scholarly journals DIVERSITY AES IN MIXCOLUMNS STEP WITH 8X8 CIRCULANT MATRIX

2021 ◽  
Vol 8 (9) ◽  
pp. 19-35
Author(s):  
Yan-Wen Chen ◽  
Jeng-Jung Wang ◽  
Yan-Haw Chen ◽  
Chong-Dao Lee
Keyword(s):  
Embedded Systems ◽  
Efficient Method ◽  
Matrix Multiplication ◽  
Circulant Matrix ◽  
Circulant Matrices ◽  
Matrix Operation ◽  
Branch Number ◽  
Involutory Matrix ◽  
Software Implementations ◽  
Encryption Decryption

In AES MixColumns operation, the branch number of circulant matrix is raised from 5 to 9 with 8´8 circulant matrices that can be enhancing the diffusion power. An efficient method to compute the circulant matrices in AES MixColumns transformation for speeding encryption is presented. Utilizing 8´8 involutory matrix multiplication is required 64 multiplications and 56 additions in in AES Mix-Columns transformation. We proposed the method with diversity 8´8 circulant matrices is only needed 19 multiplications and 57 additions. It is not only to encryption operations but also to decryption operations. Therefore, 8´8 circlant matrix operation with AES key sizes of 128bits, 192bits, and 256 bits are above 29.1%, 29.3%, and 29.8% faster than using 4´4 involutory matrix operation (16 multiplications, 12 additions), respectively. 8´8 circulant matrix encryption/decryption speed is above 78% faster than 8´8 involutory matrix operation. Ultimately, the proposed method for evaluating matrix multiplication can be made regular, simple and suitable for software implementations on embedded systems.

scholarly journals Accelerating Deep Neural Networks by Combining Block-Circulant Matrices and Low-Precision Weights

Electronics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 78 ◽  
Author(s):  
Zidi Qin ◽  
Di Zhu ◽  
Xingwei Zhu ◽  
Xuan Chen ◽  
Yinghuan Shi ◽  
...  
Keyword(s):  
Neural Networks ◽  
Deep Neural Networks ◽  
Circulant Matrix ◽  
Circulant Matrices ◽  
Matrix Vector Multiplication ◽  
Processing Power ◽  
Measurement Results ◽  
Block Circulant Matrix ◽  
Storage Complexity ◽  
Fully Connected

As a key ingredient of deep neural networks (DNNs), fully-connected (FC) layers are widely used in various artificial intelligence applications. However, there are many parameters in FC layers, so the efficient process of FC layers is restricted by memory bandwidth. In this paper, we propose a compression approach combining block-circulant matrix-based weight representation and power-of-two quantization. Applying block-circulant matrices in FC layers can reduce the storage complexity from O ( k 2 ) to O ( k ) . By quantizing the weights into integer powers of two, the multiplications in the reference can be replaced by shift and add operations. The memory usages of models for MNIST, CIFAR-10 and ImageNet can be compressed by 171 × , 2731 × and 128 × with minimal accuracy loss, respectively. A configurable parallel hardware architecture is then proposed for processing the compressed FC layers efficiently. Without multipliers, a block matrix-vector multiplication module (B-MV) is used as the computing kernel. The architecture is flexible to support FC layers of various compression ratios with small footprint. Simultaneously, the memory access can be significantly reduced by using the configurable architecture. Measurement results show that the accelerator has a processing power of 409.6 GOPS, and achieves 5.3 TOPS/W energy efficiency at 800 MHz.

scholarly journals On the Spectrum and Spectral Norms of r-Circulant Matrices with Generalized k-Horadam Numbers Entries

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Lele Liu
Keyword(s):  
Explicit Formula ◽  
Circulant Matrix ◽  
Circulant Matrices ◽  
Sufficient Condition ◽  
Abel Transformation

This work is concerned with the spectrum and spectral norms of r-circulant matrices with generalized k-Horadam numbers entries. By using Abel transformation and some identities we obtain an explicit formula for the eigenvalues of them. In addition, a sufficient condition for an r-circulant matrix to be normal is presented. Based on the results we obtain the precise value for spectral norms of normal r-circulant matrix with generalized k-Horadam numbers, which generalize and improve the known results.

A Neuron Library for Rapid Realization of Artificial Neural Networks on FPGA: A Case Study of Rössler Chaotic System

2016 ◽  
Vol 26 (01) ◽  
pp. 1750015 ◽  
Author(s):  
İsmail Koyuncu ◽  
İbrahim Şahin ◽  
Clay Gloster ◽  
Namık Kemal Sarıtekin
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Embedded Systems ◽  
Neural Cells ◽  
Activation Functions ◽  
Design Time ◽  
Software Implementations ◽  
Artificial Neural ◽  
Automation Tools

