A General Algorithm for Biorthogonal Functions and Performance Analysis of Biorthogonal Scramble Modulation System

Applying the theorems of Mobius inverse and Dirichlet inverse, a general algorithm to obtain biorthogonal functions based on generalized Fourier series analysis is introduced. In the algorithm, the orthogonal function can be not only Fourier or Legendre series, but also can be any one of all orthogonal function systems. These kinds of biorthogonal function sets are used as scramble signals to construct biorthogonal scramble modulation (BOSM) wireless transmission systems. In a BOSM system, the transmitted signal has significant security performance. Several different BOSM and orthogonal systems are compared on aspects of BER performance and spectrum efficiency, simulation results show that the BOSM systems based on Chebyshev polynomial and Legendre polynomial are better than BOSM system based on Fourier series, also better than orthogonal MCM and OFDM systems.

Double quantum images encryption scheme based on chaotic system

This paper explores a double quantum images representation(DNEQR)model that allows for simultaneous storage of two digital images in a quantum superposition state.Additionally,a new type of two-dimensional hyperchaotic system based on sine and logistic maps is investigated,offering a wider parameter space and better chaotic behavior compared to the sine and logistic maps.Based on the DNEQR model and the hyperchaotic system,a double quantum images encryption algorithm is proposed.Firstly,two classical plaintext images are transformed into quantum states using the DNEQR model.Then,the proposed hyperchaotic system is employed to iteratively generate pseudo-random sequences.These chaotic sequences are utilized to perform pixel value and position operations on the quantum image,resulting in changes to both pixel values and positions.Finally,the ciphertext image can be obtained by qubit-level diffusion using two XOR operations between the position-permutated image and the pseudo-random sequences.The corresponding quantum circuits are also given.Experimental results demonstrate that the proposed scheme ensures the security of the images during transmission,improves the encryption efficiency,and enhances anti-interference and anti-attack capabilities.

A color image encryption scheme based on a 2D coupled chaotic system and diagonal scrambling algorithm

A novel color image encryption scheme is developed to enhance the security of encryption without increasing the complexity. Firstly, the plain color image is decomposed into three grayscale plain images, which are converted into the frequency domain coefficient matrices(FDCM) with discrete cosine transform(DCT) operation. After that, a twodimensional(2D) coupled chaotic system is developed and used to generate one group of embedded matrices and another group of encryption matrices, respectively. The embedded matrices are integrated with the FDCM to fulfill the frequency domain encryption, and then the inverse DCT processing is implemented to recover the spatial domain signal. Eventually,under the function of the encryption matrices and the proposed diagonal scrambling algorithm, the final color ciphertext is obtained. The experimental results show that the proposed method can not only ensure efficient encryption but also satisfy various sizes of image encryption. Besides, it has better performance than other similar techniques in statistical feature analysis, such as key space, key sensitivity, anti-differential attack, information entropy, noise attack, etc.

Image encryption algorithm based on multiple chaotic systems and improved Joseph block scrambling

With the rapid development of digital information technology,images are increasingly used in various fields.To ensure the security of image data,prevent unauthorized tampering and leakage,maintain personal privacy,and protect intellectual property rights,this study proposes an innovative color image encryption algorithm.Initially,the Mersenne Twister algorithm is utilized to generate high-quality pseudo-random numbers,establishing a robust basis for subsequent operations.Subsequently,two distinct chaotic systems,the autonomous non-Hamiltonian chaotic system and the tentlogistic-cosine chaotic mapping,are employed to produce chaotic random sequences.These chaotic sequences are used to control the encoding and decoding process of the DNA,effectively scrambling the image pixels.Furthermore,the complexity of the encryption process is enhanced through improved Joseph block scrambling.Thorough experimental verification,research,and analysis,the average value of the information entropy test data reaches as high as 7.999.Additionally,the average value of the number of pixels change rate(NPCR)test data is 99.6101%,which closely approaches the ideal value of 99.6094%.This algorithm not only guarantees image quality but also substantially raises the difficulty of decryption.

Remote sensing image encryption algorithm based on novel hyperchaos and an elliptic curve cryptosystem

Remote sensing images carry crucial ground information,often involving the spatial distribution and spatiotemporal changes of surface elements.To safeguard this sensitive data,image encryption technology is essential.In this paper,a novel Fibonacci sine exponential map is designed,the hyperchaotic performance of which is particularly suitable for image encryption algorithms.An encryption algorithm tailored for handling the multi-band attributes of remote sensing images is proposed.The algorithm combines a three-dimensional synchronized scrambled diffusion operation with chaos to efficiently encrypt multiple images.Moreover,the keys are processed using an elliptic curve cryptosystem,eliminating the need for an additional channel to transmit the keys,thus enhancing security.Experimental results and algorithm analysis demonstrate that the algorithm offers strong security and high efficiency,making it suitable for remote sensing image encryption tasks.

