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arXiv:1010.0702

A Weak Quantum Oblivious Transfer

Kai-Yuen Cheong, Min-Hsiu Hsieh, Takeshi Koshiba

Published Oct 4, 2010• 0 citations
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Abstract

Due to the commonly known impossibility results, information theoretic security is considered impossible for oblivious transfer (OT) in both the classical and the quantum world. In this paper, we proposed a weak version of the all-or-nothing OT. In our protocol the honest parties do not need long term quantum memory, entanglements, or sophisticated quantum computations. We observe some difference between the classical and quantum OT impossibilities.

DOI
10.48550/arxiv.1010.0702

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Due to the commonly known impossibility results, information theoretic security is considered impossible for oblivious transfer (OT) in both the classical and the quantum world. In this paper, we proposed a weak version of the all-or-nothing OT. In our protocol the honest parties do not need long term quantum memory, entanglements, or sophisticated quantum computations. We observe some difference between the classical and quantum OT impossibilities.
Due to the commonly known impossibility results, unconditional security for oblivious transfer is seen as impossible even in the quantum world. In this paper, we try to overcome these impossibility results by proposing a protocol which is asymptotically secure. The protocol makes use of the basic properties of non-orthogonal quantum states. Apart from security, the advantages of our protocol include the fact that the honest players do not need to have quantum memory or create entanglement between individual qubits. The relation of our work to the known impossibility results is also discussed.
Oblivious transfer (OT) is one of the keystones of secure multi-party computation. It is generally believed that unconditionally secure OT is impossible. In this article, we propose a practical and secure quantum all-or-nothing oblivious transfer protocol based on the quantum one-way function. The protocol is built upon a quantum public-key encryption construction, and its security relies on the no-cloning theorem and no-communication theorem. Practical security is reflected in limitations on non-demolition measurements.
Oblivious transfer (OT) is an important tool in cryptography. It serves as a subroutine to other complex procedures of both theoretical and practical significance. A common attribute of OT protocols is that one party (Alice) has to send a message to another party (Bob) and has to stay oblivious to whether Bob did receive the message. Specific (OT) protocols vary by exact definition of the task---in the all-or-nothing protocol, Alice sends a single bit-string message, which Bob is able to read with only 5050%50 probability, whereas in a 1-out-of-2 OT protocol Bob reads one out of two messages sent by Alice. These two flavors of protocol are known to be equivalent. Recently, a computationally secure all-or-nothing OT protocol based on quantum states was developed by A. Souto et al. [Phys. Rev. A 91, 042306 (2015)], which, however, cannot be reduced to a 1-out-of-2 OT protocol by standard means. Here we present an elaborate reduction of this protocol that retains the security of the original.
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 an important cryptographic primitive.Any multiparty computation can be realized with OT as building block.XOR oblivious transfer (XOT) is a variant where the sender Alice has two bits and a receiver Bob obtains either the first bit, the second bit, or their XOR.Bob should not learn anything more than this and Alice should not learn what Bob has learnt.Perfect quantum OT with information-theoretic security is known to be impossible.We determine the smallest possible cheating probabilities for unrestricted dishonest parties in noninteractive quantum XOT protocols using symmetric pure states and present an optimal protocol, which outperforms classical protocols.We also "reverse" this protocol, so that Bob becomes sender of a quantum state and Alice the receiver who measures it, while still implementing oblivious transfer from Alice to Bob.Cheating probabilities for both parties stay the same as for the unreversed protocol.We optically implement both the unreversed and the reversed protocols, and cheating strategies, noting that the reversed protocol is easier to implement.
Abstract Oblivious transfer (OT) protocol is an essential building block for secure multiparty computation. The transmission of quantum messages is conductive in executing complex secure multiparty quantum computation tasks and even distributed quantum computation tasks. However, as an important form of OT protocol, existing all‐or‐nothing OT protocols only work for the transmission of classical messages thus limiting application scenarios. To tackle this issue, a counterfactual all‐or‐nothing OT protocol is proposed for quantum messages. Compared with existing all‐or‐nothing OT protocols for classical messages, the proposed protocol has three advantages: i) it is achieved without any physical particles traveling between the sender and the receiver thus reducing the communication complexity; ii) no prior entanglement between the sender and the receiver is required thus facilitating protocol implementation, and iii) it works for known even unknown quantum messages thereby offering broader application scenarios.