Artificial neural networks (ANNs) are implemented in hardware when software implementations are inadequate in terms of performance. Implementing an ANN as hardware without using design automation tools is a time consuming process. On the other hand, this process can be automated using pre-designed neurons. Thus, in this work, several artificial neural cells were designed and implemented to form a library of neurons for rapid realization of ANNs on FPGA-based embedded systems. The library contains a total of 60 different neurons, two-, four- and six-input biased and non-biased, with each having 10 different activation functions. The neurons are highly pipelined and were designed to be connected to each other like Lego pieces. Chip statistics of the neurons showed that depending on the type of the neuron, about 25 selected neurons can be fit in to the smallest Virtex-6 chip and an ANN formed using the neurons can be clocked up to 576.89[Formula: see text]MHz. ANN based Rössler system was constructed to show the effectiveness of using neurons in rapid realization of ANNs on embedded systems. Our experiments with the neurons showed that using these neurons, ANNs can rapidly be implemented as hardware and design time can significantly be reduced.

scholarly journals The Determinants, Inverses, Norm, and Spread of Skew Circulant Type Matrices Involving Any Continuous Lucas Numbers

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Jin-jiang Yao ◽  
Zhao-lin Jiang
Keyword(s):  
Circulant Matrix ◽  
Circulant Matrices ◽  
Lucas Numbers ◽  
Transformation Matrices ◽  
Skew Circulant ◽  
The Relationship

We consider the skew circulant and skew left circulant matrices with any continuous Lucas numbers. Firstly, we discuss the invertibility of the skew circulant matrices and present the determinant and the inverse matrices by constructing the transformation matrices. Furthermore, the invertibility of the skew left circulant matrices is also discussed. We obtain the determinants and the inverse matrices of the skew left circulant matrices by utilizing the relationship between skew left circulant matrices and skew circulant matrix, respectively. Finally, the four kinds of norms and bounds for the spread of these matrices are given, respectively.

scholarly journals Synthetic direct demodulation method and its applications in Insight-HXMT data analysis

2018 ◽  
Vol 620 ◽  
pp. A151 ◽  
Author(s):  
Zhuoxi Huo ◽  
Yang Zhang
Keyword(s):  
Data Analysis ◽  
Sparse Representation ◽  
Matrix Multiplication ◽  
Circulant Matrices ◽  
Large Set ◽  
Kernel Matrix ◽  
Statistical Solution ◽  
Modulation Equation ◽  
X Ray ◽  
Direct Demodulation

Aims. A modulation equation relates the observed data to the object where the observation is approximated by a linear system. Reconstructing the object from the observed data is therefore equivalent to solving the modulation equation. In this work we present the synthetic direct demodulation (synDD) method to reduce the dimensionality of a general modulation equation and solve the equation in its sparse representation. Methods. A principal component analysis is used to reduce the dimensionality of the kernel matrix and k-means clustering is applied to its sparse representation in order to decompose the kernel matrix into a weighted sum of a series of circulant matrices. The matrix-vector and matrix-matrix multiplication complexities are therefore reduced from polynomial time to linear-logarithmic time. A general statistical solution of the modulation equation in sparse representation is derived. Several data-analysis pipelines are designed for the Hard X-ray modulation Telescope (Insight-HXMT) based on the synDD method. Results. In this approach, a large set of data originating from the same object but sampled irregularly and/or observed with different instruments in multiple epochs can be reduced simultaneously in a synthetic observation model. We suggest using the proposed synDD method in Insight-HXMT data analysis especially for the detection of X-ray transients and monitoring time-varying objects with scanning observations.

scholarly journals A New Method of Matrix Decomposition to Get the Determinants and Inverses of r -Circulant Matrices with Fibonacci and Lucas Numbers

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Jiangming Ma ◽  
Tao Qiu ◽  
Chengyuan He
Keyword(s):  
Fibonacci Numbers ◽  
Matrix Decomposition ◽  
Circulant Matrix ◽  
New Method ◽  
Circulant Matrices ◽  
Computational Time ◽  
Lucas Numbers ◽  
Fibonacci And Lucas Numbers

We use a new method of matrix decomposition for r -circulant matrix to get the determinants of A n = Circ r F 1 , F 2 , … , F n and B n = Circ r L 1 , L 2 , … , L n , where F n is the Fibonacci numbers and L n is the Lucas numbers. Based on these determinants and the nonsingular conditions, inverse matrices are derived. The expressions of the determinants and inverse matrices are represented by Fibonacci and Lucas Numbers. In this study, the formulas of determinants and inverse matrices are much simpler and concise for programming and reduce the computational time.

scholarly journals On the circulant matrices with Ducci sequences and Fibonacci numbers

Filomat ◽  
2018 ◽  
Vol 32 (15) ◽  
pp. 5501-5508
Author(s):  
Süleyman Solak ◽  
Mustafa Bahşi ◽  
Osman Kan
Keyword(s):  
Fibonacci Numbers ◽  
Circulant Matrix ◽  
Circulant Matrices

A Ducci sequence generated by A = (a1,a2,...,an)? Zn is the sequence {A,DA,D2A,...} where the Ducci map D : Zn ? Zn is defined by D(A) = D(a1, a2,...,an) = (|a2-a1|, |a3-a2|,..., |an-an-1|, |an-a1|). In this study, we examine some properties of the matrices Cn, DCn, D2Cn; where Cn =Circ(c0,c1,..., cn-1) is a circulant matrix whose entries consist of Fibonacci numbers.

Sign in / Sign up

Export Citation Format

Share Document