Bipartite secret sharing and staircases

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F24%3A00582343" target="_blank" >RIV/67985556:_____/24:00582343 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0012365X24000402?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0012365X24000402?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.disc.2024.113909" target="_blank" >10.1016/j.disc.2024.113909</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Bipartite secret sharing and staircases

Popis výsledku v původním jazyce

Bipartite secret sharing schemes have a bipartite access structure in which the set of participants is divided into two parts and all participants in the same part play an equivalent role. Such a bipartite scheme can be described by a staircase: the collection of its minimal points. The complexity of a scheme is the maximal share size relative to the secret size, and the kappa-complexity of an access structure is the best lower bound provided by the entropy method. An access structure is kappa-ideal if it has kappa-complexity 1. Motivated by the abundance of open problems in this area, the main results can be summarized as follows. First, a new characterization of kappa-ideal multipartite access structures is given which offers a straightforward and simple approach to describe ideal bipartite and tripartite access structures. Second, the kappa-complexity is determined for a range of bipartite access structures, including those determined by two points, staircases with equal widths and heights, and staircases with all heights 1. Third, matching linear schemes are presented for some non-ideal cases, including staircases where all heights are 1 and all widths are equal. Finally, finding the Shannon complexity of a bipartite access structure can be considered as a discrete submodular optimization problem. An interesting and intriguing continuous version is defined which might give further insight to the large-scale behavior of these optimization problems.

Název v anglickém jazyce

Bipartite secret sharing and staircases

Popis výsledku anglicky

Bipartite secret sharing schemes have a bipartite access structure in which the set of participants is divided into two parts and all participants in the same part play an equivalent role. Such a bipartite scheme can be described by a staircase: the collection of its minimal points. The complexity of a scheme is the maximal share size relative to the secret size, and the kappa-complexity of an access structure is the best lower bound provided by the entropy method. An access structure is kappa-ideal if it has kappa-complexity 1. Motivated by the abundance of open problems in this area, the main results can be summarized as follows. First, a new characterization of kappa-ideal multipartite access structures is given which offers a straightforward and simple approach to describe ideal bipartite and tripartite access structures. Second, the kappa-complexity is determined for a range of bipartite access structures, including those determined by two points, staircases with equal widths and heights, and staircases with all heights 1. Third, matching linear schemes are presented for some non-ideal cases, including staircases where all heights are 1 and all widths are equal. Finally, finding the Shannon complexity of a bipartite access structure can be considered as a discrete submodular optimization problem. An interesting and intriguing continuous version is defined which might give further insight to the large-scale behavior of these optimization problems.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Discrete Mathematics

ISSN

0012-365X

e-ISSN

1872-681X

Svazek periodika

347

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

18

Strana od-do

113909

Kód UT WoS článku

001173957400001

EID výsledku v databázi Scopus

2-s2.0-85183938750