New bounds on the information rate of secret sharing schemes

Author

Blundo, Carlo ; De Santis, Alfred ; Gaggia, Antonio Giorgio ; Vaccaro, Ugo

Author_Institution

Dipartimento di Inf. ed Applicazioni, Salerno Univ., Italy

Volume

41

Issue

2

fYear

1995

fDate

3/1/1995 12:00:00 AM

Firstpage

549

Lastpage

554

Abstract

´A secret sharing scheme permits a secret to be shared among participants in such a way that only qualified subsets of participants can recover the secret, but any nonqualified subset has absolutely no information on the secret. We derive new limitations on the information rate of secret sharing schemes, that measures how much information is being distributed as shares as compared to the size of the secret key, and the average information rate, that is the ratio between the secret size and the arithmetic mean of the size of the shares. By applying the substitution technique, we are able to construct many new examples of access structures where the information rate is bounded away from 1. The substitution technique is a method used to obtain a new access structure by replacing a participant in a previous structure with a new access structure

Keywords

channel capacity; cryptography; access structures; arithmetic mean; average information rate; cryptography; information distribution; information rate; information theory; lower bound; ratio; secret key size; secret sharing schemes; secret size; shares size; substitution technique; upper bound; Arithmetic; Computer science; Councils; Cryptography; Degradation; Entropy; Indium tin oxide; Information rates; Information security; Size measurement;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.370169

Filename

370169