Privacy Amplification Research Articles

High-Agreement Uncorrelated Secret Key Generation Based on Principal Component Analysis Preprocessing

Random and high-agreement secret key generation from noisy wideband channels is challenging due to the autocorrelation inside the channel samples and compromised cross correlation between channel measurements of two keying parties. This paper studies the signal preprocessing algorithms to establish high-agreement uncorrelated secret key in the presence of channel independent eavesdroppers. We first propose a general mathematical model for various preprocessing schemes, including principal component analysis (PCA), discrete cosine transform (DCT) and wavelet transform (WT). Among preprocessing schemes, PCA is proved to achieve the optimal secret key rate. Next, PCA with common eigenvector has been found to outperform PCA with private eigenvector in terms of an overall consideration of key agreement, information leakage, and computational expense. Then, we propose a system level design of key generation, including quantization, information reconciliation, and privacy amplification. Numerical results verify that the key generation enhanced by PCA with common eigenvector can achieve secret key with high key generation rate, low key error rate, and good randomness.

10-Mb/s Quantum Key Distribution

We report the first quantum key distribution (QKD) systems capable of delivering sustainable, real-time secure keys continuously at rates exceeding 10 Mb/s. To achieve such rates, we developed high speed post-processing modules, achieving maximum data throughputs of 60 MC/s, 55 Mb/s, and 108 Mb/s for standalone operation of sifting, error correction and privacy amplification modules, respectively. The photonic layer of the QKD systems features high-speed single photon detectors based on self-differencing InGaAs avalanche photodiodes, phase encoding using asymmetric Mach-Zehnder interferometer, and active stabilization of the interferometer phase and photon polarisation. An efficient variant of the decoy-state BB84 protocol is implemented for security analysis, with a large dataset size of $10^8$ bits selected to mitigate finite-size effects. Over a 2 dB channel, a record secure key rate of 13.72 Mb/s has been achieved averaged over 4.4 days of operation. We confirm the robustness and long-term stability on a second QKD system continuously running for 1 month without any user intervention.

High-Speed Implementation of Length-Compatible Privacy Amplification in Continuous-Variable Quantum Key Distribution

Privacy amplification is an indispensable step in postprocessing of continuous-variable quantum key distribution (CV-QKD), which is used to distill unconditional secure keys from identical corrected keys between two distant legal parties. The processing speed of privacy amplification has a significant effect on the secret key rate of CV-QKD system. We report the high-speed parallel implementation of length-compatible privacy amplification algorithm based on graphic processing unit. Length-compatible algorithm is used to satisfy the security requirement of privacy amplification at different transmission distances when considering finite-size effect. We achieve the speed of privacy amplification over 1 Gbps at arbitrary input length and the speed is one to two orders of magnitude faster than previous demonstrations, which supports high-speed real-time CV-QKD system and ensures the security of privacy amplification.

Optimal attacks on qubit-based Quantum Key Recycling

Quantum Key Recycling (QKR) is a quantum cryptographic primitive that allows one to reuse keys in an unconditionally secure way. By removing the need to repeatedly generate new keys, it improves communication efficiency. Škorić and de Vries recently proposed a QKR scheme based on 8-state encoding (four bases). It does not require quantum computers for encryption/decryption but only single-qubit operations. We provide a missing ingredient in the security analysis of this scheme in the case of noisy channels: accurate upper bounds on the required amount of privacy amplification. We determine optimal attacks against the message and against the key, for 8-state encoding as well as 4-state and 6-state conjugate coding. We provide results in terms of min-entropy loss as well as accessible (Shannon) information. We show that the Shannon entropy analysis for 8-state encoding reduces to the analysis of quantum key distribution, whereas 4-state and 6-state suffer from additional leaks that make them less effective. From the optimal attacks we compute the required amount of privacy amplification and hence the achievable communication rate (useful information per qubit) of qubit-based QKR. Overall, 8-state encoding yields the highest communication rates.

Duality of Channels and Codes

For any given channel $W$ with classical inputs and possibly quantum outputs, a dual classical-input channel $W^\perp$ can be defined by embedding the original into a channel $\mathcal N$ with quantum inputs and outputs. Here we give new uncertainty relations for a general class of entropies that lead to very close relationships between the original channel and its dual. Moreover, we show that channel duality can be combined with duality of linear codes, whereupon the uncertainty relations imply that the performance of a given code over a given channel is entirely characterized by the performance of the dual code on the dual channel. This has several applications. In the context of polar codes, it implies that the rates of polarization to ideal and useless channels must be identical. Duality also relates the tasks of channel coding and privacy amplification, implying that the finite blocklength performance of extractors and codes is precisely linked, and that optimal rate extractors can be transformed into capacity-achieving codes, and vice versa. Finally, duality also extends to the EXIT function of any channel and code. Here it implies that for any channel family, if the EXIT function for a fixed code has a sharp transition, then it must be such that the rate of the code equals the capacity at the transition. This may give a different route to proving a code family achieves capacity by establishing sharp EXIT function transitions.

