Cryptographic problems in groups of users. Information theoretical description of secret sharing schemes and
relations to matroid and polymatroid theories.
Last update: JUDr. Dana Macharová (16.12.2010)
Kryptografické problémy ve skupinách uživatelů. Informačně teoretický popis schémat sdílení tajemství a
souvislosti s teorií matroidů a polymatroidů. Úvod do Shannovy kryptografie.
Literature -
Last update: JUDr. Dana Macharová (16.12.2010)
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)
Last update: JUDr. Dana Macharová (16.12.2010)
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.
(nová rozšířená edice)
Syllabus -
Last update: JUDr. Dana Macharová (16.12.2010)
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.
Last update: JUDr. Dana Macharová (16.12.2010)
Úvod do informačních měr. Shannonova informace, vzájemná entropie,
multiinformace, podmíněná nezávislost, entropické funkce a region.
Kryptografické problémy ve skupinách uživatelů. Schémata sdílení tajemství,
