Privacy Amplification Research Articles

Research on time-division multiplexing for error correction and privacy amplification in post-processing of quantum key distribution

The post-processing of quantum key distribution mainly includes error correction and privacy amplification. The error correction algorithms and privacy amplification methods used in the existing quantum key distribution are completely unrelated. Based on the principle of correspondence between error-correcting codes and hash function families, we proposed the idea of time-division multiplexing for error correction and privacy amplification for the first time. That is to say, through the common error correction algorithms and their corresponding hash function families or the common hash function families and their corresponding error-correcting codes, error correction and privacy amplification can be realized by time-division multiplexing with the same set of devices. In addition, we tested the idea from the perspective of error correction and privacy amplification, respectively. The analysis results show that the existing error correction algorithms and their corresponding hash function families or the common privacy amplification methods and their corresponding error-correcting codes cannot realize time-division multiplexing for error correction and privacy amplification temporarily. However, according to the principle of correspondence between error-correcting codes and hash function families, the idea of time-division multiplexing is possible. Moreover, the research on time-division multiplexing for error correction and privacy amplification has some practical significance. Once the idea of time-division multiplexing is realized, it will further reduce the calculation and storage cost of the post-processing process, reduce the deployment cost of quantum key distribution, and help to remote the practical engineering of quantum key distribution.

Trojan-horse attack on a real-world quantum key distribution system: Theoretical and experimental security analysis

This paper presents a theoretical and experimental demonstration of a security analysis of a Trojan-horse attack (THA) on a real-world quantum key distribution (QKD) system. We show that the upper bound on the information leakage depends solely on the fidelity between the states of the adversary. We find the lower bound for fidelity between THA states in both the polarization- and phase-coding BB84 protocols, considering both pure and mixed states. Our bounds depend only on the mean photon number per pulse available to an adversary. We also present an experimental analysis of a QKD system, including optical time-domain reflectometry measurements with centimeter resolution and spectral transmittance measurements for optical defense elements ranging from 1100 to 1800 nm with a noise floor lower than −100 dB. Finally, by considering the optimal attack, we obtain the value of the mean photon number per pulse available to an adversary and calculate the key leakage that needs to be eliminated during the privacy amplification procedure. Published by the American Physical Society 2024

Overcoming noise limitations in quantum key distribution with quantum privacy amplification

Overcoming noise limitations in quantum key distribution with quantum privacy amplification

An Overview of Postprocessing in Quantum Key Distribution

Quantum key distribution (QKD) technology is a frontier in the field of secure communication, leveraging the principles of quantum mechanics to offer information-theoretically secure keys. Postprocessing is an important part of a whole QKD system because it directly impacts the secure key rate and the security of the system. In particular, with the fast increase in the photon transmission frequency in a QKD system, the processing speed of postprocessing becomes an essential issue. Our study embarks on a comprehensive review of the development of postprocessing of QKD, including five subprotocols, namely, parameter estimation, sifting, information reconciliation, privacy amplification, and channel authentication. Furthermore, we emphasize the issues raised in the implementation of these subprotocols under practical scenarios, such as limited computation or storage resources and fluctuations in channel environments. Based on the composable security theory, we demonstrate how enhancements in each subprotocol influence the secure key rate and security parameters, which can provide meaningful insights for future advancements in QKD.

Simulation of an entanglement-based quantum key distribution protocol

Since the 80 s when it was first proposed, Quantum Key Distribution (QKD) elicited great interest in the field of cryptography as a unique procedure for key generation that could in principle guarantee unconditionally secure communication “by the laws of Physics”. In the last fifteen years commercial solutions have started appearing on the market, showing that practical implementations of the protocol were not only possible but also competitive in terms of security and achievable secret-key rate. In this work we describe a simulation of the historical QKD protocol E91 on the IBM Quantum platform, making use of the qubit formalism to represent the quantum states received by two communicating nodes. Having implemented also the post-processing steps for the error correction and the privacy amplification, this model can represent a simple stand-alone tool to study the performance not only of one-to-one communication but of more complex systems that rely on QKD for security, one above all QKD networks.

