Post-quantum and UC-Secure Oblivious Transfer from SPHF with Grey Zone

Oblivious Transfer (OT) is a major primitive for secure multi-party computation. Indeed, combined with symmetric primitives along garbled circuits, it allows any function evaluation between two parties. In this paper, we propose new approach to build OT protocols. Interestingly, our paradigm features security analysis in the Universal Composability (UC) framework and may be instantiated from post-quantum primitives. order do so, define named Smooth Projective Hash Function Grey Zone (SPHFwGZ) which can seen as relaxation of classical Functions, subset words one cannot claim correctness nor smoothness: grey zone. As concrete application, provide instantiations SPHFwGZ respectively based on Diffie-Hellman Learning With Errors (LWE) problems. Hence, quantum-resistant protocol UC-security random oracle model.