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Quantum Information and Computation

On the existence of loss-tolerant quantum oblivious transfer protocols

Jamie Sikora

Published Jul 1, 2012• 3 citations
Publisher

Abstract

Oblivious transfer is the cryptographic primitive where Alice sends one of two bits to Bob but is oblivious to the bit received. Using quantum communication, we can build oblivious transfer protocols with security provably better than any protocol built using classical communication. However, with imperfect apparatus, one needs to consider other attacks. In this paper, we present an oblivious transfer protocol which is impervious to lost messages.

DOI
10.26421/qic12.7-8-6

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Oblivious transfer is the cryptographic primitive where Alice sends one of two bits to Bob but is oblivious to the bit received. Using quantum communication, we can build oblivious transfer protocols with security provably better than any protocol built using classical communication. However, with imperfect apparatus, one needs to consider other attacks. In this paper, we present an oblivious transfer protocol which is impervious to lost messages.
We propose a quantum protocol for 1-out-of-2, 1-out-of-n and k-out-of-n oblivious transfer. Oblivious transfer is a counter-intuitive cryptographic primitive in which the receiver receives only the information he is authorized for, while the sender does not know what information receiver received. In 1-out-of-2 oblivious transfer, Alice sends two bits to Bob who can choose only one of them to read, while Alice does not know which bit Bob read. k-out-of-n oblivious transfer is an extension of this idea. The proposed protocols do not require any classical communication, are practical, secure and can be implemented using current technology.
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.
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.
Abstract Oblivious transfer is considered as a cryptographic primitive task for quantum information processing over a quantum network. It is an essential building block for secure multiparty computation. It is known that one‐server oblivious transfer is impossible. When the task is the transmission of classical messages, protocols for two‐server oblivious transfer exist, i.e., existing protocols work under the assumption that two servers do not communicate with each other. However, when the task is the transmission of a quantum state, no existing method works even under the above two‐server assumption. Two‐server oblivious transfer protocols for quantum messages are proposed for the first time.