Paper 2013/262

An efficient FHE based on the hardness of solving systems of non-linear multivariate equations

Gérald Gavin

Abstract

We propose a general framework to develop fully homomorphic encryption schemes (FHE) without using the Gentry's technique. The security relies on the difficulty of solving systems of non-linear equations (which is a $\mathcal{NP}$-complete problem). While the security of our scheme has not been reduced to a provably hard instance of this problem, security is globally investigated.

Note: In this second version, Problem 1 and Problem 2 are slightly modified (see Section 2). The symmetric functions s_j should be constrained to be polynomials : this is needed In the proof of Proposition 1 to ensure that s_j(y_1,y_2,....)=s_j(y_2',y_1',...).

Metadata
Available format(s)
PDF
Publication info
Published elsewhere. Unknown where it was published
Keywords
FHEhomomorphic cryptosystem
Contact author(s)
gavin @ univ-lyon1 fr
History
2013-05-19: revised
2013-05-13: received
See all versions
Short URL
https://ia.cr/2013/262
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2013/262,
      author = {Gérald Gavin},
      title = {An efficient FHE based on the hardness of solving systems of non-linear multivariate equations},
      howpublished = {Cryptology ePrint Archive, Paper 2013/262},
      year = {2013},
      note = {\url{https://eprint.iacr.org/2013/262}},
      url = {https://eprint.iacr.org/2013/262}
}
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