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arXiv:0712.4241 · Physical Review A

Entanglement-enhanced quantum key distribution

Olli Ahonen, Mikko Möttönen, Jeremy L. O’Brien

Published Sep 11, 2008• 26 citations
arXivHTMLPDF

Abstract

We present and analyze a quantum key distribution protocol based on sending entangled $N$-qubit states instead of single-qubit ones as in the trail-blazing scheme by Bennett and Brassard 1984 (BB84). Since the qubits are sent and acknowledged individually, an eavesdropper is limited to accessing them one by one. In an intercept-resend attack, this fundamental restriction allows one to make the eavesdropper's information on the transmitted key vanish if even one of the qubits is not intercepted. The implied upper bound $1∕(2N)$ for this information is further shown not to be the lowest, as the information can be reduced to less than 30% of that in the BB84 scheme in the case $N=2$. In general, the protocol is at least as secure as BB84.

DOI
10.1103/physreva.78.032314

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We present and analyze a quantum key distribution protocol based on sending entangled NNN-qubit states instead of single-qubit ones as in the trail-blazing scheme by Bennett and Brassard 1984 (BB84). Since the qubits are sent and acknowledged individually, an eavesdropper is limited to accessing them one by one. In an intercept-resend attack, this fundamental restriction allows one to make the eavesdropper's information on the transmitted key vanish if even one of the qubits is not intercepted. The implied upper bound 1∕(2N)1∕(2N)1∕(2N) for this information is further shown not to be the lowest, as the information can be reduced to less than 30% of that in the BB84 scheme in the case N=2N=2N=2. In general, the protocol is at least as secure as BB84.
The quantum key distribution protocol BB84, published by C. H. Bennett and G. Brassard in 1984, describes how two spatially separated parties can generate a random bit string fully known only to them by transmission of single-qubit quantum states. Any attempt to eavesdrop on the protocol introduces disturbance which can be detected by the legitimate parties. In this Master's Thesis a novel modification to the BB84 protocol is analyzed. Instead of sending single particles one-by-one as in BB84, they are grouped and a non-local transformation is applied to each group before transmission. Each particle is sent to the intended receiver, always delaying the transmission until the receiver has acknowledged the previous particle on an authenticated classical channel, restricting eavesdropping to accessing the quantum transmission one particle at a time. Hence, an eavesdropper cannot undo the non-local transformation perfectly. Even if perfect cloning of quantum states was possible the state of the group could not be cloned. We calculate the maximal information on the established key provided by an intercept-resend attack and the induced disturbance for different transformations. We observe that it is possible to significantly reduce the eavesdropper's maximal information on the key--to one eighth of that in BB84 for a fixed, reasonable amount of disturbance. We also show that the individual access to the particles poses a fundamental restriction to the eavesdropper, and discuss a novel attack type against the proposed protocol.
Quantum key distribution (QKD) allows two spatially separated parties to securely generate a cryptographic key. The first QKD protocol, published by C. H. Bennett and G. Brassard in 1984 (BB84), describes how this is achieved by transmitting individual qubits and exchanging classical authenticated information. Any attempt to eavesdrop on the protocol introduces errors detectable by the legitimate parties. This Licentiate Thesis studies the recently introduced EEQKD protocol which builds on BB84. In EEQKD, the qubits sent individually in BB84 are entangled and thus not directly available to an eavesdropper who is, in this protocol, provided only one-by-one access to the transmission. The maximal information an eavesdropper can gain using a straightforward intercept-resend (IR) attack, is obtained for a given error rate. The secure key generation rate of EEQKD is estimated in practical scenarios including qubit loss and quantum channel noise. In addition, an exquisite vulnerability is exposed: For a particular setting of qubit entanglement, paradoxically proving most useful in the face of an IR attack, EEQKD reduces to BB84. Part of this research has been published in O. Ahonen et al., Physical Review A 78, 032314 (2008).
