Bivariate Hermitian Polynomial Coding for Efficient Distributed Matrix Multiplication

We improve the performance of lattice-based cryptosystems Dilithium on Cortex-M3 with expensive multiplications. Our contribution is two-fold: (i) We generalize Barrett multiplication and show that the resulting shape-independent modular multiplication performs comparably to long multiplication on some platforms without special hardware when precomputation is free. We call a modular multiplication “shape-independent” if its correctness and efficiency depend only on the magnitude of moduli and not the shapes of the moduli. This was unknown in the literature even though modular multiplication has been studied for more than 40 years. In the literature, shape-independent modular multiplications often perform several times slower than long multiplications even if we ignore the cost of the precomputation. (ii) We show that polynomial multiplications based on Nussbaumer fast Fourier transform and Toom–Cook over Z2k perform the best when modular multiplications are expensive and k is not very close to the arithmetic precision.For practical evaluation, we implement assembly programs for the polynomial arithmetic used in the digital signature Dilithium on Cortex-M3. For the modular multiplications in Dilithium, our generalized Barrett multiplications are 1.92 times faster than the state-of-the-art assembly-optimized Montgomery multiplications, leading to 1.38−1.51 times faster Dilithium NTT/iNTT. Along with the improvement in accumulating products, the core polynomial arithmetic matrix-vector multiplications are 1.71−1.77 times faster. We further apply the FFT-based polynomial multiplications over Z2k to the challenge polynomial multiplication ct0, leading to 1.31 times faster computation for ct0.We additionally apply the ideas to Saber on Cortex-M3 and demonstrate their improvement to Dilithium and Saber on our 8-bit AVR environment. For Saber on Cortex-M3, we show that matrix-vector multiplications with FFT-based polynomial multiplications over Z2k are 1.42−1.46 faster than the ones with NTT-based polynomial multiplications over NTT-friendly coefficient rings. When moving to a platform with smaller arithmetic precision, such as 8-bit AVR, we improve the matrix-vector multiplication of Dilithium with our Barrett-based NTT/iNTT by a factor of 1.87−1.89. As for Saber on our 8-bit AVR environment, we show that matrixvector multiplications with NTT-based polynomial multiplications over NTT-friendly coefficient rings are faster than polynomial multiplications over Z2k due to the large k in Saber.

Artificial intelligence for medical imaging: U-Net technology for anatomical feature analysis

This chapter describes state-of-the art techniques to improve performance of spectrum sensing and spectrum management in Cognitive Radio Networks (CRN) by leveraging services available in cloud computing platforms. CRNs are capable of adaptive learning and reconfiguration to provide consistent communications in dynamic environments. However, ensuring adaptation and learning in CRN will require availability of large volume of data and fast processing. However, the performance and security of CRN is considerably constrained by its limited power, memory and computational capacity, it may not be able to achieve its full capability. Fortunately, the advent of cloud computing has the potential to mitigate these constraints due its vast storage and computational capacity.

We consider the problems of Private and Secure Matrix Multiplication (PSMM) and Fully Private Matrix Multiplication (FPMM), for which matrices privately selected by a master node are multiplied at distributed worker nodes without revealing the indices of the selected matrices, even when a certain number of workers collude with each other. We propose a novel systematic approach to solve PSMM and FPMM with colluding workers, which leverages solutions to a related Secure Matrix Multiplication (SMM) problem where the data (rather than the indices) of the multiplied matrices are kept private from colluding workers. Specifically, given an SMM strategy based on polynomial codes or Lagrange codes, one can exploit the special structure inspired by the matrix encoding function to design private coded queries for PSMM/FPMM, such that the algebraic structure of the computation result at each worker resembles that of the underlying SMM strategy. Adopting this systematic approach provides novel insights in private query designs for private matrix multiplication, substantially simplifying the processes of designing PSMM and FPMM strategies. Furthermore, the PSMM and FPMM strategies constructed following the proposed approach outperform the state-of-the-art strategies in one or more performance metrics including recovery threshold (minimal number of workers the master needs to wait for before correctly recovering the multiplication result), communication cost, and computation complexity, demonstrating a more flexible tradeoff in optimizing system efficiency.

The operational matrix consisting of the product of two time functions, and the operational matrices for forward or backward integration consisting of general orthogonal polynomials are derived, respectively, for the analysis and optimal control of linear time-varying systems with a quadratic performance measure. The present results include results obtained via Chebyshev, Legendre, Laguerre, Jacobi, Hermite and ultraspherical polynomials as special cases.

