How to garble arithmetic circuits

Yao's garbled circuit construction transforms a boolean circuit C : {0, 1}n →{0, 1}m into a "garbled circuit" Ĉ along with n pairs of k-bit keys, one for each input bit, such that Ĉ 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 : Zn → Zm over integers from a bounded (but possibly exponential) range into a garbled circuit Ĉ along with n affine functions Li : Z → Zk such that °C together with the n integer vectors Li(xi) reveal C(x) and no additional information about x. The security of our construction relies on the intractability of the learning with errors problem.