Quantum cryptography is anticipated to drive substantial advancements in cybersecurity. The impending arrival of quantum cryptography compromises current encryption methods, possibly compromising the effectiveness of traditional key management-based security protocols. One fundamental Quantum Key Distribution (QKD) protocol, BB84, encounters challenges when operating with fewer Quantum bits (Qubits) and bases that only support up to 8 Qubits. This limitation weakens the system’s security, making brute force, intercept, and resend attacks less challenging. Consequently, this study proposes a method to enhance the security of the BB84 protocol, to reduce susceptibility to attacks and eavesdropping. The improved BB84 protocol utilizes 9, 12, and 16 quantum bits along with two, and three bases to significantly bolster security. This allows authorized parties to eliminate the use of compromised keys. Additionally, the study implements the E91 QKD protocol utilizing the Entanglement Pair Generation (EPR) method to produce secure keys. While the existing E91 protocol ensures security through Bell’s theorem and Bell’s inequality, it overlooks the impact of noise, leading to inaccuracies in eavesdropper detection. To address this, the study introduces an additional security measure. Whenever an eavesdropper attempts to measure the quantum state, the proposed E91 protocol collapses its state from$\vert 10\rangle tototo\vert 11\rangle ,settingthefirstQubitto, setting the first Qubit to,settingthefirstQubitto\vert 1\rangle andtheotherQubittoand the other Qubit toandtheotherQubitto\vert 0\rangle $, thus providing the eavesdropper with incorrect information, accompanied by a phase angle of$15\pi $/8. This leads to a misconception, preventing eavesdroppers from obtaining useful details about transferred quantum states. Additionally, considering that the proposed E91 protocol relies on entangled particles and utilizes double Qubit gates, which are inherently noisier than single Qubit gates and more susceptible to quantum decoherence, this study employs error mitigation techniques during the final measurement to predict outcomes more efficiently.
In this paper, we propose a method of enciphering quantum states of two-state systems (qubits) for sending them in secrecy without entangled qubits shared by two legitimate users (Alice and Bob). This method has the following two properties. First, even if an eavesdropper (Eve) steals qubits, she can extract information from them with only a certain probability at most. Second, Alice and Bob can confirm that the qubits are transmitted between them correctly by measuring a signature. If Eve measures m qubits one by one from n enciphered qubits and sends alternative ones (the intercept/resend attack), the probability that Alice and Bob do not notice Eve's action is equal to (3/4) m or less. Passwords for decryption and the signature are given by classical binary strings and they are disclosed through a public channel. Enciphering classical information by this method is equivalent to the one-time pad method with distributing a classical key (random binary string) by the BB84 protocol. If Eve takes away qubits, Alice and Bob lose the original quantum information. If we apply our method to a state in iteration, Eve's success probability decreases exponentially. We cannot examine security against the case that Eve makes an attack using entanglement. This remains to be solved in the future.
The theoretical Quantum Key-Distribution scheme of Bennett and Brassard (BB84) has been proven secure against very strong attacks including the collective attacks and the joint attacks. Though the latter are the most general attacks, collective attacks are much easier to analyze, yet, they are conjectured to be as informative to the eavesdropper. Thus, collective attacks are likely to be useful in the analysis of many theoretical and practical schemes that are still lacking a proof of security, including practical BB84 schemes. We show how powerful tools developed in previous works for proving security against the joint attack, are simplified when applied to the security of BB84 against collective attacks whilst providing the same bounds on leaked information and the same error threshold.
We devise a simple modification that essentially doubles the efficiency of a well-known quantum key distribution scheme proposed by Bennett and Brassard (BB84). Our scheme assigns significantly different probabilities for the different polarization bases during both transmission and reception to reduce the fraction of discarded data. The actual probabilities used in the scheme are announced in public. As the number of transmitted signals increases, the efficiency of our scheme can be made to approach 100%. An eavesdropper may try to break such a scheme by eavesdropping mainly along the predominant basis. To defeat such an attack, we perform a refined analysis of accepted data: Instead of lumping all the accepted data together to estimate a single error rate, we separate the accepted data into various subsets according to the basis employed and estimate an error rate for each subset individually.