Optimal Second-Order Rates for Quantum Soft Covering and Privacy Amplification

Optimal Second-Order Rates for Quantum Soft Covering and Privacy Amplification

PA-iMFL: Communication-Efficient Privacy Amplification Method Against Data Reconstruction Attack in Improved Multilayer Federated Learning

PA-iMFL: Communication-Efficient Privacy Amplification Method Against Data Reconstruction Attack in Improved Multilayer Federated Learning

Privacy Amplification via Shuffling: Unified, Simplified, and Tightened

The shuffle model of differential privacy provides promising privacy-utility balances in decentralized, privacy-preserving data analysis. However, the current analyses of privacy amplification via shuffling lack both tightness and generality. To address this issue, we propose the variation-ratio reduction as a comprehensive framework for privacy amplification in both single-message and multi-message shuffle protocols. It leverages two new parameterizations: the total variation bounds of local messages and the probability ratio bounds of blanket messages, to determine indistinguishability levels. Our theoretical results demonstrate that our framework provides tighter bounds, especially for local randomizers with extremal probability design, where our bounds are exactly tight. Additionally, variation-ratio reduction complements parallel composition in the shuffle model, yielding enhanced privacy accounting for popular sampling-based randomizers employed in statistical queries (e.g., range queries, marginal queries, and frequent itemset mining). Empirical findings demonstrate that our numerical amplification bounds surpass existing ones, conserving up to 30% of the budget for single-message protocols, 75% for multi-message ones, and a striking 75%-95% for parallel composition. Our bounds also result in a remarkably efficient Õ ( n ) algorithm that numerically amplifies privacy in less than 10 seconds for n = 10 8 users.

Privacy Amplification by Iteration for ADMM with (Strongly) Convex Objective Functions

We examine a private ADMM variant for (strongly) convex objectives which is a primal-dual iterative method. Each iteration has a user with a private function used to update the primal variable, masked by Gaussian noise for local privacy, without directly adding noise to the dual variable. Privacy amplification by iteration explores if noises from later iterations can enhance the privacy guarantee when releasing final variables after the last iteration. Cyffers et al. explored privacy amplification by iteration for the proximal ADMM variant, where a user's entire private function is accessed and noise is added to the primal variable. In contrast, we examine a private ADMM variant requiring just one gradient access to a user's function, but both primal and dual variables must be passed between successive iterations. To apply Balle et al.'s coupling framework to the gradient ADMM variant, we tackle technical challenges with novel ideas. First, we address the non-expansive mapping issue in ADMM iterations by using a customized norm. Second, because the dual variables are not masked with any noise directly, their privacy guarantees are achieved by treating two consecutive noisy ADMM iterations as a Markov operator. Our main result is that the privacy guarantee for the gradient ADMM variant can be amplified proportionally to the number of iterations. For strongly convex objective functions, this amplification exponentially increases with the number of iterations. These amplification results align with the previously studied special case of stochastic gradient descent.

A Generalized Shuffle Framework for Privacy Amplification: Strengthening Privacy Guarantees and Enhancing Utility

The shuffle model of local differential privacy is an advanced method of privacy amplification designed to enhance privacy protection with high utility. It achieves this by randomly shuffling sensitive data, making linking individual data points to specific individuals more challenging. However, most existing studies have focused on the shuffle model based on (ε0,0)-Locally Differentially Private (LDP) randomizers, with limited consideration for complex scenarios such as (ε0,δ0)-LDP or personalized LDP (PLDP). This hinders a comprehensive understanding of the shuffle model's potential and limits its application in various settings. To bridge this research gap, we propose a generalized shuffle framework that can be applied to PLDP setting. This generalization allows for a broader exploration of the privacy-utility trade-off and facilitates the design of privacy-preserving analyses in diverse contexts. We prove that the shuffled PLDP process approximately preserves μ-Gaussian Differential Privacy with μ = O(1/√n). This approach allows us to avoid the limitations and potential inaccuracies associated with inequality estimations. To strengthen the privacy guarantee, we improve the lower bound by utilizing hypothesis testing instead of relying on rough estimations like the Chernoff bound or Hoeffding's inequality. Furthermore, extensive comparative evaluations clearly show that our approach outperforms existing methods in achieving strong central privacy guarantees while preserving the utility of the global model. We have also carefully designed corresponding algorithms for average function, frequency estimation, and stochastic gradient descent.

