Computationally Secure Semi‐Quantum All‐Or‐Nothing Oblivious Transfer from Dihedral Coset States

Abstract

The quest for perfect quantum oblivious transfer (QOT) with information‐theoretic security remains a challenge, necessitating the exploration of computationally secure QOT as a viable alternative. Unlike the unconditionally secure quantum key distribution (QKD), the computationally secure QOT relies on specific quantum‐safe computational hardness assumptions, such as the post‐quantum hardness of learning with errors (LWE) problem and quantum‐hard one‐way functions. This raises an intriguing question: Are there additional efficient quantum hardness assumptions that are suitable for QOT? In this work, leveraging the dihedral coset state derived from the dihedral coset problem (DCP), a basic variant of OT, known as the all‐or‐nothing OT, is studied in the semi‐quantum setting. Specifically, the DCP originates from the dihedral hidden subgroup problem (DHSP), conjectured to be challenging for any quantum polynomial‐time algorithms. First, a computationally secure quantum protocol is presented for all‐or‐nothing OT, which is then simplified into a semi‐quantum OT protocol with minimal quantumness, where the interaction needs merely classical communication. To efficiently instantiate the dihedral coset state, a powerful cryptographic tool called the LWE‐based noisy trapdoor claw‐free functions (NTCFs) is used. The construction requires only a three‐message interaction and ensures perfect statistical privacy for the receiver and computational privacy for the sender.