Post-Quantum Oblivious Transfer from Smooth Projective Hash Functions with Grey Zone

TL;DR

This paper introduces a new cryptographic primitive called SPHFwGZ, enabling the construction of post-quantum secure Oblivious Transfer protocols with UC-security, based on LWE and Diffie-Hellman assumptions.

Contribution

It defines the novel SPHFwGZ primitive, analyzes its security in the UC framework, and provides instantiations based on post-quantum assumptions for secure OT.

Findings

SPHFwGZ can be instantiated from LWE and Diffie-Hellman problems.

The proposed OT protocol is secure against quantum adversaries.

The protocol achieves UC-security in the random oracle model.

Abstract

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