## Cryptology ePrint Archive: Report 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 $2$ 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.

Short URL: ia.cr/2012/078

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