Efficient key generation leveraging wireless channel reciprocity for MANETs

Wireless channel reciprocity ensures that transceivers can generate the shared secret key from their communicating channels. However, various interferences in real environments make channel measurement sequences of different transceivers are highly correlated accompanying with many discrepancies. Then, if these measurements are directly quantified (and encoded) to bit sequences, the bit mismatch rate might be extremely high. Consequently, the efficiency and security of key generation might be reduced since some information might be leaked during key agreement. In this paper, an efficient key generation scheme is proposed, which is available to generate the shared secret key for transceivers even facing the referred challenge. During key generation, curve fitting is implemented to pre-process measurements so that the reciprocity of outputs of curve fitting processes are better than original channel measurements. Then, the bit mismatch rate can be greatly reduced when these outputs are used to generate bit sequences. To extract the shared bit sequence, the interactive Cascade is implemented during information reconciliation. Finally, 2-universal hash functions are used to achieve privacy amplification so that the leaked information can be eliminated and randomness of the shared key can be guaranteed. Several experiments in real mobile scenarios are conducted to evaluate the proposed scheme, where the received signal strength measurements are derived from heterogeneous devices. The results show that the implementation of pre-processing can effectively reduce the bit mismatch rate and the proposed scheme can efficiently generate shared secret keys for transceivers in real environments.

FPGA-Based Implementation of Size-Adaptive Privacy Amplification in Quantum Key Distribution

In a quantum key distribution (QKD) system, privacy amplification (PA) is an essential procedure that can effectively eliminate the leaked information to an eavesdropper and distill a secret key. The processing speed of the PA algorithm inevitably affects the final key rate of the QKD system. We propose a high-speed PA algorithm based on field-programmable gate array (FPGA), where the matrix multiplications are divided into a number of rhomboid-block operations. The implementation of the PA reduces significantly the required number of FPGA Block RAMs. Meanwhile, it automatically adapts to different lengths of input and output blocks. Finally, we verified the correctness and high-speed of the algorithm when implemented in a Xilinx Virtex-7 FPGA.

Modeling optimized decoy state protocol for enhanced quantum key distribution

Quantum key distribution (QKD) has been proved superior over classical encryption techniques due to its unconditional security. Yet it remains vulnerable due to imperfect real system implementations. It is observed that decoy state method overcome the photon number splitting attack and additionally improves performance of QKD. This paper investigates a model for Decoy state QKD protocol, which ensures enhanced secret key rates and secure distance. Typically a two-state (vacuum + very weak coherent state) decoy QKD protocol with global lower bound equation for privacy amplification is analyzed. The model is tested with sets of experimental parameters and verified for its optimum performance. It is observed that global lower bound equation for privacy amplification improves secret key rates significantly.

Security of quantum key distribution with iterative sifting

Several quantum key distribution (QKD) protocols employ iterative sifting. After each quantum transmission round, Alice and Bob disclose part of their setting information (including their basis choices) for the detected signals. This quantum phase then ends when the basis dependent termination conditions are met, i.e., the numbers of detected signals per basis exceed certain pre-agreed threshold values. Recently, however, Pfister et al (2016 New J. Phys. 18 053001) showed that the basis dependent termination condition makes QKD insecure, especially in the finite key regime, and they suggested to disclose all the setting information after finishing the quantum phase. However, this protocol has two main drawbacks: it requires that Alice possesses a large memory, and she also needs to have some a priori knowledge about the transmission rate of the quantum channel. Here we solve these two problems by introducing a basis-independent termination condition to the iterative sifting in the finite key regime. The use of this condition, in combination with Azuma’s inequality, provides a precise estimation on the amount of privacy amplification that needs to be applied, thus leading to the security of QKD protocols, including the loss-tolerant protocol (Tamaki et al 2014 Phys. Rev. A 90 052314), with iterative sifting. Our analysis indicates that to announce the basis information after each quantum transmission round does not compromise the key generation rate of the loss-tolerant protocol. Our result allows the implementation of wider classes of classical post-processing techniques in QKD with quantified security.

