<?xml version="1.0" encoding="UTF-8"?>
<article article-type="Research Article">
  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher">journal-of-discrete-mathematical-sciences-and-cryptography</journal-id>
      <journal-title-group>
        <journal-title>Journal of Discrete Mathematical Sciences and Cryptography</journal-title>
      </journal-title-group>
      <issn publication-format="electronic">2169-0065</issn>
      <issn publication-format="print">0972-0529</issn>
      <publisher>
        <publisher-name>Taru Publications</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.1080/09720529.2021.1923920</article-id>
      <title-group>
        <article-title>A new ideal secret sharing scheme based on a tree</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Meriem</surname>
            <given-names>Ghanem</given-names>
          </name>
          <aff>L’IFORCE Laboratory, Faculty of Mathematics, Bab-Ezzouar, Algiers 16111, USTHB University, P. O. Box 32, El Alia, Algeria</aff>
        </contrib>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Bouroubi</surname>
            <given-names>Sadek</given-names>
          </name>
          <aff>L’IFORCE Laboratory, Faculty of Mathematics, Bab-Ezzouar, Algiers 16111, USTHB University, P. O. Box 32, El Alia, Algeria</aff>
        </contrib>
      </contrib-group>
      <volume>26</volume>
      <issue>1</issue>
      <fpage>121</fpage>
      <lpage>138</lpage>
      <pub-date date-type="pub">
        <day>27</day>
        <month>10</month>
        <year>2021</year>
      </pub-date>
      <abstract>
        <p>One of the methods used in order to protect a secret K is a secret sharing scheme. In this method, the secret K is distributed among a finite set of participants P by a special participant called the dealer, assumed to be honest, in such a way that only predefined subsets of participants can recover the secret after collaborating with their secret shares. The construction of secret sharing schemes has received a considerable attention of many researchers whose main goal was to improve the information rate. In this paper, we focused on the hierarchical secret sharing. Related to the previous works, we propose a novel simpler construction of a secret sharing scheme, where the access structure is a tree according to the hierarchical concept of companies illustrated through its organization chart. We prove that the proposed scheme is ideal by showing that the information rate equals 1. In order to show the efficiency of the proposed scheme, we discuss all possible kinds of attacks and prove that the security is ensured. Finally, we include a detailed didactic example of a small company organization chart.</p>
      </abstract>
      <kwd-group>
        <kwd>Hierarchical secret sharing scheme</kwd>
        <kwd>Qualified subsets</kwd>
        <kwd>Access structure</kwd>
        <kwd>Interpolation</kwd>
        <kwd>Information rate</kwd>
      </kwd-group>
      <custom-meta-group>
        <custom-meta>
          <meta-name>access</meta-name>
          <meta-value>open</meta-value>
        </custom-meta>
        <custom-meta>
          <meta-name>retracted</meta-name>
          <meta-value>no</meta-value>
        </custom-meta>
      </custom-meta-group>
    </article-meta>
  </front>
</article>
