On Cut-and-Choose Oblivious Transfer and Its Variants.

Motivated by the recent progress in improving efficiency of secure computation, we study cut-and-choose oblivious transfer--a basic building block of state-of-the-art constant round two-party secure computation protocols that was introduced by Lindell and Pinkas TCC 2011. In particular, we study the question of realizing cut-and-choose oblivious transfer and its variants in the OT-hybrid model. Towards this, we provide new definitions of cut-and-choose oblivious transfer and its variants that suffice for its application in cut-and-choose techniques for garbled circuit based two-party protocols. Furthermore, our definitions conceptually simplify previous definitions including those proposed by Lindell Crypto 2013, Huang et al., Crypto 2014, and Lindell and Riva Crypto 2014. Our main result is an efficient realization under our new definitions of cut-and-choose OT and its variants with small concrete communication overhead in an OT-hybrid model. Among other things this implies that we can base cut-and-choose OT and its variants under a variety of assumptions, including those that are believed to be resilient to quantum attacks. By contrast, previous constructions of cut-and-choose OT and its variants relied on DDH and could not take advantage of OT extension. Also, our new definitions lead us to more efficient constructions for multistage cut-and-choose OT--a variant proposed by Huang et al.﾿Crypto 2014 that is useful in the multiple execution setting.