An Efficient Advantage Distillation Scheme for Bidirectional Secret-Key Agreement

The classical secret-key agreement (SKA) scheme includes three phases: (a) advantage distillation (AD), (b) reconciliation, and (c) privacy amplification. Define the transmission rate as the ratio between the number of raw key bits obtained by the AD phase and the number of transmitted bits in the AD. The unidirectional SKA, whose transmission rate is 0 . 5, can be realized by using the original two-way wiretap channel as the AD phase. In this paper, we establish an efficient bidirectional SKA whose transmission rate is nearly 1 by modifying the two-way wiretap channel and using the modified two-way wiretap channel as the AD phase. The bidirectional SKA can be extended to multiple rounds of SKA with the same performance and transmission rate. For multiple rounds of bidirectional SKA, we have provided the bit error rate performance of the main channel and eavesdropper’s channel and the secret-key capacity. It is shown that the bit error rate (BER) of the main channel was lower than the eavesdropper’s channel and we prove that the transmission rate was nearly 1 when the number of rounds was large. Moreover, the secret-key capacity C s was from 0 . 04 to 0 . 1 as the error probability of channel was from 0 . 01 to 0 . 15 in binary symmetric channel (BSC). The secret-key capacity was close to 0 . 3 as the signal-to-noise ratio increased in the additive white Gaussian noise (AWGN) channel.

A largely self-contained and complete security proof for quantum key distribution

In this work we present a security analysis for quantum key distribution, establishing a rigorous tradeoff between various protocol and security parameters for a class of entanglement-based and prepare-and-measure protocols. The goal of this paper is twofold: 1) to review and clarify the stateof-the-art security analysis based on entropic uncertainty relations, and 2) to provide an accessible resource for researchers interested in a security analysis of quantum cryptographic protocols that takes into account finite resource effects. For this purpose we collect and clarify several arguments spread in the literature on the subject with the goal of making this treatment largely self-contained. More precisely, we focus on a class of prepare-and-measure protocols based on the Bennett-Brassard (BB84) protocol as well as a class of entanglement-based protocols similar to the Bennett-Brassard-Mermin (BBM92) protocol. We carefully formalize the different steps in these protocols, including randomization, measurement, parameter estimation, error correction and privacy amplification, allowing us to be mathematically precise throughout the security analysis. We start from an operational definition of what it means for a quantum key distribution protocol to be secure and derive simple conditions that serve as sufficient condition for secrecy and correctness. We then derive and eventually discuss tradeoff relations between the block length of the classical computation, the noise tolerance, the secret key length and the security parameters for our protocols. Our results significantly improve upon previously reported tradeoffs.

Implementation of continuous-variable quantum key distribution with discrete modulation

We have developed a continuous-variable quantum key distribution (CV-QKD) system that employs discrete quadrature-amplitude modulation and homodyne detection of coherent states of light. We experimentally demonstrated automated secure key generation with a rate of 50 kbps when a quantum channel is a 10 km optical fibre. The CV-QKD system utilises a four-state and post-selection protocol and generates a secure key against the entangling cloner attack. We used a pulsed light source of 1550 nm wavelength with a repetition rate of 10 MHz. A commercially available balanced receiver is used to realise shot-noise-limited pulsed homodyne detection. We used a non-binary LDPC code for error correction (reverse reconciliation) and the Toeplitz matrix multiplication for privacy amplification. A graphical processing unit card is used to accelerate the software-based post-processing.

Efficient key generation leveraging wireless channel reciprocity and discrete cosine transform

Key generation is essential for protecting wireless networks. Based on wireless channel reciprocity, transceivers can generate shared secret keys by measuring their communicating channels. However, due to non-simultaneous measurements, asymmetric noises and other interferences, channel measurements collected by different transceivers are highly correlated but not identical and thus might have some discrepancies. Further, these discrepancies might lead to mismatches of bit sequences after quantization. The referred mismatches significantly affect the efficiency of key generation. In this paper, an efficient key generation scheme leveraging wireless channel reciprocity is proposed. To reduce the bit mismatch rate and enhance the efficiency of key generation, the involved transceivers separately apply discrete cosine transform (DCT) and inverse discrete cosine transform (IDCT) to pre-process their measurements. Then, the outputs of IDCT are quantified and encoded to establish the bit sequence. With the implementations of information reconciliation and privacy amplification, the shared secret key can be generated. Several experiments in real environments are conducted to evaluate the proposed scheme. During each experiment, the shared key is established from the received signal strength (RSS) of heterogeneous devices. The results of experiments demonstrate that the proposed scheme can efficiently generate shared secret keys between transceivers.

