.
Class:	M Bc. MMIB M Bc. MMIB > Povinně volitelné M Bc. MMIB > 2. ročník M Bc. MMIT M Bc. MMIT > Povinně volitelné M Bc. OM M Bc. OM > Zaměření MSTR M Bc. OM > Povinně volitelné M Bc. OM > 2. ročník
Classification:	Mathematics > Algebra
Incompatibility :	NMIB001
Interchangeability :	NMIB001
Is pre-requisite for:	NMMB349
Is interchangeable with:	NMIB001

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Annotation -

Last update: G_M (16.05.2012)

Required course for bachelor's program in Information security. An introduction to fundamental concepts of number theory. Focuses on primality testing and methods of integer factorization in connection with the RSA cryptosystem.

Literature - Czech

Last update: doc. RNDr. David Stanovský, Ph.D. (22.02.2021)

Borevič, Šafarevič: Number Theory, Academic Press 1966;

Riesel: Prime numbers and computer methods for factorization, Birkhäuser 1985;

Cohen: A course in computational algebraic number theory, Springer-Verlag 1993.

Syllabus -

Last update: doc. RNDr. David Stanovský, Ph.D. (22.02.2021)

Properties of integers with algebraic interpretation (Euler function, primitive elements, Gauss integers and squares). Quadratic residues and reciprocity law. RSA cryptosystem. Searching for prime numbers (prime numbers of special type, density of primes, Bertrand postulate). Simple composite-number tests (Carmichael numbers, Solovay-Strassen test, Rabin-Miller test). An outline of other methods used for primality testing and factorization. Continued fractions. Diophantine equations.