Two-Round Oblivious Linear Evaluation from Learning with Errors

Oblivious Linear Evaluation (OLE) is the arithmetic analogue of the well-know oblivious transfer primitive. It allows a sender, holding an affine function f(x)=a+bx over a finite field or ring, to let a receiver learn f(w) for a w of the receiver’s choice. In terms of security, the sender remains oblivious of the receiver’s input w, whereas the receiver learns nothing beyond f(w) about f. In recent years, OLE has emerged as an essential building block to construct efficient, reusable and maliciously-secure two-party computation. In this work, we present efficient two-round protocols for OLE over large fields based on the Learning with Errors (LWE) assumption, providing a full arithmetic generalization of the oblivious transfer protocol of Peikert, Vaikuntanathan and Waters (CRYPTO 2008). At the technical core of our work is a novel extraction technique which allows to determine if a non-trivial multiple of some vector is close to a q-ary lattice.