scholarly journals THE APPLICATION OF ISOMORPHIC MATRIX REPRESENTATIONS FOR MODELING THE PROTOCOL FOR THE FORMATION OF SECRET KEYS-PERMUTATIONS OF HUGE SIZES

2021 ◽  
Vol 295 (2) ◽  
pp. 78-88
Author(s):  
VLADIMIR KRASILENKO ◽  
◽  
NATALIYA YURCHUK ◽  
DIANA NIKITOVICH ◽  
◽  
...  
Keyword(s):  
Permutation Matrix ◽  
Affine Transformations ◽  
Matrix Representations ◽  
Software Module ◽  
Black And White ◽  
Permutation Matrices ◽  
The Matrix ◽  
Secret Keys ◽  
Software Modules ◽  
Fixed Matrix

A The article considers the peculiarities of the application of isomorphic matrix representations for modeling the protocol of matching secret keys-permutations of significant dimension. The situation is considered when for cryptographic transformations of blocks with a length of 256 * 256 bytes, presented in the form of a matrix of a black-and-white image, it is necessary to rearrange all bytes in accordance with the matrix keys. To generate a basic matrix key and the appearance of the components KeyA and KeyB in the format of two black and white images, a software module using engineering mathematical software Mathcad is proposed. Simulations are performed, for example, with sets of fixed matrix representations. The essence of the protocol of coordination of the main matrix of permutations by the parties is considered. Also shown are software modules in Mathcad for accelerated methods that display the procedure of iterative permutations in a permutation matrix isomorphic to the elevation of the permutation matrix to the desired degree with a certain side, corresponding to specific bits of bits or other code representations of selected random numbers. It is demonstrated that the parties receive new permutation matrices after the first step of the protocol, those sent to the other party, and the identical new permutation matrices received by the parties after the second step of the protocol, ie the secret permutation matrix. Similar qualitative cryptographic transformations have been confirmed using the proposed representations of the permutation matrix based on the results of modeling matrix affine-permutation ciphers and multi-step matrix affine-permutation ciphers for different cases when the components of affine transformations are first executed in different sequences. , and then permutation using the permutation matrix, or vice versa. The model experiments performed in the study demonstrated the adequacy of the functioning of the models proposed by the protocol and methods of generating a permutation matrix and demonstrated their advantages.

scholarly journals Permutation Matrices, Their Discrete Derivatives and Extremal Properties

2020 ◽  
Vol 48 (4) ◽  
pp. 719-740
Author(s):  
Richard A. Brualdi ◽  
Geir Dahl
Keyword(s):  
Permutation Matrix ◽  
Permutation Matrices ◽  
Discrete Derivative ◽  
The Relationship ◽  
Derivatives Of ◽  
Extremal Properties

AbstractFor a permutation π, and the corresponding permutation matrix, we introduce the notion of discrete derivative, obtained by taking differences of successive entries in π. We characterize the possible derivatives of permutations, and consider questions for permutations with certain properties satisfied by the derivative. For instance, we consider permutations with distinct derivatives, and the relationship to so-called Costas arrays.

DISCRETE TESTING RESOURCE ALLOCATION IN MODULE TESTING

1999 ◽  
Vol 06 (01) ◽  
pp. 57-64 ◽  
Author(s):  
TETSUO ICHIMORI
Keyword(s):  
Resource Allocation ◽  
Allocation Problem ◽  
Software Module ◽  
Equal Share ◽  
Software Modules

This paper treats an allocation problem of discrete testing resources in module testing where software modules are tested independently. The total amount of discrete testing resources is given beforehand. When an allocation is determined in module testing, each software module defines the share per size. Since discrete resources do not allow each software module to get an equal share per size, there exists a dispersion. The aim of this paper is to find an allocation minimizing the variance of this dispersion.

scholarly journals EXTENSION OF THE POINCARÉ GROUP AND NON-ABELIAN TENSOR GAUGE FIELDS

2010 ◽  
Vol 25 (31) ◽  
pp. 5765-5785 ◽  
Author(s):  
GEORGE SAVVIDY
Keyword(s):  
Gauge Group ◽  
Gauge Transformation ◽  
Space Time ◽  
Gauge Fields ◽  
Poincaré Group ◽  
Matrix Representations ◽  
Poincare Group ◽  
Yang Mills ◽  
The Matrix ◽  
Transversal Plane

In the recently proposed generalization of the Yang–Mills theory, the group of gauge transformation gets essentially enlarged. This enlargement involves a mixture of the internal and space–time symmetries. The resulting group is an extension of the Poincaré group with infinitely many generators which carry internal and space–time indices. The matrix representations of the extended Poincaré generators are expressible in terms of Pauli–Lubanski vector in one case and in terms of its invariant derivative in another. In the later case the generators of the gauge group are transversal to the momentum and are projecting the non-Abelian tensor gauge fields into the transversal plane, keeping only their positively definite spacelike components.

scholarly journals Computing mu-values for Representations of Symmetric Groups in Engineering Systems

2018 ◽  
Vol 11 (3) ◽  
pp. 774-792
Author(s):  
Mutti-Ur Rehman ◽  
M. Fazeel Anwar
Keyword(s):  
Control Systems ◽  
Symmetric Groups ◽  
Singular Values ◽  
Linear Control ◽  
Linear Control Systems ◽  
Complex Numbers ◽  
Engineering Systems ◽  
Matrix Representations ◽  
The Matrix

In this article we consider the matrix representations of finite symmetric groups Sn over the filed of complex numbers. These groups and their representations also appear as symmetries of certain linear control systems [5]. We compute the structure singular values (SSV) of the matrices arising from these representations. The obtained results of SSV are compared with well-known MATLAB routine mussv.

