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arXiv:2507.04015 · Leibniz international proceedings in informatics

Quantum Protocols for Rabin Oblivious Transfer

Erika Andersson, Bansal, Akshay, Peat, James T., Jamie Sikora, Jiawei Wu

Published Jan 1, 2025• 0 citations
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Abstract

Rabin oblivious transfer is the cryptographic task where Alice wishes to receive a bit from Bob but it may get lost with probability 1/2. In this work, we provide protocol designs which yield quantum protocols with improved security. Moreover, we provide a constant lower bound on any quantum protocol for Rabin oblivious transfer. To quantify the security of this task with asymmetric cheating definitions, we introduce the notion of cheating advantage which may be of independent interest in the study of other asymmetric cryptographic primitives.

DOI
10.4230/lipics.fsttcs.2025.7

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Rabin oblivious transfer is the cryptographic task where Alice wishes to receive a bit from Bob but it may get lost with probability 1/2. In this work, we provide protocol designs which yield quantum protocols with improved security. Moreover, we provide a constant lower bound on any quantum protocol for Rabin oblivious transfer. To quantify the security of this task with asymmetric cheating definitions, we introduce the notion of cheating advantage which may be of independent interest in the study of other asymmetric cryptographic primitives.
Oblivious transfer between two untrusting parties is an important primitive in cryptography. There are different variants of oblivious transfer. In Rabin oblivious transfer, the sender Alice holds a bit, and the receiver Bob either obtains the bit, or obtains no information with probability p ? . Alice should not know whether or not Bob obtained the bit. We examine a quantum Rabin oblivious transfer (OT) protocol that uses two pure states. Investigating different cheating scenarios for the sender and for the receiver, we determine optimal cheating probabilities in each case. Comparing the quantum Rabin oblivious transfer protocol to classical Rabin oblivious transfer protocols, we show that the quantum protocol outperforms classical protocols, which do not use a third party, for some values of p ? . We find that quantum Rabin OT protocols that use mixed states can outperform quantum Rabin OT protocols that use pure states for some values of p ? . Published by the American Physical Society 2024
Oblivious transfer is a fundamental cryptographic primitive in which Bob transfers one of two bits to Alice in such a way that Bob cannot know which of the two bits Alice has learned. We present an optimal security bound for quantum oblivious transfer protocols under a natural and demanding definition of what it means for Alice to cheat. Our lower bound is a smooth tradeoff between the probability B with which Bob can guess Alice's bit choice and the probability A with which Alice can guess both of Bob's bits given that she learns one of the bits with certainty. We prove that 2B + A is greater than or equal to 2 in any quantum protocol for oblivious transfer, from which it follows that one of the two parties must be able to cheat with probability at least 2/3. We prove that this bound is optimal by exhibiting a family of protocols whose cheating probabilities can be made arbitrarily close to any point on the tradeoff curve.
Oblivious transfer has been the interest of study as it can be used as a building block for multiparty computation. There are many forms of oblivious transfer; we explore a variant known as Rabin oblivious transfer. Here the sender Alice has one bit, and the receiver Bob obtains this bit with a certain probability. The sender does not know whether the receiver obtained the bit or not. For a previously suggested protocol, we show a possible attack using a delayed measurement. This allows a cheating party to pass tests carried out by the other party, while gaining more information than if they would have been honest. We show how this attack allows perfect cheating, unless the protocol is modified, and suggest changes which lower the cheating probability for the examined cheating strategies.
Oblivious transfer is a fundamental cryptographic primitive that 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 receives only 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's bit value. We instead investigate incomplete protocols, where the receiver obtains an incorrect bit value with probability p f . We present optimal noninteractive protocols where Alice's 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 p f , Bob's cheating probability p r is as low as possible, and vice versa. Furthermore, we show that noninteractive quantum protocols can outperform noninteractive classical protocols and give a lower bound on Bob's cheating probability in interactive quantum protocols. Importantly for optical implementations, our protocols do not require entanglement nor quantum memory.
Oblivious transfer (OT) is a fundamental cryptographic primitive that is useful for realizing any two-party computation. Since information-theoretically secure perfect OT is impossible classically and quantumly, research has focused on imperfect protocols, exploring how close to perfect one can get against unbounded dishonest parties. While current approaches often make use of pure quantum states, recent work suggests that mixed quantum states may improve performance. In this paper, we investigate the use of mixed quantum states in Rabin oblivious transfer, where a sender holds one bit and a receiver learns its value with a certain probability while the sender remains ignorant of whether the receiver learned it. We present three mixed-state protocols constructed with two distinct methods, extending an existing pure-state scheme and employing a probabilistic approach, and demonstrate improved performance compared to classical and quantum pure-state protocols across varying parameters.
Oblivious transfer is a fundamental primitive in cryptography. While perfect information theoretic security is impossible, quantum oblivious transfer protocols can limit the dishonest players' cheating. Finding the optimal security parameters in such protocols is an important open question. In this paper we show that every 1-out-of-2 oblivious transfer protocol allows a dishonest party to cheat with probability bounded below by a constant strictly larger than 1/2. Alice's cheating is defined as her probability of guessing Bob's index, and Bob's cheating is defined as his probability of guessing both input bits of Alice. In our proof, we relate these cheating probabilities to the cheating probabilities of a coin flipping protocol and conclude by using Kitaev's coin flipping lower bound. Then, we present an oblivious transfer protocol with two messages and cheating probabilities at most 3/4. Last, we extend Kitaev's semidefinite programming formulation to more general primitives, where the security is against a dishonest player trying to force the outcome of the other player, and prove optimal lower and upper bounds for them.