Permutation Step Research Articles

Color image encryption by a non-chain Galois ring extension

The S-box is a vital component for producing nonlinearity in a block cipher. Seldom this component is constructed through finite fields; however, sometimes Galois rings are used for its construction. In this work, we utilize the extended Galois ring to construct a Substitution box (S-box) over the ring The designed S-box is generated by multiple elements and thus exhibits a high level of confusion compared to typical S-boxes. An encrypted color image is compared to existing encrypted S-box images to investigate their effects. First, we separate the distinct channels from a digital image and create 256-order matrices with 16-bit entries for each channel. We then apply the designed image encryption algorithm to these matrices. For the permutation step, we use the 1-dimensional logistic map to generate the key. Then, we apply the exclusive-or operation to all three layers of the image using the key. Finally, concatenate all these layers to create the encrypted image. The result is the proposal of a new RGB image encryption technique. The proposed encryption technique can replace several image encryption techniques that rely on S-boxes. In general, this technique aims to achieve optimal values.

Hybrid Encryption Algorithm Based on Gray Curve and Josephus Permutation.

This paper proposes a new image encryption algorithm based on chaos map systems, hash algorithm, and Josephus permutation. The algorithm consists of chaos initialization, pixel position permutation, and pixel information diffusion. The algorithm's initialization is generated by the original image, which has a high sensitivity to the initial value. The permutation step length is composed of Josephus permutation and gray curve permutation, which completely disturbs the pixel distribution. The diffusion process is composed of cross operation and ciphertext feedback, which breaks the strong correlation between pixels. The simulation results of the encryption algorithm are used to analyze its information entropy, the correlation between elements, and other indicators. The ciphertext image is attacked in several ways, and we analyzed its defense ability. Simulation results show that the algorithm can effectively encrypt image information and has a good defense against various attacks.

A Novel and Fast Encryption System Based on Improved Josephus Scrambling and Chaotic Mapping.

To address the shortcomings of weak confusion and high time complexity of the existing permutation algorithms, including the traditional Josephus ring permutation (TJRP), an improved Josephus ring-based permutation (IJRBP) algorithm is developed. The proposed IJRBP replaces the remove operation used in TJRP with the position exchange operation and employs random permutation steps instead of fixed steps, which can offer a better scrambling effect and a higher permutation efficiency, compared with various scrambling methods. Then, a new encryption algorithm based on the IJRBP and chaotic system is developed. In our scheme, the plaintext feature parameter, which is related to the plaintext and a random sequence generated by a chaotic system, is used as the shift step of the circular shift operation to generate the diffusion matrix, which means that a minor change in the source image will generate a totally different encrypted image. Such a strategy strikes a balance between plaintext sensitivity and ciphertext sensitivity to obtain the ability to resist chosen-plaintext attacks (CPAs) and the high robustness of resisting noise attacks and data loss. Simulation results demonstrate that the proposed image cryptosystem has the advantages of great encryption efficiency and the ability to resist various common attacks.

Secure network coding for data encoded using subspace codes

Subspace coding is a solution to the error-control problem in noncoherent networks using Random Linear Network Coding (RLNC) as a transmission mechanism. In this paper, we propose a secure error-correction scheme based on a codeword selection method called the Subspace Coding Strategy (SCS) along with a permutation step, as a possible solution for secure transmission of data encoded using subspace codes. Our scheme also makes use of the correction capability of the used code to induce correctable random errors to further mislead the wiretapper. Numerical results and comparative analysis with other schemes from the literature are presented as a verification of the impact of the proposed scheme on transmission security.

High throughput resource efficient reconfigurable interleaver for MIMO WLAN application.

Demand for high-speed wireless broadband internet service is ever increasing. Multiple-input-multiple-output (MIMO) Wireless LAN (WLAN) is becoming a promising solution for such high-speed internet service requirements. This paper proposes a novel algorithm to efficiently model the address generation circuitry of the MIMO WLAN interleaver. The interleaver used in the MIMO WLAN transceiver has three permutation steps involving floor function whose hardware implementation is the most challenging task due to the absence of corresponding digital hardware. In this work, we propose an algorithm with a mathematical background for the address generator, eliminating the need for floor function. The algorithm is converted into digital hardware for implementation on the reconfigurable FPGA platform. Hardware structure for the complete interleaver, including the read address generator and memory module, is designed and modeled in VHDL using Xilinx Integrated Software Environment (ISE) utilizing embedded memory and DSP blocks of Spartan 6 FPGA. The functionality of the proposed algorithm is verified through exhaustive software simulation using ModelSim software. Hardware testing is carried out on Zynq 7000 FPGA using Virtual Input Output (VIO) and Integrated Logic Analyzer (ILA) core. Comparisons with few recent similar works, including the conventional Look-Up Table (LUT) based technique, show the superiority of our proposed design in terms of maximum improvement in operating frequency by 196.83%, maximum reduction in power consumption by 74.27%, and reduction of memory occupancy by 88.9%. In the case of throughput, our design can deliver 8.35 times higher compared to IEEE 802.11n requirement.

A novel randomized bit-level two-dimensional hyperchaotic image encryption algorithm

In this paper, we designed a new hyperchaotic two-dimensional map with wide distribution and two large positive Lyapunov exponents. Then, we used it to construct a new randomized bit-level chaotic image encryption algorithm with the proposed hyperchaotic map as the source of randomization for permutation and diffusion. The input image is randomized by appending an extra random row and an additional random column to it. Then, the whole permutation and diffusion process are randomized by relating the parameters of the hyperchaotic mapping dependent on the hash value of the randomized image. In the permutation step, the randomized image is split into binary images, and then each binary image is randomly and independently permuted. Then, the permuted binary images are combined, and diffusion is applied to each pixel. Various security experiments are designed to assess the performance of the proposed encryption algorithm, including entropy analysis, histogram analysis, key-space analysis, the pixel-level and the bit-level correlation analysis, and differential attacks as well as key-sensitivity and randomization analysis. According to these experiments, the proposed algorithm shows an excellent security performance compared to several recent image encryption algorithms. Moreover, the proposed encryption algorithm is robust against data loss and noise attacks. Finally, the running time of the proposed algorithm is smaller compared to several recent algorithms.

A novel discrete image encryption algorithm based on finite algebraic structures

The arithmetic properties of a finite field have a remarkable impact on the security features of symmetric and asymmetric cryptosystems. Conventionally, in modern symmetric-key cryptosystems, a 256 elements Galois field depending on a single 8 degree primitive irreducible polynomial over ℤ2 is used for designing an S-box, the main nonlinear component in AES. The experience of S-box based image encryption schemes is not appreciable than chaotic systems based methods. In this study, we improve the S-box based image encryption algorithms by the usage of all 16 distinct degree 8 primitive irreducible polynomials over ℤ2 and by introducing a new role of the ring ℤn of integers modulo n in the permutation steps. The strength of this novel 2-algebraic structures based image encryption scheme is evaluated by some statistical analyses and a significant performance level is achieved. A comparison of encryption quality with some of the recent chaos-based image encryption algorithms is given and evidently the newly launched scheme spectacles high performance. