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IEEE International Conference on Advanced Networks and Telecommunications Systems

Limits on detecting eavesdropper in QKD protocols

Pranav Subramaniam, Abhishek Parakh

Published Dec 1, 2014• 11 citations
Publisher

Abstract

Quantum key distribution (QKD) protocols form a natural choice for encryption in optical networks. All the QKD protocols use errors caused due to random measurements by Eve to detect her presence. In this paper, we present a fundamental limitation of using such bases to detect an eavesdropper in two QKD protocols - the BB84 and the new quantum Diffie-Hellman key exchange protocol. It is shown that the eavesdropper will go undetected in each exchange in both the protocols at least half the time.

DOI
10.1109/ants.2014.7057239

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Quantum key distribution (QKD) protocols form a natural choice for encryption in optical networks. All the QKD protocols use errors caused due to random measurements by Eve to detect her presence. In this paper, we present a fundamental limitation of using such bases to detect an eavesdropper in two QKD protocols - the BB84 and the new quantum Diffie-Hellman key exchange protocol. It is shown that the eavesdropper will go undetected in each exchange in both the protocols at least half the time.
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.
Quantum Key Distribution (QKD) has been shown to be provably secure when certain idealized conditions are met in a physical realization. All implementations of QKD to date require non-orthogonal basis measurements to implement it; making it commonly assumed that measurement basis variation is fundamental to making QKD protocols secure from eavesdropping. We show here that in particular physical conditions this assumption is incorrect, and that provable security can be achieved without use of multiple bases. Basis setting information can in fact be shared with all potential eavesdroppers, as they are unable to use it to acquire or influence any part of the encryption key generation. Furthermore the key generation efficiency is limited to 100 % as compared with an inherent 50 % limit for alternating bases in BB84 or Entangled Ekert protocols.
Quantum key distribution is one of the essential developments to reduce the vulnerability in the security of the systems due to the emergence of quantum computers. As long as large-scale quantum computers emerge, all the systems will be vulnerable to attack. To secure the communication, we can use quantum key distribution protocols in the near future. In this work, I have experimentally verified the BB84 protocol with an eavesdropper. We have used a classical channel to send polarization states of light. Our source is a readily available He-Ne laser (632.8nm). To send secret Information in a secure way, we use Quantum key distribution. Sender Alice sends randomly chosen polarization states of light to Bob. The states Alice sends are |H>,|V>,|D>, and |A>, and similarly, Bob also selects some random basis and detects this Information. In this experiment, |H>,|V> states belong to the '+' basis and |D>,|A> on the 'X' basis. Detecting |H>,|D> states at the detector is considered as '1' and detecting |V>,|A> represents the '0' bit as the output. Alice and Bob can choose the basis randomly. We got these | H>,|V>,|D>, and |A> states by rotating the half-wave plate at angles respectively 0°,90°,45°, and -45°. We used a motorized rotator to rotate the two half-wave plates, one at Alice's side and one at Bob's side, to select the basis and generate these states. The motorized rotator runs on a python code. Python code is designed in such a way that it can generate random bits and can run Alice and Bob parts simultaneously. A polarized beam splitter is used just before the detector to split the beam into | H> and |V> states with 100% intensity at one detector and 0% at the other and |D> and |A> states with 50:50 intensity. Therefore we used one half-wave plate just before the PBS, which can convert |H> and |V> states into |D> and |A> states when we rotate at these particular angles. Using this, we can detect |D> and |A> states with 100% intensity at one detector and 0% at the other. Based upon the basic choices of Alice and Bob, at the receiver part, Bob will receive the bits. At the end of the process, both parties will verify the basis. When the basis is matching, they will keep those bits, and which are not matching, they will discard them. The successful bits will become the encryption key. I did this experiment by sending 1000 bits, and 452 bits among them were successful. For the security analysis of this protocol, we implemented a third-person Eve who tries to steal the Information Alice sends to Bob. Eve used one Beam splitter to take half part of the light intensity and sent another half to Bob. Eve's part has one 50:50 beam splitter, which splits the beam into two. Then, one beam goes to a PBS, then to the detectors, and the other beam goes to a setup that has HWP and PBS, then to the detectors. In this experiment, Eve is successful in stealing the Information correctly. As we are using classical light, which has a huge number of photons, anyone can take some photons and execute a photon number splitting attack; the security of this process is very low. We need a single-photon source and a single photon detector to get total security from this protocol. Right now, I have done this experiment with the available pieces of equipment I have. When the needed types of equipment are available to me, I can implement the single-photon QKD experiment also. After the experiment, we realized that the superposition of states always holds in this experiment, but states do not collapse, as we are not performing the quantum measurement. Also, I have implemented the QKD protocol in the IBM Quantum lab, where Alice sends 1000 bits to Bob, and 474 bits among them were successful. Also, Eve’s interception was detected successfully.
Quantum key distribution algorithms are considered secure because they leverage quantum phenomena to provide security. As such, eavesdroppers can be detected by analyzing the error rate in the shared key obtained by the parties performing the key exchange. Nevertheless, this paper developed and investigated a novel attack strategy capable of being undetected through error analysis of the shared key. Said attack entails an eavesdropper measuring the quantum channel (i.e., the channel used to transmit quantum particles between two parties) using a higher dimension than that used by the legitimate parties. By measuring a particle in a dimension that spans all possible states in a given quantum key distribution algorithm, the collapsed state of the measured particle should be undetectable when measured in the lower dimension. To analyze the proposed high-dimensional eavesdropping attack, the simulator Cirq was used to model the attack on BB84, a four-dimensional variant of BB84, and the Six-State Protocol. The results of these simulations show the efficiency of this attack, with an eavesdropper being undetectable through quantum bit error rate analysis in each algorithm This promotes the need for further analysis of the high-dimensional eavesdropping attack on physical hardware and other quantum key distribution algorithms
Quantum key distribution protocols printed a prominent mark in the old path of digital communication by making it even more secure. Unlike its classical counterpart, quantum key distribution protocols exploit the key principles of quantum elements, such as superposition and entanglement, to expose the intrusion in an efficient way. This paper presents a prepare and measure quantum key distribution protocol that detects the eavesdropper more efficiently by inflating bit mismatch between the sender and receiver. The proposed work achieves bit mismatch up to 62.5 percent while Eve is present in the quantum communication channel. The improvement is remarkable in comparison with the classical BB84 protocol, which has a bit mismatch up to 37.5 percent in presence of Eve.
The nature of quantum mechanics provides us with an opportunity to statistically detect eavesdropping in quantum key distribution (QKD) protocols, which is unimaginable in classical digital communications. By utilizing Hoeffding’s inequality, this study analyzes the upper bounds of the false-positive ratio (FPR) and false-negative ratio (FNR) of eavesdropping detection in the Bennett–Brassard-84 (BB84) QKD protocol, where eavesdropping is detected if the measured quantum bit error rate (QBER) is equal to or higher than a threshold. The analysis clarifies the trade-off between the accuracy of eavesdropping detection and the economy of quantum resources in the BB84 protocol. Owing to the central limit theorem, the QBER measured by 300 quantum bits (qubits) is sufficient to guarantee lower than 0.009% of the FPR and FNR of eavesdropping detection. To deal with rapidly varying quantum channel conditions, this study further introduces grouped BB84 protocol and combinatory eavesdropping detection algorithms. A polarization basis is changeable for a group of qubits, and eavesdropping is judged by a combination of criteria between QBER and group-QBER in the proposed protocol and algorithms. In our extensive simulation study, the grouped BB84 protocol with 300 qubits comparison guarantees at least 99.92% accuracy in eavesdropping detection under rapidly varying quantum channel conditions.