David Reichmuth | Searcharxiv

arXiv2024

Incomplete quantum oblivious transfer with perfect one-sided security

Oblivious transfer is a fundamental cryptographic primitive which is useful for secure multiparty computation. There are several variants of oblivious transfer. We consider 1 out of 2 oblivious transfer, where a sender sends two bits of information to a receiver. The receiver only receives one of the two bits, while the sender does not know which bit the receiver has received. Perfect quantum oblivious transfer with information theoretic security is known to be impossible. We aim to find the lowest possible cheating probabilities. Bounds on cheating probabilities have been investigated for complete protocols, where if both parties follow the protocol, the bit value obtained by the receiver matches the sender bit value. We instead investigate incomplete protocols, where the receiver obtains an incorrect bit value with probability pf. We present optimal non interactive protocols where Alice bit values are encoded in four symmetric pure quantum states, and where she cannot cheat better than with a random guess. We find the protocols such that for a given pf, Bob cheating probability pr is as low as possible, and vice versa. Furthermore, we show that non-interactive quantum protocols can outperform non-interactive classical protocols, and give a lower bound on Bob cheating probability in interactive quantum protocols. Importantly for optical implementations, our protocols do not require entanglement nor quantum memory.

quant-ph↗

arXiv2021

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

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.

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