Privacy Amplification by Sampling under User-level Differential Privacy

Random sampling is an effective tool for reducing the computational costs of query processing in large databases. It has also been used frequently for private data analysis, in particular, under differential privacy (DP). An interesting phenomenon that the literature has identified, is that sampling can amplify the privacy guarantee of a mechanism, which in turn leads to reduced noise scales that have to be injected. All existing privacy amplification results only hold in the standard, record-level DP model. Recently, user-level differential privacy (user-DP) has gained a lot of attention as it protects all data records contributed by any particular user, thus offering stronger privacy protection. Sampling-based mechanisms under user-DP have not been explored so far, except naively running the mechanism on a sample without privacy amplification, which results in large DP noises. In fact, sampling is in even more demand under user-DP, since all state-of-the-art user-DP mechanisms have high computational costs due to the complex relationships between users and records. In this paper, we take the first step towards the study of privacy amplification by sampling under user-DP, and give the amplification results for two common user-DP sampling strategies: simple sampling and sample-and-explore. The experimental results show that these sampling-based mechanisms can be a useful tool to obtain some quick and reasonably accurate estimates on large private datasets.

Utility-aware Privacy Perturbation for Training Data

Data perturbation under differential privacy constraint is an important approach of protecting data privacy. However, as the data dimensions increase, the privacy budget allocated to each dimension decreases and thus the amount of noise added increases, which eventually leads to lower data utility in training tasks. To protect the privacy of training data while enhancing data utility, we propose a Utility-aware training data Privacy Perturbation scheme based on attribute Partition and budget Allocation (UPPPA). UPPPA includes three procedures: the quantification of attribute privacy and attribute importance, attribute partition, and budget allocation. The quantification of attribute privacy and attribute importance based on information entropy and attribute correlation provide an arithmetic basis for attribute partition and budget allocation. During the attribute partition, all attributes of training data are classified into high and low classes to achieve privacy amplification and utility enhancement. During the budget allocation, a γ-privacy model is proposed to balance data privacy and data utility so as to provide privacy constraint and guide budget allocation. Three comprehensive sets of real-world data are applied to evaluate the performance of UPPPA. Experiments and privacy analysis show that our scheme can achieve the tradeoff between privacy and utility.

Single photon hybrid quantum key distribution

In this work, we propose a quantum key distribution protocol using the polarization and transverse spatial degrees of freedom of single photons. We show that the protocol is secure and easy to implement experimentally, thus being able to be used in investigations on optical communication. In addition, we show that the information transmitted between two separate parties is always greater than the information retained by a eavesdropper. In this way, it is always possible to employ classical error correction and privacy amplification to minimize eavesdropper information.

A quantum digital signature protocol with state preparation error tolerance

<sec>The quantum digital signature (QDS) has attracted much attention as it ensures the nonrepudiation, unforgeability, and transferability of signature messages based on information-theoretic security. Amiri et al. (<ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://doi.org/10.1103/PhysRevA.93.032325"><i>Phys. Rev. A</i> <b>93</b> 032325</ext-link>) proposed the first practical QDS protocol based on orthogonal coding, which has realized information-theoretic security and become the mainstream paradigm in QDS research. The procedure of QDS involves two essential stages, the one is the distribution stage, in which Alice-Bob and Alice-Charlie individually utilize the three-intensity decoy-state quantum key distribution protocol but without error correction or privacy amplification, namely, key-generation protocol, to generate correlated bit strings, the other is the messaging stage, in which Alice transmits signature messages to the two recipients.</sec><sec>However, previous theoretical and experimental studies both overlooked the modulation errors that may be introduced in the state preparation process due to the imperfections in modulator devices. Under the traditional framework of GLLP analysis method, these errors will significantly reduce the actual signature rates. Therefore, we propose a state-preparation-error tolerant QDS and use parameter analysis to characterize the state preparation error to make the simulation analysis more realistic. In addition, we analyze the signature rates of the present scheme by using the three-intensity decoy-state method.</sec><sec>Compared with previous QDS protocols, our protocol almost shows no performance degradation under practical state preparation errors and exhibits a maximum transmission distance around 180 km. Furthermore, state preparation errors do not have a significant influence on the bit error rate induced by normal communication between the legitimate users or the one produced by an eavesdropper. These results prove that the method proposed in this paper has excellent robustness against state preparation errors and it can achieve much higher signature rates and signature distances than other standard methods. Besides, signature rates are basically unchanged under different total pulse numbers, which shows that our protocol also has good robustness against the finite-size effect. Additionally, in the key generation process, our method is only required to prepare three quantum states, which will reduce the difficulty of experiment realizations.</sec><sec>Furthermore, the proposed method can also be combined with the measurement-device-independent QDS protocol and the twin-field QDS protocol to further increase the security level of QDS protocol. Therefore, our work will provide an important reference value for realizing the practical application of QDS in the future.</sec>

