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Quantum Computing, Communication, and Simulation

Quantum cryptography beyond quantum key distribution: variants of quantum oblivious transfer

Erika Andersson, Lara Stroh, Ittoop Vergheese Puthoor, David Reichmuth, Nikola Horová, Robert Stárek, Michal Mičuda, Miloslav Dušek, Petros Wallden

Published Mar 8, 2023• 1 citation
Publisher

Abstract

Modern cryptography is more than sending secret messages, and quantum cryptography is more than quantum key distribution. One example is oblivious transfer, which is interesting partly because it can be used to implement secure multiparty computation. We discuss a protocol for quantum XOR oblivious transfer, and how non-interactive quantum oblivious transfer protocols can be “reversed”, so that oblivious transfer is still implemented from a sender to a receiver, but so that it is the receiver who sends a quantum state to the sender, who measures it, instead of the other way round. This is useful when one party can only prepare and send quantum states, and the other party can only measure them, which is often the case in practical quantum communication systems. Both the “original” XOR oblivious transfer protocol and its reversed version have been implemented optically. We also discuss how quantum random access codes can be connected with quantum oblivious transfer.

DOI
10.1117/12.2656196

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Modern cryptography is more than sending secret messages, and quantum cryptography is more than quantum key distribution. One example is oblivious transfer, which is interesting partly because it can be used to implement secure multiparty computation. We discuss a protocol for quantum XOR oblivious transfer, and how non-interactive quantum oblivious transfer protocols can be “reversed”, so that oblivious transfer is still implemented from a sender to a receiver, but so that it is the receiver who sends a quantum state to the sender, who measures it, instead of the other way round. This is useful when one party can only prepare and send quantum states, and the other party can only measure them, which is often the case in practical quantum communication systems. Both the “original” XOR oblivious transfer protocol and its reversed version have been implemented optically. We also discuss how quantum random access codes can be connected with quantum oblivious transfer.
Quantum cryptography is the field of cryptography that explores the quantum properties of matter. Generally, it aims to develop primitives beyond the reach of classical cryptography and to improve existing classical implementations. Although much of the work in this field covers quantum key distribution (QKD), there have been some crucial steps towards the understanding and development of quantum oblivious transfer (QOT). One can show the similarity between the application structure of both QKD and QOT primitives. Just as QKD protocols allow quantum-safe communication, QOT protocols allow quantum-safe computation. However, the conditions under which QOT is fully quantum-safe have been subject to intense scrutiny and study. In this review article, we survey the work developed around the concept of oblivious transfer within theoretical quantum cryptography. We focus on some proposed protocols and their security requirements. We review the impossibility results that daunt this primitive and discuss several quantum security models under which it is possible to prove QOT security.
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.
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.
Cryptography literally means “The art & science of secret writing & sending a message between two parties in such a way that its contents cannot be understood by someone other than the intended recipient. ” and Quantum word is related with “Light”. Thus, Quantum Cryptography is a way of descripting any information in the form of quantum particles. There are no classical cryptographic systems which are perfectly secure. In contrast to Classical cryptography which depends upon Mathematics, Quantum Cryptography utilizes the concepts of Quantum Physics which provides us the security against the cleverest marauders of the present age. In the view of increasing need of Network and Information Security, we do require methods to overcome the Molecular Computing technologies (A future technology) and other techniques of the various codebrakers. Both the parts i.e. Quantum Key distribution and Information transference from Sender to Receiver are much efficient and secure. It is based upon BB84 protocol. It can be of great use for Govt. agencies such as Banks, Insurance, Brokerages firms, financial institutions, e-commerce and most important is the Defense & security of any country. It is a Cryptographic communication system in which the original users can detect unauthorized eavesdropper and in addition it gives a guarantee of no eavesdropping. It proves to be the ultra secure mode of communication b/w two intended parties.
Quantum cryptography is the art and science of exploiting quantum mechanical effects in order to perform cryptographic tasks. While the most well-known example of this discipline is quantum key distribution (QKD), there exist many other applications such as quantum money, randomness generation, secure two- and multi-party computation and delegated quantum computation. Quantum cryptography also studies the limitations and challenges resulting from quantum adversaries-including the impossibility of quantum bit commitment, the difficulty of quantum rewinding and the definition of quantum security models for classical primitives. In this review article, aimed primarily at cryptographers unfamiliar with the quantum world, we survey the area of theoretical quantum cryptography, with an emphasis on the constructions and limitations beyond the realm of QKD.
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.