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Physical Review A

Communication channels analogous to one out of two oblivious transfers based on quantum uncertainty. II. Closing EPR-type loopholes

Kaoru Shimizu, Nobuyuki Imoto

Published Mar 11, 2003• 6 citations
Publisher

Abstract

In a recent proposal for a quantum cryptographic scheme analogous to one out of two oblivious transfers [Phys. Rev. A 66, 052316 (2002)], a sender, Bob, can encode two bits of information (X,Y) in a quantum carrier but a receiver, Alice, can decode only either X or Y dependent on her choice. Although Bob can discover her choice whenever he desires, she can detect this with a 50% probability. This paper clarifies the amount of information that Bob can expect to obtain from Alice without being detected by her by means of an Einstein-Podolsky-Rosen (EPR) type of attack. We can show that Bob inevitably fails to discover her choice with a 50% probability even though he can always completely escape her detection.

DOI
10.1103/physreva.67.034301

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In a recent proposal for a quantum cryptographic scheme analogous to one out of two oblivious transfers [Phys. Rev. A 66, 052316 (2002)], a sender, Bob, can encode two bits of information (X,Y) in a quantum carrier but a receiver, Alice, can decode only either X or Y dependent on her choice. Although Bob can discover her choice whenever he desires, she can detect this with a 50% probability. This paper clarifies the amount of information that Bob can expect to obtain from Alice without being detected by her by means of an Einstein-Podolsky-Rosen (EPR) type of attack. We can show that Bob inevitably fails to discover her choice with a 50% probability even though he can always completely escape her detection.
This paper proposes a cryptographic quantum communication scheme analogous to one out of two oblivious transfers based on quantum conjugate coding defined in a four-dimensional Hilbert space. The quantum uncertainty principle ensures that our scheme can satisfy the following two conditions: (i) a sender, Bob, can encode two bits of information $X\ensuremath{\in}{0,1}$ and $Y\ensuremath{\in}{0,1},$ but a receiver, Alice, can only obtain either X or Y dependent on her choice; and (ii) honest Bob, who attempts to encode (X,Y),(X,Y),(X,Y), cannot reveal Alice's choice. By contrast, when malicious Bob tries to reveal her choice, honest Alice can detect malicious Bob with a finite probability. Moreover, by using our proposed scheme many times, we can construct a protocol for quantum bit commitment (QBC) from Alice to Bob. Contrary to common belief, the security of our QBC protocol may not be violated by the well-known no-go theorem of QBC. This is because our QBC protocol does not meet the assumptions in which the no-go theorem holds.
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.
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.
We present a quantum secure direct communication scheme achieved by swapping quantum entanglement. In this scheme a set of ordered Einstein-Podolsky-Rosen (EPR) pairs is used as a quantum information channel for sending secret messages directly. After insuring the safety of the quantum channel, the sender Alice encodes the secret messages directly by applying a series local operations on her particles sequence according to their stipulation. Using three EPR pairs, three bits of secret classical information can be faithfully transmitted from Alice to remote Bob without revealing any information to a potential eavesdropper. By both Alice and Bob's GHZ state measurement results, Bob is able to read out the encoded secret messages directly. The protocol is completely secure if perfect quantum channel is used, because there is not a transmission of the qubits carrying the secret message between Alice and Bob in the public channel.
We presen a secure direct communication protocol by using step-split Einstein-Podolsky-Rosen (EPR) pair. In this communication protocol, Alice first sends one qubit of an EPR pair to Bob. Bob sends a receipt signal to Alice through public channel when he receives Alice's first qubit. Alice performs her encoding operations on the second qubit and sends this qubit to Bob. Bob performs a Bell-basis measurement to draw Alice's information. The security of this protocol is based on `High fidelity implies low entropy'. If Eve want to eavesdrop Alice's information, she has to attack both qubits of the EPR pair, which results in that any effective eavesdropping attack can be detected. Bob's receipt signal can protect this protocol against the eavesdropping hiding in the quantum channel losses. And this protocol is strictly secure to perform a quantum key distribution by using Calderbank-Shor-Steane codes.