Quantum oblivious transfer with authentication for remote CNOT operation

Teleportation-based distributed quantum gates generate classical dependency data (Pauli-frame by-products) whose integrity is decisive under active attacks. This work gives a composable (UC-style) methodology for authenticated distributed quantum computation that separates the cryptographic requirements of Clifford and non-Clifford operations. We formalize Quantum Oblivious Transfer with Authentication (QOT-A) as a selection-hiding, tamper-detecting interface for delivering branch-dependent correction data with explicit leakage metadata and show how to realize it from any UC-secure OT with only additive security loss. Our main contribution is a circuit-level compiler: any two-party Clifford + T circuit can be UC-realized as an authenticated ideal functionality using only (i) authenticated one-bit delivery (AuthBit) for all Clifford/remote-CNOT correction traffic and (ii) exactly one invocation of QOT-A per non-Clifford T-correction point. We provide a full simulation-based proof outline with explicit distinguishing bounds that compose linearly in the number of authenticated correction deliveries, link-verification soundness, and quantum authentication soundness, together with detailed simulator structure and formal reduction statements. We further prove a separation showing that integrity-only correction delivery (AuthBit) suffices for Clifford gates but is insufficient for frame-private authenticated non-Clifford corrections, thereby characterizing where OT-type privacy becomes necessary.