Fully Homomorphic Encryption without Modulus Switching from Classical GapSVP

Zvika Brakerski

Paper 2012/078

Fully Homomorphic Encryption without Modulus Switching from Classical GapSVP

Zvika Brakerski

Abstract

We present a new tensoring technique for LWE-based fully homomorphic encryption. While in all previous works, the ciphertext noise grows quadratically ( $B \to B^{2} \cdot \poly (n)$ ) with every multiplication (before ``refreshing''), our noise only grows linearly ( $B \to B \cdot \poly (n)$ ). We use this technique to construct a \emph{scale-invariant} fully homomorphic encryption scheme, whose properties only depend on the ratio between the modulus $q$ and the initial noise level $B$ , and not on their absolute values. Our scheme has a number of advantages over previous candidates: It uses the same modulus throughout the evaluation process (no need for ``modulus switching''), and this modulus can take arbitrary form, including a power of which carries obvious advantages for implementation. In addition, security can be \emph{classically} reduced to the worst-case hardness of the GapSVP problem (with quasi-polynomial approximation factor), whereas previous constructions could only exhibit a quantum reduction to GapSVP.

Note: Revised due to typos.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: fully homomorphic encryption learning with errors
Contact author(s): zvika @ stanford edu
History: 2012-05-18: last of 5 revisions; 2012-02-23: received; See all versions
Short URL: https://ia.cr/2012/078
License: CC BY

BibTeX

@misc{cryptoeprint:2012/078,
      author = {Zvika Brakerski},
      title = {Fully Homomorphic Encryption without Modulus Switching from Classical {GapSVP}},
      howpublished = {Cryptology {ePrint} Archive, Paper 2012/078},
      year = {2012},
      url = {https://eprint.iacr.org/2012/078}
}