Novel Approach to Data Encryption Based on Matrix Computations

In this paper,we provide a new approach to data encryption using generalized inverses.Encryption is based on the implementation of weighted Moore–Penrose inverse A y MNenxmT over the nx8 constant matrix.The square Hermitian positive definite matrix N8x8 p is the key.The proposed solution represents a very strong key since the number of different variants of positive definite matrices of order 8 is huge.We have provided NIST(National Institute of Standards and Technology)quality assurance tests for a random generated Hermitian matrix(a total of 10 different tests and additional analysis with approximate entropy and random digression).In the additional testing of the quality of the random matrix generated,we can conclude that the results of our analysis satisfy the defined strict requirements.This proposed MP encryption method can be applied effectively in the encryption and decryption of images in multi-party communications.In the experimental part of this paper,we give a comparison of encryption methods between machine learning methods.Machine learning algorithms could be compared by achieved results of classification concentrating on classes.In a comparative analysis,we give results of classifying of advanced encryption standard(AES)algorithm and proposed encryption method based on Moore–Penrose inverse.

MatDEM-fast matrix computing of the discrete element method

Discrete element method can effectively simulate the discontinuity,inhomogeneity and large deformation and failure of rock and soil.Based on the innovative matrix computing of the discrete element method,the highperformance discrete element software MatDEM may handle millions of elements in one computer,and enables the discrete element simulation at the engineering scale.It supports heat calculation,multi-field and fluidsolid coupling numerical simulations.Furthermore,the software integrates pre-processing,solver,postprocessing,and powerful secondary development,allowing recompiling new discrete element software.The basic principles of the DEM,the implement and development of the MatDEM software,and its applications are introduced in this paper.The software and sample source code are available online(http://matdem.com).

Silicon-based optoelectronics for general-purpose matrix computation:a review

Conventional electronic processors,which are the mainstream and almost invincible hardware for computation,are approaching their limits in both computational power and energy efficiency,especially in large-scale matrix computation.By combining electronic,photonic,and optoelectronic devices and circuits together,silicon-based optoelectronic matrix computation has been demonstrating great capabilities and feasibilities.Matrix computation is one of the few general-purpose computations that have the potential to exceed the computation performance of digital logic circuits in energy efficiency,computational power,and latency.Moreover,electronic processors also suffer from the tremendous energy consumption of the digital transceiver circuits during high-capacity data interconnections.We review the recent progress in photonic matrix computation,including matrix-vector multiplication,convolution,and multiply–accumulate operations in artificial neural networks,quantum information processing,combinatorial optimization,and compressed sensing,with particular attention paid to energy consumption.We also summarize the advantages of siliconbased optoelectronic matrix computation in data interconnections and photonic-electronic integration over conventional optical computing processors.Looking toward the future of silicon-based optoelectronic matrix computations,we believe that silicon-based optoelectronics is a promising and comprehensive platform for disruptively improving general-purpose matrix computation performance in the post-Moore’s law era.

Secure outsourcing of large matrix determinant computation

Cloud computing provides the capability to con-nect resource-constrained clients with a centralized and shared pool of resources,such as computational power and storage on demand.Large matrix determinant computation is almost ubiquitous in computer science and requires large-scale data computation.Currently,techniques for securely outsourcing matrix determinant computations to untrusted servers are of utmost importance,and they have practical value as well as theoretical significance for the scientific community.In this study,we propose a secure outsourcing method for large matrix determinant computation.We em-ploy some transformations for privacy protection based on the original matrix,including permutation and mix-row/mix-column operations,before sending the target matrix to the cloud.The results returned from the cloud need to be de-clypled anul verified U ubtainl te cullett delinall.Il1 comparison with previously proposed algorithms,our new al-gorithm achieves a higher security level with greater cloud ef-ficiency.The experimental results demonstrate the efficiency and effectiveness of our algorithm.

On-chip photonic spatial-temporal descrambler

As an indispensable part to compensate for the signal crosstalk in fiber communication systems,conventional digital multi-input multi-output(MIMO)signal processor is facing the challenges of high com-putational complexity,high power consumption and relatively low processing speed.The optical MIMOenables the best use of light and has been proposed to remedy this limitation.However,the currently existing optical MIMO methods are all restricted to the spatial di-mension,while the temporal dimension is neglected.Here,an on-chip spatial-temporal descrambler with four channels were devised and its MIMO functions were experimentally verified simultaneously in both spatial and temporal dimensions.The spatial crosstalk of single-channel descrambler and four-channel descrambler is respectively less than-21 dB and-18 dB,and the time delay is simultaneously com-pensated successfully.Moreover,a more universal model extended to mode-dependent loss and gain(MDL)compensation was further de-veloped,which is capable of being cascaded for the real optical trans-mission system.The first attempt at photonic spatial-temporal de-scrambler enriched the varieties of optical MIMO,and the proposed scheme provided a new opportunity for all-optical MIMO signal pro-cessing.