Revision #1 Authors: Benny Applebaum, Yuval Ishai, Eyal Kushilevitz

Accepted on: 4th July 2013 08:59

Downloads: 672

Keywords:

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.

TR12-058 Authors: Benny Applebaum, Yuval Ishai, Eyal Kushilevitz

Publication: 7th May 2012 18:03

Downloads: 1206

Keywords:

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.