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:ℤ ⁿ → ℤ ^m over integers from a bounded (but possibly exponential)range into a garbled circuit Ĉ along with n affine functions L _i:ℤ → ℤ ^k such that Ĉ 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.