Imperfect 1-out-of-2 quantum oblivious transfer: bounds, a protocol, and its experimental implementation

Abstract

Oblivious transfer is an important primitive in modern cryptography. Applications include secure multiparty computation, oblivious sampling, e-voting, and signatures. Information-theoretically secure perfect 1-out-of 2 oblivious transfer is impossible to achieve. Imperfect variants, where both participants' ability to cheat is still limited, are possible using quantum means while remaining classically impossible. Precisely what security parameters are attainable remains unknown. We introduce a theoretical framework for studying semirandom quantum oblivious transfer, which is shown to be equivalent to regular oblivious transfer in terms of cheating probabilities. We then use it to derive bounds on cheating. We also present a protocol with lower cheating probabilities than previous schemes, together with its optical realization. We show that a lower bound of 2/3 on the minimum achievable cheating probability can be directly derived for semirandom protocols using a different method and definition of cheating than used previously. The lower bound increases from 2/3 to approximately 0.749 if the states output by the protocol are pure and symmetric. The oblivious transfer scheme we present uses unambiguous state elimination measurements and can be implemented with the same technological requirements as standard quantum cryptography. The cheating probabilities are 3/4 and approximately 0.729 for sender and receiver respectively, which is lower than in existing protocols. Using a photonic test-bed, we have implemented the protocol with honest parties, as well as optimal cheating strategies.

arXiv comment22 pages, 1 figure, v2 moderate changes, published version

References in corpus (25)

• On the reality of the quantum state
• Unconditionally secure quantum bit commitment is impossible
• Insecurity of Quantum Secure Computations
• Linear Optics C-Phase gate made simple
• Demonstration of a simple entangling optical gate and its use in Bell-state analysis
• Demonstration of an optical quantum controlled-NOT gate without path interference
• Quantum inference of states and processes
• Maximum Confidence Quantum Measurements
• Quantum digital signatures with quantum key distribution components
• Secure Quantum Signatures Using Insecure Quantum Channels
• Conditions for compatibility of quantum state assignments
• Complete Insecurity of Quantum Protocols for Classical Two-Party Computation
• Conclusive Exclusion of Quantum States
• Upper bounds on the error probabilities and asymptotic error exponents in quantum multiple state discrimination
• Communication tasks with infinite quantum-classical separation
• Spacetime-constrained oblivious transfer
• No-Signalling Bound on Quantum State Discrimination
• Antidistinguishability of Pure Quantum States
• Quantum advantage for probabilistic one-time programs
• Practical and unconditionally secure spacetime-constrained oblivious transfer
• Minimum-cost quantum measurements for quantum information
• Communication of partial ignorance with qubits
• One-out-of-$m$ spacetime-constrained oblivious transfer
• Strong connections between quantum encodings, non-locality and quantum cryptography
• Unambiguous quantum state elimination for qubit sequences

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• Privacy and correctness trade-offs for information-theoretically secure quantum homomorphic encryption
• Error-tolerant oblivious transfer in the noisy-storage model
• Experimental demonstration of optimal unambiguous two-out-of-four quantum state elimination
• Quantum Rabin oblivious transfer using two pure states
• Breaking barriers in two-party quantum cryptography via stochastic semidefinite programming
• Quantum Universally Composable Oblivious Linear Evaluation
• Incomplete quantum oblivious transfer with perfect one-sided security
• Quantum oblivious transfer: a short review