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International Conference on Advanced Communication Technology

A Computationally Secure Quantum Oblivious Transfer Scheme

Xin Lü, Zhi Ma, Dengguo Feng

Published Jan 1, 2006• 2 citations
Publisher

Abstract

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

DOI
10.1109/icact.2006.206280

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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
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.
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 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 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.
Motivated by the applications of secure multi-party computation as a privacy-protecting data analysis tool, and identifying oblivious transfer as one of its main practical enablers, we propose a practical realization of randomized quantum oblivious transfer. By using only symmetric cryptography primitives to implement commitments, we construct computationally secure randomized oblivious transfer without the need for public-key cryptography or assumptions imposing limitations on the adversarial devices. We show that the protocol is secure under an indistinguishability-based notion of security and demonstrate an experimental implementation to test its real-world performance. Its security and performance are then compared to both quantum and classical alternatives, showing potential advantages over existing solutions based on the noisy storage model and public-key cryptography.
Oblivious transfer protocol is a basic building block in cryptography and is used to transfer information from a sender to a receiver in such a way that, at the end of the protocol, the sender does not know if the receiver got the message or not. Since Shor's quantum algorithm appeared, the security of most of the classical cryptographic schemes has been compromised, as they rely on the fact that factoring is infeasible. To overcome this, quantum mechanics has been used intensively in the past decades, and alternatives resistant to quantum attacks have been developed in order to fulfill the (potential) lack of security of a significant number of classical schemes. In this paper, we present a quantum computationally secure protocol for bit-string oblivious transfer between two parties, under the assumption of quantum hardness of state distinguishability and the constraint of performing at most few-qubit measurements (leaving open the question of general attacks performed on all qubits involved). The protocol is feasible, in the sense that it is implementable in polynomial time.