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Journal of Modern Optics

Quantum Oblivious Transfer

Claude Crépeau

Published Dec 1, 1994• 104 citations
Publisher

Abstract

In a one-out-of-two oblivious transfer, a party Alice has two messages m 0, m 1 that she sends to another party Bob in such a way that he can decide to obtain either of them at his choosing, but not both. Alice never finds out which message Bob received. First introduced by Wiesner as ‘conjugate coding’, this cryptographic tool was later introduced to the world of public-key cryptography, first by Rabin (in a slightly different form) and then by Even, Goldreich and Lempel who named it after Rabin's primitive, called oblivious transfer. The one-out-of-two oblivious transfer was later shown to be extremely powerful in designing general cryptographic tools. The current paper presents a new design for a one-out-of-two oblivious transfer based on the transmission of polarized light, improving the work of Wiesner and Bennett, Brassard, Breidbart and Wiesner, and shows that the scheme is robust to general attacks.

DOI
10.1080/09500349414552291

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In a one-out-of-two oblivious transfer, a party Alice has two messages m 0, m 1 that she sends to another party Bob in such a way that he can decide to obtain either of them at his choosing, but not both. Alice never finds out which message Bob received. First introduced by Wiesner as ‘conjugate coding’, this cryptographic tool was later introduced to the world of public-key cryptography, first by Rabin (in a slightly different form) and then by Even, Goldreich and Lempel who named it after Rabin's primitive, called oblivious transfer. The one-out-of-two oblivious transfer was later shown to be extremely powerful in designing general cryptographic tools. The current paper presents a new design for a one-out-of-two oblivious transfer based on the transmission of polarized light, improving the work of Wiesner and Bennett, Brassard, Breidbart and Wiesner, and shows that the scheme is robust to general attacks.
Oblivious transfer is an important primitive in modern cryptography and is widely utilized in designing more complex protocols. In a one-out-of-two oblivious transfer, a party Alice has two messages x0, x1send to another party Bob in such a way that he can decide to obtain one of them at his choice but not both. In the literature (A. Kawachi et al., EUROCRYPT 2005, 268-284), the quantum states ppi+and ppi-are used as public keys to construct an encryption algorithm. In the paper, we further demonstrate that, for pi ne thetas, the quantum states ppiplusmnand pthetasplusmncan't been distinguished by quantum computers. Using this result, we devise a one-out-of-two oblivious transfer scheme, in which any cheating of the entities are detected at the end of the protocol. Correctness and privacy of this protocol are analyzed and results show that the proposed scheme is computationally secured
In the m-out-of-n oblivious transfer (OT) model, one party Alice sends n bits to another party Bob, Bob can get only m bits from the n bits. However, Alice cannot know which m bits Bob received. Y. Mu and Naor presented classical m-out-of-n oblivious transfer based on discrete logarithm. As the work of Shor, the discrete logarithm can be solved in polynomial time by quantum computers, so such OTs are unsecure to the quantum computer. In this paper, we construct a quantum m-out-of-n OT (QOT) scheme based on the transmission of polarized light and show that the scheme is robust to general attacks, i.e. the QOT scheme satisfies statistical correctness and statistical privacy.
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 (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.
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.
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.