Recently, transformer models have demonstrated excellent performance across various intelligent applications owing to their ability to understand global context through self-attention mechanism. However, the extensive...
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Recently, transformer models have demonstrated excellent performance across various intelligent applications owing to their ability to understand global context through self-attention mechanism. However, the extensively investigated multiplicative-based attention mechanism is inadequate for capturing relationship-based feature representations, as the dot product cannot depict the intricate semantic information between objects. Moreover, it has a great computational burden with a complexity of O(n2), ( n 2 ) , due to the global feature representation capability achieved by calculating the relationship between each token within the entire feature sequence. To solve the current problem, this paper proposes a granular transformer framework with linear complexity, wherein diverse granulation functions can be employed to supersede the prevailing multiplicative relationships, and an innovative linearization methodology in the form of matrix factorization is designed to reduce the computational burden. Relying on the intricate semantics information embedded within granular structures, the capacity for feature extraction is significantly more comprehensive. Then, a novel matrix factorization methodology is developed for the linearity of granulation-based attention, accomplished by implementing separate deformable convolution sampling and using an approximate iterative algorithm based on cubic equations to calculate the Moore-Penrose inverse. The mathematical proof that our method is approximate with the complete granulation-based attention matrix is investigated in detail. Finally, the performance of Granformer, an innovative reconfiguration of plug-and-play transformer block, is evaluated on representative intelligent applications, including 3D point cloud classification, emotion recognition and sentiment analysis, and object detection. The experimental results suggest that our methodologies outperform the state-of-the-art models.
We first introduce a family of binary pq(2)-periodic sequences based on the Euler quotients modulo pq, where p and q are two distinct odd primes and p divides q - 1. The minimal polynomials and linear complexities are...
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We first introduce a family of binary pq(2)-periodic sequences based on the Euler quotients modulo pq, where p and q are two distinct odd primes and p divides q - 1. The minimal polynomials and linear complexities are determined for the proposed sequences provided that 2(q-1) not equivalent to 1 mod q(2). The results show that the proposed sequences have high linear complexities.
linear complexity is a much used metric of the security of any binary sequence with application in communication systems and cryptography. In this work, we propose a method of computing the linear complexity of a popu...
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linear complexity is a much used metric of the security of any binary sequence with application in communication systems and cryptography. In this work, we propose a method of computing the linear complexity of a popular family of cryptographic sequences, the so-called generalized sequences. Such a family is generated by means of the irregular decimation of a single Pseudo Noise sequence (PN-sequence). The computation method is based on the comparison of the PN-sequence with shifted versions of itself. The concept of linear recurrence relationship and the rows of the Sierpinski triangle play a leading part in this computation.
In this paper, firstly we extend the polynomial quotient modulo an odd prime p to its general case with modulo p(r) and r >= 1. From the new quotient proposed, we define a class of p(r+1)-periodic binary threshold ...
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In this paper, firstly we extend the polynomial quotient modulo an odd prime p to its general case with modulo p(r) and r >= 1. From the new quotient proposed, we define a class of p(r+1)-periodic binary threshold sequences. Then combining the Legendre symbol and Euler quotient modulo pr together, with the condition of 2(p-1) not equivalent to 1 (mod p(2)), we present exact values of the linear complexity for p equivalent to +/- 3 (mod 8), and all the possible values of the linear complexity for p equivalent to +/- 1 (mod 8). The linear complexity is very close to the period and is of desired value for cryptographic purpose. Our results extend the linear complexity results of the corresponding p(2)-periodic binary sequences in earlier work.
Nowadays, the necessity of electronic information increases rapidly. As a consequence, often, that information needs to be shared among mutually distrustful parties. In this area, private set intersection (PSI) and it...
