### Exploring Naccache-Stern Knapsack Encryption

Éric Brier, Rémi Géraud, and David Naccache

##### Abstract

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.

Available format(s)
Category
Public-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
EncryptionSecurity proofsDLP
Contact author(s)
david naccache @ ens fr
History
Short URL
https://ia.cr/2017/421

CC BY

BibTeX

@misc{cryptoeprint:2017/421,
author = {Éric Brier and Rémi Géraud and David Naccache},
title = {Exploring Naccache-Stern Knapsack Encryption},
howpublished = {Cryptology ePrint Archive, Paper 2017/421},
year = {2017},
note = {\url{https://eprint.iacr.org/2017/421}},
url = {https://eprint.iacr.org/2017/421}
}

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