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

Ryan Amiri, Robert Stárek, David Reichmuth, Ittoop V. Puthoor, Michal Mičuda, Ladislav Mišta, Miloslav Dušek, Petros Wallden, Erika Andersson

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Abstract

Oblivious transfer is an important primitive in modern cryptography. Applications include secure multiparty computation, oblivious sampling, e-voting, and signatures. Information-theoretically secure perfect1-out-of 2 oblivious transfer is impossible to achieve. Imperfect variants, where both participants’ abilityto 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 frameworkfor studying semirandom quantum oblivious transfer, which is shown to be equivalent to regular oblivioustransfer in terms of cheating probabilities. We then use it to derive bounds on cheating. We also presenta protocol with lower cheating probabilities than previous schemes, together with its optical realization.We show that a lower bound of 23 on the minimum achievable cheating probability can be directly derivedfor semirandom protocols using a different method and definition of cheating than used previously. Thelower bound increases from 23 to approximately 0.749 if the states output by the protocol are pure andsymmetric. The oblivious transfer scheme we present uses unambiguous state elimination measurementsand can be implemented with the same technological requirements as standard quantum cryptography.In particular, it does not require honest participants to prepare or measure entangled states. The cheatingprobabilities are 34 and approximately 0.729 for sender and receiver, respectively, which is lower thanin existing protocols. Using a photonic testbed, we have implemented the protocol with honest parties,as well as optimal cheating strategies. Because of the asymmetry of the receiver’s and sender’s cheatingprobabilities, the protocol can be combined with a “trivial” protocol to achieve an overall protocol withlower average cheating probabilities of approximately 0.74 for both sender and receiver. This demonstrates that, interestingly, protocols where the final output states are pure and symmetric are not optimal interms of average cheating probability.
Original languageEnglish
Article number010335
JournalPRX Quantum
Volume2
Issue number1
DOIs
Publication statusPublished - 1 Mar 2021

Keywords

  • quantum communication
  • quantum cryptography
  • quantum oblivious transfer

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

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