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Nowadays, the necessity of electronic information increases rapidly. As a consequence, often, that information needs to be shared among mutually distrustful parties. In this area, private set intersection (PSI) and its variants play an important role when the participants wish to do secret operations on their input sets. Unlike the most modern public key cryptosystems relying on number theoretic problems, lattice-based cryptographic constructions provide security in the presence of a quantum computer. Consequently, developing PSI and its variants using lattice based cryptosystem becomes an interesting direction for research. This study presents thefirst size-hiding post quantumPSI cardinality (PSI-CA) protocol whose complexity islinearin the size of the sets of the participants. The authors use space-efficient probabilistic data structure (Bloom filter) as its building block. Further, they extend the authors' PSI-CA to its authorised version, i.e. authorised PSI-CA. Security for both of them is achieved in the standard model based on the hardness of the decisional learning with errors problem.
Low-rankness has been widely observed in real world data and there is often a need to recover low-rank matrices in many machine learning and data mining problems. Robust principal component analysis (RPCA) has been us...
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Low-rankness has been widely observed in real world data and there is often a need to recover low-rank matrices in many machine learning and data mining problems. Robust principal component analysis (RPCA) has been used for such problems by separating the data into a low-rank and a sparse part. The convex approach to RPCA has been well studied due to its elegant properties in theory and many extensions have been developed. However, the state-of-the-art algorithms for the convex approach and their extensions are usually expensive in complexity due to the need for solving singular value decomposition (SVD) of large matrices. In this paper, we propose a novel RPCA model based on matrix tri-factorization, which only needs the computation of SVDs for very small matrices. Thus, this approach reduces the complexity of RPCA to be linear and makes it fully scalable. It also overcomes the drawback of the state-of-the-art scalable approach such as AltProj, which requires the precise knowledge of the true rank of the low-rank component. As a result, our method is about 4 times faster than AltProj. Our method can be used as a light-weight, scalable tool for RPCA in the absence of the precise value of the true rank. (C) 2019 Elsevier Inc. All rights reserved.
For an odd prime p and positive integers r,d such that 0r,a generic construction of dary sequence based on Euler quotients is presented in this *** with the known construction,in which the support set of the sequence ...
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For an odd prime p and positive integers r,d such that 0r,a generic construction of dary sequence based on Euler quotients is presented in this *** with the known construction,in which the support set of the sequence is fixed and d is usually required to be a prime,the support set of the proposed sequence is flexible and d could be any positive integer less then prin our ***,the linear complexity of the proposed sequence over prime field GF(q)with the assumption of qp-1■ mod p2is *** algorithm of computing the linear complexity of the sequence is also *** results indicate that,with some constrains on the support set,the new sequences possess large linear complexities.
Several classes of quaternary sequences of even period with optimal autocorrelation have been constructed by Su et al. based on interleaving certain kinds of binary sequences of odd period, i.e. Legendre sequence, twi...
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Several classes of quaternary sequences of even period with optimal autocorrelation have been constructed by Su et al. based on interleaving certain kinds of binary sequences of odd period, i.e. Legendre sequence, twin-prime sequence and generalized GMW sequence. In this correspondence, the exact values of linear complexity over finite fieldF4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb {F}_{4}$\end{document}and Galois ringDOUBLE-STRUCK CAPITAL Z4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb {Z}_{4}$\end{document}of the quaternary sequences are derived, respectively.
The linear complexity of a sequence is an important parameter for many applications, especially those related to information security, and hardware implementation. It is desirable to develop a corresponding measure an...
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The linear complexity of a sequence is an important parameter for many applications, especially those related to information security, and hardware implementation. It is desirable to develop a corresponding measure and theory for multidimensional arrays that are consistent with those of sequences. In this paper we use Grobner bases to develop a theory for analyzing the multidimensional linear complexity of general periodic arrays. We also analyze arrays constructed using the method of composition and establish tight bounds for their multidimensional linear complexity.
The linear complexity and the error linear complexity are two important security measures for stream ciphers. We construct periodic sequences from function fields and show that the error linear complexity of these per...
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The linear complexity and the error linear complexity are two important security measures for stream ciphers. We construct periodic sequences from function fields and show that the error linear complexity of these periodic sequences is large. We also give a lower bound for the error linear complexity of a class of nonperiodic sequences.
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