Dynamics of Non-Markovianity, Quantum Correlations and Information Scrambling of Three Qubits Systems Interacting via Rashba Interaction

The behavior of the quantum correlations, information scrambling and the non-Markovianity of three entangling qubits systems via Rashba is discussed. The results showed that, the three physical quantities oscillate between their upper and lower bounds, where the number of oscillations increases as the Rashba interaction strength increases. The exchanging rate of these three quantities depends on the Rashba strength, and whether the entangled state is generated via direct/indirect interaction. Moreover, the coherence parameter can be used as a control parameter to maximize or minimize the three physical quantities.

Severity Based Light-Weight Encryption Model for Secure Medical Information System

As the amount of medical images transmitted over networks and kept on online servers continues to rise,the need to protect those images digitally is becoming increasingly important.However,due to the massive amounts of multimedia and medical pictures being exchanged,low computational complexity techniques have been developed.Most commonly used algorithms offer very little security and require a great deal of communication,all of which add to the high processing costs associated with using them.First,a deep learning classifier is used to classify records according to the degree of concealment they require.Medical images that aren’t needed can be saved by using this method,which cuts down on security costs.Encryption is one of the most effective methods for protecting medical images after this step.Confusion and dispersion are two fundamental encryption processes.A new encryption algorithm for very sensitive data is developed in this study.Picture splitting with image blocks is nowdeveloped by using Zigzag patterns,rotation of the image blocks,and random permutation for scrambling the blocks.After that,this research suggests a Region of Interest(ROI)technique based on selective picture encryption.For the first step,we use an active contour picture segmentation to separate the ROI from the Region of Background(ROB).Permutation and diffusion are then carried out using a Hilbert curve and a Skew Tent map.Once all of the blocks have been encrypted,they are combined to create encrypted images.The investigational analysis is carried out to test the competence of the projected ideal with existing techniques.

Video Transmission Secrecy Improvement Based on Fractional Order Hyper Chaotic System

In the Digital World scenario,the confidentiality of information in video transmission plays an important role.Chaotic systems have been shown to be effective for video signal encryption.To improve video transmission secrecy,compressive encryption method is proposed to accomplish compression and encryption based on fractional order hyper chaotic system that incorporates Compressive Sensing(CS),pixel level,bit level scrambling and nucleotide Sequences operations.The measurement matrix generates by the fractional order hyper chaotic system strengthens the efficiency of the encryption process.To avoid plain text attack,the CS measurement is scrambled to its pixel level,bit level scrambling decreases the similarity between the adjacent measurements and the nucleotide sequence operations are done on the scrambled bits,increasing the encryption.Two stages are comprised in the reconstruction technique,the first stage uses the intra-frame similarity and offers robust preliminary retrieval for each frame,and the second stage iteratively improves the efficiency of reconstruction by integrating inter frame Multi Hypothesis(MH)estimation and weighted residual sparsity modeling.In each iteration,the residual coefficient weights are modified using a mathematical approach based on the MH predictions,and the Split Bregman iteration algorithm is defined to resolve weighted l1 regularization.Experimental findings show that the proposed algorithm provides good compression of video coupled with an efficient encryption method that is resistant to multiple attacks.

Distinction of self-synchronous scrambled linear blockcodes based on multi-fractal spectrum

This study proposes a novel multi-fractal spectrumbasedapproach to distinguish linear block codes from its selfsynchronousscrambled codes. Given that the linear block codeand self-synchronous scrambled linear block code share the propertyof linear correlation, the existing linear correlation-basedidentification method is invalid for this case. This drawback can becircumvented by introducing a novel multi-fractal spectrum-basedmethod. Simulation results show that the new method has highrobustness and under the same conditions of bit error, the lowerthe code rate, the higher the recognition rate. Thus, the methodhas significant potential for future application in engineering.

Parallel Techniques for Frame Synchronous Scrambler

In high speed transmission system such as SDH,parallel scrambling technique is re-quired.This paper presents a method of expanding matrix,which makes the traditional ma-trix method capable of realizing parallel scramblers of any size.A novel method called delayoperator method is also described in this paper.The 8-bit parallel scrambling circuitry ofSDH has been realized with the two methods.

Multispectral image compression and encryption method based on tensor decomposition in wavelet domain

Multispectral image compression and encryption algorithms commonly suffer from issues such as low compression efficiency,lack of synchronization between the compression and encryption proces-ses,and degradation of intrinsic image structure.A novel approach is proposed to address these is-sues.Firstly,a chaotic sequence is generated using the Lorenz three-dimensional chaotic mapping to initiate the encryption process,which is XORed with each spectral band of the multispectral image to complete the initial encryption of the image.Then,a two-dimensional lifting 9/7 wavelet transform is applied to the processed image.Next,a key-sensitive Arnold scrambling technique is employed on the resulting low-frequency image.It effectively eliminates spatial redundancy in the multispectral image while enhancing the encryption process.To optimize the compression and encryption processes further,fast Tucker decomposition is applied to the wavelet sub-band tensor.It effectively removes both spectral redundancy and residual spatial redundancy in the multispectral image.Finally,the core tensor and pattern matrix obtained from the decomposition are subjected to entropy encoding,and real-time chaotic encryption is implemented during the encoding process,effectively integrating compression and encryption.The results show that the proposed algorithm is suitable for occasions with high requirements for compression and encryption,and it provides valuable insights for the de-velopment of compression and encryption in multispectral field.

