**How to Garble Arithmetic Circuits**

*Benny Applebaum and Yuval Ishai and Eyal Kushilevitz*

**Abstract: **Yao's garbled circuit construction transforms a boolean circuit $C:\{0,1\}^n\to\{0,1\}^m$ into a ``garbled circuit'' $\hat{C}$ along with $n$ pairs of $k$-bit keys, one for each input bit, such that $\hat{C}$ together with the $n$ keys corresponding to an input $x$ reveal $C(x)$ and no additional information about $x$. The garbled circuit construction is a central tool for constant-round secure computation and has several other applications.

Motivated by these applications, we suggest an efficient arithmetic variant of Yao's original construction. Our construction transforms an arithmetic circuit $C : \mathbb{Z}^n\to\mathbb{Z}^m$ over integers from a bounded (but possibly exponential) range into a garbled circuit $\hat{C}$ along with $n$ affine functions $L_i : \mathbb{Z}\to \mathbb{Z}^k$ such that $\hat{C}$ together with the $n$ integer vectors $L_i(x_i)$ reveal $C(x)$ and no additional information about $x$. The security of our construction relies on the intractability of the learning with errors (LWE) problem.

**Category / Keywords: **foundations / secure computation, randomized rencoding

**Publication Info: **An extended abstract of this work appears in FOCS 2011.

**Date: **received 5 May 2012, last revised 4 Jul 2013

**Contact author: **benny applebaum at gmail com

**Available format(s): **PDF | BibTeX Citation

**Version: **20130704:065254 (All versions of this report)

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