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.
Category / Keywords: public-key cryptography / fully homomorphic encryption, learning with errors Date: received 19 Feb 2012, last revised 18 May 2012 Contact author: zvika at stanford edu Available format(s): PDF | BibTeX Citation Note: Revised due to typos. Version: 20120518:231322 (All versions of this report) Short URL: ia.cr/2012/078