Contourlet watermarking algorithm based on Arnold scrambling and singular value decomposition

A new digital watermarking algorithm based on the contourlet transform is proposed to improve the robustness and anti-attack performances of digital watermarking. The algorithm uses the Arnold scrambling technique and the singular value decomposition （SVD） scheme. The Arnold scrambling technique is used to preprocess the watermark, and the SVD scheme is used to find the best suitable hiding points. After the contourlet transform of the carrier image, intermediate frequency sub-bands are decomposed to obtain the singularity values. Then the watermark bits scrambled in the Arnold rules are dispersedly embedded into the selected SVD points. Finally, the inverse contourlet transform is applied to obtain the carrier image with the watermark. In the extraction part, the watermark can be extracted by the semi-blind watermark extracting algorithm. Simulation results show that the proposed algorithm has better hiding and robustness performances than the traditional contourlet watermarking algorithm and the contourlet watermarking algorithm with SVD. Meanwhile, it has good robustness performances when the embedded watermark is attacked by Gaussian noise, salt- and-pepper noise, multiplicative noise, image scaling and image cutting attacks, etc. while security is ensured.

关于两种混沌映射的有限乘积性质

首先在一般度量空间上给出有限积映射是Li-Yorke混沌的一个判据,并且用反例展示:当有限积映射是Li-Yorke混沌时,未必一定存在因子映射是Li-Yorke混沌的.然后,利用上述判据,在[0,1]N上证明有限积映射有不可数scrsmbled集的一个充要条件.进而,推出关于有限积映射为Li-Yorke混沌的一组等价刻画.最后指出:Devaney混沌的有限乘积性质与Li-Yorke混沌的情形恰好相反,即有限积映射是Devaney混沌的,它的每个因子映射必然都是Devaney混沌的,并且,反之则不然.

本原有向图D_(n,q,s)的scrambling指数

设n,q,s是正整数,满足1≤s<q≤n,g.c.d.(q,s)=1,且q+s≥n+1.定义有向图D n,q,s=(V,E),其中V={1,2,…,n},E={(i,i+1)1≤i≤n-1}∪{(s,1),(n,n-q+1)}.显然,D n,q,s是本原有向图,且是一类重要的极图.运用了数论和图论的方法得到了Dn,q,s的scrambling指数,根据本原有向图D的本原指数exp(D)与scrambling指数k(D)的已知结论,猜想lim n→∞k(D)exp(D)=1/2.

半群作用Li-Yorke对的存在性

设X为紧度量空间,T为半群,本文研究了动力系统(X,T)上Li-Yorke对的存在性问题,证明了当(X,T)拓扑可迁且包含周期点时,在(X,T)上存在无限scrambled集.另外,列举了一些不包含Li-Yorke对的动力系统.

一类特殊本原有向图的广义competiton指数

在2010年,Hwa Kyung Kim和Sung Gi Park共同提出了本原有向图的广义com-petiton指数这一概念.文章考虑了一类特殊本原有向图的广义competiton指数,它含有t个2长圈和一个n-t长圈,n与t的奇偶性不同,其中1≤t≤n-3,n≥4,给出了该类本原有向图的广义competiton指数.

几类本原有向图Scrambling指数极图的广义Competition指数

设D为n阶本原有向图,对于D中的每一对顶点x,y,存在正整数m,1≤m≤n,在D中总能找到m个不同的顶点v1,v2,…,vm,使得x和y到vi(1≤i≤m)都存在k长的途径,上述k中的最小者称为D的广义Competition指数(m-Competition指数).广义Competition指数是本原指数和Scrambling指数的推广.采用图论与组合矩阵论的方法,对几类本原有向图Scrambling指数极图的广义Competition指数进行研究,给出了这几类极图的广义Competition指数.

本原θ-图与本原广义θ-图的Scrambling指数

设D是本原有向图,存在正整数k,对任意一对顶点x,y,一定存在一个顶点w,使得x到y与y到x皆有k长的途径,这样的正整数中的最小者称为D的Scrambling指数.对本原θ-图与本原广义θ-图的Scrambling指数进行了研究.采用图论与组合矩阵论的方法,得到了本原θ-图与本原广义θ-图的Scrambling指数的上界,并且给出了一类Scrambling指数达到上界的本原θ-图与本原广义θ-图.

本原有向图的scrambling指数和m-competition指数

分别研究了一类仅含三个圈本原有向图的scrambling指数和另一类仅含两个圈本原有向图的mcompetition指数.利用图论理论,通过分析本原有向图D1与本原有向图Dn-21之间的关系,本原有向图D2与本原有向图Dn-32,Dn-42之间的关系,结合本原指数,scrambling指数和m-competition指数的关系,进而得到了一类含三个圈的本原有向图D1的scrambling指数的具体值,并得到了另一类仅含两个圈的本原有向图D2的m-competition指数的具体值.