SubjectsSubjects(version: 850)
Course, academic year 2019/2020
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Authentication Schemes - NMMB431
Title in English: Autentifikační schémata
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: not taught
Language: Czech
Teaching methods: full-time
Class: M Mgr. MMIB
M Mgr. MMIB > Povinně volitelné
Classification: Informatics > Theoretical Computer Science
Mathematics > Algebra
Incompatibility : NMIB105
Interchangeability : NMIB105
Annotation -
Last update: T_KA (14.05.2013)
Cryptographic problems in groups of users. Information theoretical description of secret sharing schemes and relations to matroid and polymatroid theories.
Literature -
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (06.09.2013)

D.R. Stinson (2002) Cryptography, Chapman & Hall.

J.Oxley (1992) Matroid Theory, Oxford University Press.

I. Csiszár a J. Koerner (2011) Information Theory, Cambridge University Press

(new extended edition)

Syllabus -
Last update: T_KA (14.05.2013)

Introduction to information quantities, Shannon information, relative entropy, multi-information, conditional independence, entropic functions a entropic region.

Cryptographic problems in groups of users, secret sharing schemes,

information theoretical approach, threshold schemes, n-ary quasigroups, Shamir scheme, perfect secret sharing, linear schemes, information rates, Csirmaz theorem.

Introduction to matroid theory, linear matroids, Lehman theorem. Ideal secret sharing, estimates of rates by relaxation to polymatroids, approximations by finite groups.

Mathematical models for electronic voting, licitation, distributed signatures, access to databases, secure computing, additive and multiplicative secret sharing schemes.

Introduction to Shannon cryptography, random colorings, large deviations, Ahswede-Csiszar coloring lemma, asymptotic equipartition, random bit extraction from ergodic sequences,

random bits independent from eavesdropper.

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