The smart city is a technological framework that connects the city’s different components to create new opportunities. This connection is possible with the help of the Internet of Things (IoT), which provides a digital personality to physical objects. Some studies have proposed integrating Blockchain technology with IoT in different use cases as access, orchestration, or replicated storage layer. The majority of connected objects’ capacity limitation makes the use of Blockchain inadequate due to its redundancy and its conventional processing-intensive consensus like PoW. This paper addresses these challenges by proposing a NOVEL model of a lightweight Blockchain framework (IoT-SmartChain), with a lightweight consensus and a lightweight structure. The framework architecture presents a role hierarchy of connected objects according to their computational and storage capacity. This organization allows all things to be linked even indirectly via different interfaces and to benefit from the power of high-capacity objects such as Fog and Edge computing nodes. Data is validated and added to the blockchain ledger by running a lightweight consensus called Proof of Random Participation (PoRP), which reduces the blockchain nodes’ high computing power requirement. The TOPIC subscription-based data storage strategy called Assisted Selected Relevant Data in Local Ledger (ASRDLL) reduces the data size of a node’s local ledger and the entire network’s data size. This strategy is assisted by a centralized algorithm that optimizes the overall network size by adjusting the choice of TOPICS. The storage capacity, computational power, and energy consumption have been evaluated by a proof of concept implementation under NodeJS.

An algorithm is presented for computing the resultant of two generic bivariate polynomials over a field K. For such p and q K[x,y] both of degree d in x and n in y , the algorithm computes the resultant with respect to y using (n2 - 1/ømega d) 1+o(1) arithmetic operations in K, where two n x n matrices are multiplied using O(nømega) operations. Previous algorithms required time (n2 d) 1+o(1). The resultant is the determinant of the Sylvester matrix S(x) of p and q , which is an n x n Toeplitz-like polynomial matrix of degree~ d . We use a blocking technique and exploit the structure of S(x) for reducing the determinant computation to the computation of a matrix fraction description R(x)Q(x)-1 of an m x m submatrix of the inverse S(x)-1, where młl n. We rely on fast algorithms for handling dense polynomial matrices: the fraction description is obtained from an x -adic expansion via matrix fraction reconstruction, and the resultant as the determinant of the denominator matrix. We also describe some extensions of the approach to the computation of generic Gröbner bases and of characteristic polynomials of generic structured matrices and in univariate quotient algebras.

In Industrial IoT ecosystems, resource‐constrained devices increasingly rely on searchable encryption (SE) to offload encrypted data to cloud platforms, reducing local computational burdens while preserving data privacy. However, traditional SE technologies struggle to meet the demands of IoT environments featuring large‐scale distributed devices, due to cumbersome certificate management and inherent key escrow weaknesses. While certificateless searchable encryption (CLSE) schemes have been proposed to overcome these challenges, most existing solutions remain prone to security flaws and lack support for multi‐keyword searches. To address these shortcomings, we present a novel lightweight certificateless public key encryption scheme with multi‐keyword search capabilities (CLPSE). Crucially, compared to prior work, our protocol design does not rely on bilinear pairings, but instead employs an elliptic curve algorithm involving only scalar multiplication and addition operations. In addition, to protect the privacy between keywords and ciphertexts, we design a new matrix index structure using the BM25 retrieval algorithm and VFE function. Users can retrieve the corresponding ciphertexts using their trapdoor and threshold, which improves the flexibility of retrieval. Based on this construction, our scheme (CLPSE) is tailored for devices with limited storage and computational capacity. Compared to existing methods, it guarantees the indistinguishability of keyword ciphertexts and trapdoors, while delivering robust protection against both inside and outside keyword guessing attacks (IKGA and OKGA), thereby enhancing keyword security. Experimental results substantiate that our scheme achieves significant improvements in computational and communication efficiency over prior approaches.

The software‐defined wireless sensor networks (SDWSNs) have been proposed recently to solve the energy limitation of sensor nodes and extend the lifetime of the wireless sensor networks by fast node reconstruction and dynamical resource allocation. In this study, the authors investigate an energy‐efficient resource allocation algorithm in SDWSNs, in which radio resource allocation could be handled at central controllers with powerful storage and computation capacity. In this algorithm, the authors formulate an optimisation problem to minimise the energy consumption, under the individual constraint of quality of service. Then, the initial optimisation problem is transformed using semidefinite relaxation, to achieve centralised adaptive bandwidth and power allocation (CABPA). Additionally, two special cases are derived to reveal the performance of the CABPA. Furthermore, an OpenFlow‐based scheme is proposed for information exchanging and updating to realise the centralised resource allocation. Meanwhile, a distributed scheme with limited information about the whole network is developed to serve as a performance benchmark for the CABPA in the SDWSN. Finally, the simulation results reveal that the proposed CABPA performs better than the other algorithms, and it balances the power and bandwidth utilisation.

