Paper 2015/821

A general framework for building noise-free homomorphic cryptosystems

Gérald Gavin

Abstract

We present a general framework for developing and analyzing homomorphic cryptosystems whose security relies on the difficulty of solving systems of nonlinear equations over Z/nZ, n being an RSA modulus. In this framework, many homomorphic cryptosystems can be conceptualized. Based on symmetry considerations, we propose a general assumption that ensures the security of these schemes. To highlight this, we present an additive homomorphic private-key cryptosystem and we prove its security. Finally, we propose two motivating perspectives of this work. We first propose an FHE based on the previous scheme by defining a simple multiplicative operator. Secondly, we propose ways to remove the factoring assumption in order to get pure multivariate schemes.

Metadata
Available format(s)
PDF
Category
Secret-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
Homomorphic cryptosystemFHEMultivariate encryption schemeFactoring assumption
Contact author(s)
gavin @ univ-lyon1 fr
History
2015-08-21: received
Short URL
https://ia.cr/2015/821
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2015/821,
      author = {Gérald Gavin},
      title = {A general framework for building noise-free homomorphic cryptosystems},
      howpublished = {Cryptology ePrint Archive, Paper 2015/821},
      year = {2015},
      note = {\url{https://eprint.iacr.org/2015/821}},
      url = {https://eprint.iacr.org/2015/821}
}
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