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arXiv:1403.6022 · Physical Review A

Bit-string oblivious transfer based on quantum state computational distinguishability

André Souto, Paulo Mateus, Pedro Adão, Nikola Paunković

Published Apr 8, 2015• 15 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.91.042306

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Comment on “Bit-string oblivious transfer based on quantum state computational distinguishability”

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We show that in the protocol proposed in Phys. Rev. A 91, 042306 (2015), a dishonest sender can always ensure with certainty that the receiver fails to get the secret message. Thus the security requirement of oblivious transfer is not met. This security problem also makes the protocol unsuitable for serving as a building block for 1-out-of-2 oblivious transfer.

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Abstract We present a bit-string quantum oblivious transfer protocol based on single-qubit rotations. Our protocol is built upon a previously proposed quantum public-key protocol and its practical security relies on the laws of Quantum Mechanics. Practical security is reflected in the fact that, due to technological limitations, the receiver (Bob) of the transferred bit-string is restricted to performing only ‘few-qubit’ coherent measurements. We also present a single-bit oblivious transfer based on the proposed bit-string protocol. The protocol can be implemented with current technology based on optics.

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Secure Identification in The Isolated Qubits Model

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Oblivious transfer is a powerful cryptographic primitive that is complete for secure multi-party computation. In oblivious transfer protocols a user sends one or more messages to a receiver, while the sender remains oblivious as to which messages have been received. Protocols for oblivious transfer cannot exist in a classical or fully-quantum world, but can be implemented by restricting the users' power. The isolated qubits model is a cryptographic model in which users are restricted to single-qubit operations and are not allowed to use entangling operations. Furthermore, all parties are allowed to store qubits for a long time before measuring them. In this model, a secure single-bit one-out-of-two randomised oblivious transfer protocol was recently presented by Liu. Motivated by this result, we construct a protocol for secure string one-out-of-two randomised oblivious transfer by simplifying and generalising the existing proof. We then study for the first time interactive protocols for more complex two-party functionalities in this model based on the security of our construction. In order to guarantee the composability of our construction, users are restricted to measurement at the end of each sub-protocol. It is then possible to construct secure one-out-of-two and one-out-of-k oblivious transfer protocols in the isolated qubits model. Moreover, we study secure password-based identification, where a user identifies himself to another user by evaluating the equality function on their inputs, or passwords. We use the oblivious transfer constructions mentioned above as sub-protocols to construct a secure identification protocol. Finally, we prove that constructing a secure identification protocol non-interactively is impossible, even using oblivious transfer.

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1-out-of-2 oblivious transfer using a flawed bit-string quantum protocol

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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 $50%$ 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.

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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.

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Coherent attack on oblivious transfer based on single-qubit rotations

Guang Ping He

Abstract Recently a bit-string quantum oblivious transfer (OT) protocol based on single-qubit rotations was proposed (Rodrigues et al 2017 J. Phys. A: Math. Theor . 50 205301) and proven secure against few-qubit measurements. However, it was left as an open question whether the protocol remains secure against general attacks. Here, we close the gap by showing that if the receiver Bob can perform collective measurements on all qubits, then he can learn Alice’s secret message with a probability close to one . Thus the protocol fails to meet the security criterion of OT.

Journal of Physics A Mathematical and Theoretical•Feb 12, 2018•2 citations
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.
Abstract We present a bit-string quantum oblivious transfer protocol based on single-qubit rotations. Our protocol is built upon a previously proposed quantum public-key protocol and its practical security relies on the laws of Quantum Mechanics. Practical security is reflected in the fact that, due to technological limitations, the receiver (Bob) of the transferred bit-string is restricted to performing only ‘few-qubit’ coherent measurements. We also present a single-bit oblivious transfer based on the proposed bit-string protocol. The protocol can be implemented with current technology based on optics.
Oblivious transfer is a powerful cryptographic primitive that is complete for secure multi-party computation. In oblivious transfer protocols a user sends one or more messages to a receiver, while the sender remains oblivious as to which messages have been received. Protocols for oblivious transfer cannot exist in a classical or fully-quantum world, but can be implemented by restricting the users' power. The isolated qubits model is a cryptographic model in which users are restricted to single-qubit operations and are not allowed to use entangling operations. Furthermore, all parties are allowed to store qubits for a long time before measuring them. In this model, a secure single-bit one-out-of-two randomised oblivious transfer protocol was recently presented by Liu. Motivated by this result, we construct a protocol for secure string one-out-of-two randomised oblivious transfer by simplifying and generalising the existing proof. We then study for the first time interactive protocols for more complex two-party functionalities in this model based on the security of our construction. In order to guarantee the composability of our construction, users are restricted to measurement at the end of each sub-protocol. It is then possible to construct secure one-out-of-two and one-out-of-k oblivious transfer protocols in the isolated qubits model. Moreover, we study secure password-based identification, where a user identifies himself to another user by evaluating the equality function on their inputs, or passwords. We use the oblivious transfer constructions mentioned above as sub-protocols to construct a secure identification protocol. Finally, we prove that constructing a secure identification protocol non-interactively is impossible, even using oblivious transfer.
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.
Abstract Recently a bit-string quantum oblivious transfer (OT) protocol based on single-qubit rotations was proposed (Rodrigues et al 2017 J. Phys. A: Math. Theor . 50 205301) and proven secure against few-qubit measurements. However, it was left as an open question whether the protocol remains secure against general attacks. Here, we close the gap by showing that if the receiver Bob can perform collective measurements on all qubits, then he can learn Alice’s secret message with a probability close to one . Thus the protocol fails to meet the security criterion of OT.