Rising storage and computational capacities have led to the accumulation of voluminous datasets. These datasets contain insights that describe natural phenomena, usage patterns, trends, and other aspects of complex, real-world systems. Statistical and machine learning models are often employed to identify these patterns or attributes of interest. However, a wide array of potentially relevant models and parameterizations exist, and may provide the best performance only after preprocessing steps have been carried out. Our distributed analytics platform, Trident, facilitates the modeling process by providing high-level data exploration functionality as well as guidance for creation of effective models. Trident handles (1) data partitioning and storage, (2) metadata extraction and indexing, and (3) selective retrievals or transformations to prepare and generate training data. In this study, we evaluate Trident in the context of a 1.1 petabyte epidemiology dataset generated by a disease spread simulation; such datasets are often used in planning for national-scale outbreaks in animal populations.

With rapidly increasing storage and computational capacity, a common PC can store and index hundreds of hours of speech. This suggests that new approaches based on database techniques might be useful in speech recognition and speech indexing. This paper presents a first step in such a direction. The algorithm developed relies on an indexed single-speaker database. The database consists of spoken utterances transcribed into text. The waveforms of these utterances are converted off-line to binary symbols called fingerprints through a nonlinear frequency-domain transform. The fingerprints are associated with the transcribed text. Given the fingerprint of a new waveform, the best word match from the database can be retrieved. A 3255 word database is used as a test bed. All the words from this database are mixed with white noise and time-scale modified to provide test data. The database is queried with the fingerprint of the test words and the best match is retrieved. The results of the experiments conducted are promising, showing a 99.5% recognition rate for a 20 dB signal to noise ratio (SNR).

For bivariate polynomials of degree we give fast numerical constructions of determinantal representations with matrices. Unlike some other existing constructions, our approach returns matrices of the smallest possible size for all (not just generic) polynomials of degree n and does not require any symbolic computation. We can apply these linearizations to numerically compute the roots of a system of two bivariate polynomials by using numerical methods for the two-parameter eigenvalue problems.

In this paper, we consider a secure distributed computing scenario in which a master wants to perform matrix multiplication of confidential inputs with multiple workers in parallel. In such a setting, a master does not want to reveal information about the two input matrices to the workers in an information-theoretic sense. We propose a secure distributed computing scheme that can efficiently cope with straggling effects by applying polynomial codes on sub-tasks assigned to workers. The achievable recovery threshold, i.e., the number of workers that a master needs to wait for to get the final product, of our proposed scheme is revealed to be order-optimal to the number of workers. Moreover, we derive the achievable recovery threshold of the proposed scheme is within a constant multiplicative factor from information-theoretic lower bound. As a byproduct, we extend our strategy to secure distributed computing for convolution tasks on confidential data.

Deep Neural Networks (DNNs) have shown great success in completing complex tasks. However, DNNs inevitably bring high computational cost and storage consumption due to the complexity of hierarchical structures, thereby hindering their wide deployment in Internet-of-Things (IoT) devices, which have limited computational capability and storage capacity. Therefore, it is a necessity to investigate the technologies to compact DNNs. Despite tremendous advances in compacting DNNs, few surveys summarize compacting-DNNs technologies, especially for IoT applications. Hence, this paper presents a comprehensive study on compacting-DNNs technologies. We categorize compacting-DNNs technologies into three major types: 1) network model compression, 2) Knowledge Distillation (KD), 3) modification of network structures. We also elaborate on the diversity of these approaches and make side-by-side comparisons. Moreover, we discuss the applications of compacted DNNs in various IoT applications and outline future directions.

Long-term reliable condition monitoring (CM) of blast furnace blowers is essential to avoid catastrophic failure. Due to variable working conditions, the predefined thresholds in current CM systems influence the accuracy of the monitoring process and can lead to misdiagnoses. In order to overcome this limitation, we propose a digital twin (DT)-based scheme to monitor vibrations found in blowers. Factors believed to impact the distribution of vibration amplitudes are analysed using data collected from a constant speed axial blower operating in an industrial commercial environment and, based on which, a machine learning-based adaptive amplitude simulation model is developed on our on-site private cloud computing platform. Outcomes reveal that different guide vane openings in the manufacturing process can cause changes in amplitudes. By integrating the newly-arriving sensor data, vibration amplitudes can be more accurately predicted in the virtual space. The gap between the simulated and actual value narrowed from ±5 µm to within ±3 µm, from which a dynamic threshold can be defined. The resulting DT model, coupled with the on-site private cloud computing platform, which alleviates the shortage of computational and storage capacity in steel plants, allows for a much more effective CM system.