Paper 2012/078 Original: eprint.iacr.org/2012/078 ↗
Fully Homomorphic Encryption without Modulus Switching from Classical GapSVP
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 $2$ 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.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2012-05-18: last updated
- 2012-02-23: published
- Short URL
- https://ia.cr/2012/078
- License
- https://creativecommons.org/licenses/by/4.0/
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}
}