DeepAI AI Chat
Log In Sign Up

How to Find New Characteristic-Dependent Linear Rank Inequalities using Secret Sharing

by   Victor Peña-Macias, et al.
Universidad Nacional de Colombia

Determining information ratios of access structures is an important problem in secret sharing. Information inequalities and linear rank inequalities play an important role for proving bounds. Characteristic-dependent linear rank inequalities are rank inequalities which are true over vector spaces with specific field characteristic. In this paper, using ideas of secret sharing, we show a theorem that produces characteristic-dependent linear rank inequalities. These inequalities can be used for getting lower bounds on information ratios in linear secret sharing.


page 1

page 2

page 3

page 4


Common Information, Matroid Representation, and Secret Sharing for Matroid Ports

Linear information and rank inequalities as, for instance, Ingleton ineq...

How to Find New Characteristic-Dependent Linear Rank Inequalities using Binary Matrices as a Guide

In Linear Algebra over finite fields, a characteristic-dependent linear ...

Symmetries in Linear Programming for Information Inequalities

We study the properties of secret sharing schemes, where a random secret...

Characteristic-Dependent Linear Rank Inequalities via Complementary Vector Spaces

A characteristic-dependent linear rank inequality is a linear inequality...

Randomness Requirements for Three-Secret Sharing

We study a secret sharing problem with three secrets where the secrets a...

How to Use Undiscovered Information Inequalities: Direct Applications of the Copy Lemma

We discuss linear programming techniques that help to deduce corollaries...

One method for proving inequalities by computer

In this article we consider a method for proving a class of analytical i...