Authentication Schemes

Syllabus

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.

Annotation

Cryptographic problems in groups of users. Information theoretical description of secret sharing schemes and relations to matroid and polymatroid theories.