Exploring Naccache-Stern Knapsack Encryption

The Naccache-Stern public-key cryptosystem (NS) relies on the conjectured hardness of the modular multiplicative knapsack problem: Given $$p,\{v_i\},\prod v_i^{m_i} \bmod p$$ , find the $$\{m_i\}$$ . Given this scheme’s algebraic structure it is interesting to systematically explore its variants and...

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Bibliographic Details
Published inInnovative Security Solutions for Information Technology and Communications Vol. 10543; pp. 67 - 82
Main Authors Brier, Éric, Géraud, Rémi, Naccache, David
Format Book Chapter
LanguageEnglish
Published Switzerland Springer International Publishing AG 2017
Springer International Publishing
SeriesLecture Notes in Computer Science
Online AccessGet full text
ISBN3319692836
9783319692838
ISSN0302-9743
1611-3349
DOI10.1007/978-3-319-69284-5_6

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Summary:The Naccache-Stern public-key cryptosystem (NS) relies on the conjectured hardness of the modular multiplicative knapsack problem: Given $$p,\{v_i\},\prod v_i^{m_i} \bmod p$$ , find the $$\{m_i\}$$ . Given this scheme’s algebraic structure it is interesting to systematically explore its variants and generalizations. In particular it might be useful to enhance NS with features such as semantic security, re-randomizability or an extension to higher-residues. This paper addresses these questions and proposes several such variants.
Bibliography:Original Abstract: The Naccache-Stern public-key cryptosystem (NS) relies on the conjectured hardness of the modular multiplicative knapsack problem: Given \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p,\{v_i\},\prod v_i^{m_i} \bmod p$$\end{document}, find the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{m_i\}$$\end{document}. Given this scheme’s algebraic structure it is interesting to systematically explore its variants and generalizations. In particular it might be useful to enhance NS with features such as semantic security, re-randomizability or an extension to higher-residues. This paper addresses these questions and proposes several such variants.
ISBN:3319692836
9783319692838
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-319-69284-5_6