A Reliable Physical Layer Key Generation Scheme Based on RSS and LSTM Network in VANET

With the rapid development of information and communication technology, Vehicular AD hoc Networks (VANET) has attracted more and more attention. In order to provide traffic safety services, vehicles frequently share information related to road traffic, such as vehicle motion data and traffic flow data. Reliable key generation is the basis of VANET security system construction. At present, most key generation schemes rely on a trusted third-party, so there are security risks. Traditional key agreement protocols have high overhead, and is not suitable for the latency-sensitive requirements of VANET. The physical layer security technology extracts the fingerprint of the wireless channel and the identity of the device, and generates the key quickly and in real time without the third party distribution. A physical layer key generation scheme based on Received Signal Strength (RSS) is proposed to realize Vehicle-to-Vehicle (V2V) secure communications. Firstly, a network model based on Long Short-Term Memory (LSTM) network and Kalman Filtering is proposed to effectively enhance the reciprocity of physical layer information in dynamic environment. Secondly, a lossless quantization scheme is proposed, which achieves a lower bit disagreement rate and a higher bit generation rate. Thirdly, the inconsistent bits are corrected by fuzzy extractor, the confidentiality of the key exchange process is enhanced by zero knowledge proof, and the security of the key is improved by using hash function for privacy amplification. Finally, the experimental results show that the proposed scheme has great improvements in data correlation, bit disagreement rate, bit generation rate and bit distribution randomness.

Privacy Amplification and Decoupling Without Smoothing

Privacy Amplification and Decoupling Without Smoothing

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We introduce, motivate and study ε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon $$\\end{document}-almost collision-flat universal (ACFU) hash functions f:X×S→A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f:\\mathcal X\ imes \\mathcal S\\rightarrow \\mathcal A$$\\end{document}. Their main property is that the number of collisions in any given value is bounded. Each ε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon $$\\end{document}-ACFU hash function is an ε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon $$\\end{document}-almost universal (AU) hash function, and every ε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon $$\\end{document}-almost strongly universal (ASU) hash function is an ε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon $$\\end{document}-ACFU hash function. We study how the size of the seed set S\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal S$$\\end{document} depends on ε,|X|\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon ,|\\mathcal X |$$\\end{document} and |A|\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|\\mathcal A |$$\\end{document}. Depending on how these parameters are interrelated, seed-minimizing ACFU hash functions are equivalent to mosaics of balanced incomplete block designs (BIBDs) or to duals of mosaics of quasi-symmetric block designs; in a third case, mosaics of transversal designs and nets yield seed-optimal ACFU hash functions, but a full characterization is missing. By either extending S\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal S$$\\end{document} or X\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal X$$\\end{document}, it is possible to obtain an ε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon $$\\end{document}-ACFU hash function from an ε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon $$\\end{document}-AU hash function or an ε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon $$\\end{document}-ASU hash function, generalizing the construction of mosaics of designs from a given resolvable design (Gnilke et al. in Des. Codes Cryptogr. 86(1):85–95, 2017). The concatenation of an ASU and an ACFU hash function again yields an ACFU hash function. Finally, we motivate ACFU hash functions by their applicability in privacy amplification.