Symmetries of the Degeneracy of the Vertebrate Mitochondrial Genetic Code in the Matrix Form

2010 ◽  
pp. 31-49
Author(s):  
Sergey Petoukhov ◽  
Matthew He
Keyword(s):  
Mathematical Modeling ◽  
Genetic Code ◽  
Matrix Form ◽  
Black And White ◽  
Mitochondrial Genetic Code ◽  
The Matrix

Symmetries of the degeneracy of the vertebrate mitochondrial genetic code in the mosaic matrix form of its presentation are described in this chapter. The initial black-and-white genomatrix of this code is reformed into a new mosaic matrix when internal positions in all triplets are permuted simultaneously. It is revealed unexpectedly that for all six variants of positional permutations in triplets (1-2-3, 2-3-1, 3-1-2, 1-3-2, 2-1-3, 3-2-1) the appropriate genetic matrices possess symmetrical mosaics of the code degeneracy. Moreover the six appropriate mosaic matrices in their binary presentation have the general non-trivial property of their “tetra-reproduction,” which can be utilized in particular for mathematical modeling of the phenomenon of the tetra-division of gametal cells in meiosis. Mutual interchanges of the genetic letters A, C, G, U in the genomatrices lead to new mosaic genomatrices, which possess similar symmetrical and tetra-reproduction properties as well.

scholarly journals Hashing Based Answer Selection

2020 ◽  
Vol 34 (05) ◽  
pp. 9330-9337
Author(s):  
Dong Xu ◽  
Wu-Jun Li
Keyword(s):  
Question Answering ◽  
Matrix Representation ◽  
Matrix Representations ◽  
Binary Matrix ◽  
Large Memory ◽  
The Matrix ◽  
Novel Method ◽  
Online Prediction ◽  
Memory Cost ◽  
Vector Representations

Answer selection is an important subtask of question answering (QA), in which deep models usually achieve better performance than non-deep models. Most deep models adopt question-answer interaction mechanisms, such as attention, to get vector representations for answers. When these interaction based deep models are deployed for online prediction, the representations of all answers need to be recalculated for each question. This procedure is time-consuming for deep models with complex encoders like BERT which usually have better accuracy than simple encoders. One possible solution is to store the matrix representation (encoder output) of each answer in memory to avoid recalculation. But this will bring large memory cost. In this paper, we propose a novel method, called hashing based answer selection (HAS), to tackle this problem. HAS adopts a hashing strategy to learn a binary matrix representation for each answer, which can dramatically reduce the memory cost for storing the matrix representations of answers. Hence, HAS can adopt complex encoders like BERT in the model, but the online prediction of HAS is still fast with a low memory cost. Experimental results on three popular answer selection datasets show that HAS can outperform existing models to achieve state-of-the-art performance.

scholarly journals Bidiagonalization of (k, k + 1)-tridiagonal matrices

2019 ◽  
Vol 7 (1) ◽  
pp. 20-26 ◽  
Author(s):  
S. Takahira ◽  
T. Sogabe ◽  
T.S. Usuda
Keyword(s):  
Tridiagonal Matrix ◽  
Permutation Matrix ◽  
Block Diagonalization ◽  
Tridiagonal Matrices ◽  
The Matrix ◽  
Appl Math ◽  
Diagonalization Algorithm

Abstract In this paper,we present the bidiagonalization of n-by-n (k, k+1)-tridiagonal matriceswhen n < 2k. Moreover,we show that the determinant of an n-by-n (k, k+1)-tridiagonal matrix is the product of the diagonal elements and the eigenvalues of the matrix are the diagonal elements. This paper is related to the fast block diagonalization algorithm using the permutation matrix from [T. Sogabe and M. El-Mikkawy, Appl. Math. Comput., 218, (2011), 2740-2743] and [A. Ohashi, T. Sogabe, and T. S. Usuda, Int. J. Pure and App. Math., 106, (2016), 513-523].

scholarly journals Construction of generalized rotations and quasi-orthogonal matrices

2019 ◽  
Vol 7 (1) ◽  
pp. 107-113
Author(s):  
Luis Verde-Star
Keyword(s):  
Image Processing ◽  
Hadamard Matrices ◽  
Complex Numbers ◽  
Data Communications ◽  
Matrix Representations ◽  
Orthogonal Matrices ◽  
Orthogonal Designs ◽  
The Matrix ◽  
The One

Abstract We propose some methods for the construction of large quasi-orthogonal matrices and generalized rotations that may be used in applications in data communications and image processing. We use certain combinations of constructions by blocks similar to the one used by Sylvester to build Hadamard matrices. The orthogonal designs related with the matrix representations of the complex numbers, the quaternions, and the octonions are used in our construction procedures.

The Design of Embedded System Based on DaVinci DSP6467

2013 ◽  
Vol 416-417 ◽  
pp. 1336-1340
Author(s):  
Dong Tao Ma
Keyword(s):  
Embedded System ◽  
Multimedia System ◽  
Application Framework ◽  
Software Module ◽  
Web Based ◽  
Synchronization Mechanism ◽  
Signal Vidéo ◽  
Software Modules ◽  
Platform Development ◽  
Application Requirements

For application requirements of smart multimedia system, the paper design and implements system application framework and describes the function of each software module in the whole system. After description of the overall framework,paper analyze detailed implementation of several key software modules,that is supports SD and HD video signal, video capture module, object intrusion alarm motion detection module, audio and video multimedia processing synchronization mechanism, and web-based remote control module. And the article describes the main features of the DaVinci technology and DaVinci technology platform development, elaborated the DSP6467 DaVinci platform hardware structure which used in this paper.

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