We introduce a new approach to actively secure two-party computation based on so-called oblivious linear function evaluation (OLE), a natural generalisation of oblivious transfer (OT) and a special case of the notion of oblivious polynomial evaluation introduced by Naor and Pinkas at STOC 1999. OLE works over a finite field F. In an OLE the sender inputs two field elements a ƒ F and b ƒ F, and the receiver inputs a field element x ∈ F and learns only ƒx) = ax + b. Our protocol can evaluate an arithmetic circuit over a finite field F given black-box access to OLE for F. The protocol is unconditionally secure and consumes only a constant number of OLEs per multiplication gate. An OLE over a field F of size O(2κ) be implemented with communication O(κ). This gives a protocol with communication complexity O(C κ) for large enough fields, where C is an arithmetic circuit computing the desired function.

Cut-and-choose (CC) is the standard approach to making Yao's garbled circuit two-party computation (2PC) protocol secure against malicious adversaries. Traditional cut-and-choose operates at the level of entire circuits, whereas the LEGO paradigm (Nielsen & Orlandi, TCC 2009) achieves asymptotic improvements by performing cut-and-choose at the level of individual gates. In this work we propose a unified approach called DUPLO that spans the entire continuum between these two extremes. The cut-and-choose step in our protocol operates on the level of arbitrary circuit "components," which can range in size from a single gate to the entire circuit itself.