A Novel Hybrid Protocol and Code Related Information Reconciliation Scheme for Physical Layer Secret Key Generation

Wireless networks are vulnerable to various attacks due to their open nature, making them susceptible to eavesdropping and other security threats. Eavesdropping attack takes place at the physical layer. Traditional wireless network security relies on cryptographic techniques to secure data transmissions. However, these techniques may not be suitable for all scenarios, especially in resource-constrained environments such as wireless sensor networks and adhoc networks. In these networks having limited power resources, generating cryptographic keys between mobile entities can be challenging. Also, the cryptographic keys are computationally complex and require key management infrastructure. Physical Layer Key Generation (PLKG) is an emerging solution to address these challenges. It establishes secure communication between two users by taking advantage of the wireless channel's inherent features. PLKG process involves channel probing, quantization, information reconciliation (IR) and privacy amplification to generate symmetric secret key. The researchers have used various PLKG techniques to get the secret key, sTop of Form
 till they face problems in the IR scheme to obtain symmetric keys between the users who share the same channel for communication. Both the code based and protocol based methods proposed in the literature have advantages and limitations related to their performance parameters such as information leakage, interaction delay and computation complexity. This research work proposes a novel IR mechanism that combines the protocol and code-based error correction methods to obtain reduced Bit Mismatch Rate (BMR), reduced information leakage, reduced interaction delay, and reduced computational time to enhance physical layer secret key's quality. In the proposed research work, the channel samples are generated using the Received Signal Strength (RSS) and Channel Impulse Response (CIR) parameters. These samples are quantized using Vector Quantization with Affinity Propagation Clustering (VQAPC) method to generate the preliminary key. The samples collected by the two users who wish to communicate, (for example Alice and Bob) will be different due to noise in the channel and hardware limitations. Hence their preliminary keys will be different. Removing this discrepancy between Bob's and Alice's initial keys, using novel Hybrid Protocol and Code related Information Reconciliation (HPC-IR) scheme to generate error corrected key, is the most important contribution of this research work. This key is further encoded by the MD5 hash function to generate a final secret key for exchanging information between two users over the wireless channel. It is observed that the proposed HPC-IR scheme achieves BMR of 19.4%, information leakage is 0.002, interaction delay is 0.001 seconds and computation time is 0.02 seconds.

Multi‐Party Quantum Key Distribution Using Variational Quantum Eigensolvers

AbstractThe research paper introduces a novel approach to multi‐party quantum key distribution using variational quantum eigensolvers (VQEs). The protocol aims to establish secure communication among multiple parties in a quantum network. The paper outlines a comprehensive framework incorporating quantum state preparation, VQE‐based key generation, error correction, and privacy amplification circuits. Mathematical formulations guide the design of quantum gates, variational parameters, and error correction codes. The protocol utilizes quantum entanglement, VQE optimization, and classical operations for error correction and secure key extraction. The paper's experimental focus involves implementing the proposed protocol on a quantum computer, analyzing security metrics such as mutual information and min‐entropy, and simulating circuit outcomes.

Integration of Self-Adaptive Physical-Layer Key Distribution and Encryption in Optical Coherent Communication

We propose and experimentally demonstrate a compatible physical-layer secure optical communication (PLSOC) system that integrates self-adaptive physical-layer key distribution (PLKD) and encryption (PLE) in optical coherent communication. Based on bit error rate difference of QAM signals mapped by asymmetric basis state Y-00 protocol, the secret key can be secretly exchanged over public fiber links without the pre-shared keys. Moreover, we perform a parameter self-adaptive strategy for practical and dynamic PLKD. The security of the key is evaluated in the case of a fiber-tapping attack. A secure hash algorithm, SHA3-512, is used to perform privacy amplification to obtain the virtually secure key. An error-free PLKD rate reaches 39.3 Kbits/s over 300km ultra-low loss fiber. We experimentally enable the integration of the proposed PLKD scheme and quantum noise stream cipher (QNSC) with a single wavelength, same system. Q factor penalty of the integration system compared to the QNSC system is 3.7dB (optical back-to-back) and 4.8dB (300km) respectively. By exploiting a common hardware platform, with the same wavelength, the proposed PLSOC system addresses the problem that PLKD and PLE are separately performed through independent optical fiber links or wavelengths. Since only digital signal processing is used, the scheme does not require extra hardware.