A security proof of the round-robin differential phase shift quantum key distribution protocol based on the signal disturbance

The round-robin differential phase shift (RRDPS) quantum key distribution (QKD) protocol is a unique QKD protocol whose security has not been understood through an information-disturbance trade-off relation, and a sufficient amount of privacy amplification was given independently of signal disturbance. Here, we discuss the security of the RRDPS protocol in the asymptotic regime when a good estimate of the bit error rate is available as a measure of signal disturbance. The uniqueness of the RRDPS protocol shows up as a peculiar form of information-disturbance trade-off curve. When the length of a block of pulses used for encoding and the signal disturbance are both small, it provides a significantly better key rate than that from the original security proof. On the other hand, when the block length is large, the use of the signal disturbance makes little improvement in the key rate. Our analysis will bridge a gap between the RRDPS protocol and the conventional QKD protocols.

Secret key generation scheme from WiFi and LTE reference signals

Physical layer security has emerged as a promising approach to strengthen security of wireless communications. Particularly, extracting secret keys from channel randomness has attracted an increasing interest from both academic and industrial research groups. In this paper, we present a complete implantation of a secret key generation (SKG) protocol which is compliant with existing widespread Radio Access Technologies. This protocol performs the quantization of the channel state information, then information reconciliation and privacy amplification. We also propose an innovative algorithm to reduce the correlation between quantized channel coefficients that significantly improves the reliability and the resilience of the complete SKG scheme. Finally we assess the performance of our protocol by evaluating the quality of secret keys generated in various propagation environments from real single sense LTE signals, and real single and dual sense WiFi signals.

Practical round-robin differential-phase-shift quantum key distribution

The security of quantum key distribution (QKD) relies on the Heisenberg uncertainty principle, with which legitimate users are able to estimate information leakage by monitoring the disturbance of the transmitted quantum signals. Normally, the disturbance is reflected as bit flip errors in the sifted key; thus, privacy amplification, which removes any leaked information from the key, generally depends on the bit error rate. Recently, a round-robin differential-phase-shift QKD protocol for which privacy amplification does not rely on the bit error rate (Sasaki et al 2014 Nature 509 475) was proposed. The amount of leaked information can be bounded by the sender during the state-preparation stage and hence, is independent of the behavior of the unreliable quantum channel. In our work, we apply the tagging technique to the protocol and present a tight bound on the key rate and employ a decoy-state method. The effects of background noise and misalignment are taken into account under practical conditions. Our simulation results show that the protocol can tolerate channel error rates close to 50% within a typical experiment setting. That is, there is a negligible restriction on the error rate in practice.

Teleportation-based continuous variable quantum cryptography

We present a continuous variable (CV) quantum key distribution (QKD) scheme based on the CV quantum teleportation of coherent states that yields a raw secret key made up of discrete variables for both Alice and Bob. This protocol preserves the efficient detection schemes of current CV technology (no single-photon detection techniques) and, at the same time, has efficient error correction and privacy amplification schemes due to the binary modulation of the key. We show that for a certain type of incoherent attack it is secure for almost any value of the transmittance of the optical line used by Alice to share entangled two-mode squeezed states with Bob (no 3 dB or 50% loss limitation characteristic of beam splitting attacks). The present CVQKD protocol works deterministically (no postselection needed) with efficient direct reconciliation techniques (no reverse reconciliation) in order to generate a secure key and beyond the 50% loss case at the incoherent attack level.

A novel WDM-PON based on quantum key distribution FPGA controller

To improve the potential security threats of WDM-PON access network, a novel WDM-PON based on quantum key distribution FPGA controller of passive decoy state modified model is presented here. QKD FPGA is responsible for 1.25 Gbps upstream PRBS source, clock regeneration, phase modulation control, key sifting, privacy amplification, and upstream time-divided-multiple-access control on quantum channels. An 8-user network experiment shows that over 20 km fibre, the mean secure exchange key rate can reach up to 500 bps in total, with the acceptable quantum bit error rate below safe limit and a few impact on classical channels. This scheme can provide a promising way for the coexistence between quantum key distribution and classical data service.

A novel WDM-PON based on quantum key distribution FPGA controller

To improve the potential security threats of WDM-PON access network, a novel WDM-PON based on quantum key distribution FPGA controller of passive decoy state modified model is presented here. QKD FPGA is responsible for 1.25 Gbps upstream PRBS source, clock regeneration, phase modulation control, key sifting, privacy amplification, and upstream time-divided-multiple-access control on quantum channels. An 8-user network experiment shows that over 20 km fibre, the mean secure exchange key rate can reach up to 500 bps in total, with the acceptable quantum bit error rate below safe limit and a few impact on classical channels. This scheme can provide a promising way for the coexistence between quantum key distribution and classical data service.

高效短种子量子密钥分配保密放大方案设计

高效短种子量子密钥分配保密放大方案设计