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New Ideas to Build Noise-Free Homomorphic Cryptosystems

We design a very simple private-key encryption scheme whose decryption function is a rational function. This scheme is not born naturally homomorphic. To get homomorphic properties, a nonlinear additive homomorphic operator is specifically developed. The security analysis is based on symmetry consid...

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Autores principales: Gavin, Gerald, Tainturier, Sandrine
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7334995/
http://dx.doi.org/10.1007/978-3-030-51938-4_21
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author Gavin, Gerald
Tainturier, Sandrine
author_facet Gavin, Gerald
Tainturier, Sandrine
author_sort Gavin, Gerald
collection PubMed
description We design a very simple private-key encryption scheme whose decryption function is a rational function. This scheme is not born naturally homomorphic. To get homomorphic properties, a nonlinear additive homomorphic operator is specifically developed. The security analysis is based on symmetry considerations and we prove some formal results under the factoring assumption. In particular, we prove IND-CPA security in the generic ring model. Even if our security proof is not complete, we think that it is convincing and that the technical tools considered in this paper are interesting by themselves. Moreover, the factoring assumption is just needed to ensure that solving nonlinear equations or finding non-null polynomials with many roots is difficult. Consequently, the ideas behind our construction could be re-used in rings satisfying these properties. As motivating perspectives, we then propose to develop a simple multiplicative operator. To achieve this, randomness is added in our construction giving hope to remove the factoring assumption in order to get a pure multivariate encryption scheme.
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spelling pubmed-73349952020-07-06 New Ideas to Build Noise-Free Homomorphic Cryptosystems Gavin, Gerald Tainturier, Sandrine Progress in Cryptology - AFRICACRYPT 2020 Article We design a very simple private-key encryption scheme whose decryption function is a rational function. This scheme is not born naturally homomorphic. To get homomorphic properties, a nonlinear additive homomorphic operator is specifically developed. The security analysis is based on symmetry considerations and we prove some formal results under the factoring assumption. In particular, we prove IND-CPA security in the generic ring model. Even if our security proof is not complete, we think that it is convincing and that the technical tools considered in this paper are interesting by themselves. Moreover, the factoring assumption is just needed to ensure that solving nonlinear equations or finding non-null polynomials with many roots is difficult. Consequently, the ideas behind our construction could be re-used in rings satisfying these properties. As motivating perspectives, we then propose to develop a simple multiplicative operator. To achieve this, randomness is added in our construction giving hope to remove the factoring assumption in order to get a pure multivariate encryption scheme. 2020-06-06 /pmc/articles/PMC7334995/ http://dx.doi.org/10.1007/978-3-030-51938-4_21 Text en © Springer Nature Switzerland AG 2020 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
Gavin, Gerald
Tainturier, Sandrine
New Ideas to Build Noise-Free Homomorphic Cryptosystems
title New Ideas to Build Noise-Free Homomorphic Cryptosystems
title_full New Ideas to Build Noise-Free Homomorphic Cryptosystems
title_fullStr New Ideas to Build Noise-Free Homomorphic Cryptosystems
title_full_unstemmed New Ideas to Build Noise-Free Homomorphic Cryptosystems
title_short New Ideas to Build Noise-Free Homomorphic Cryptosystems
title_sort new ideas to build noise-free homomorphic cryptosystems
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7334995/
http://dx.doi.org/10.1007/978-3-030-51938-4_21
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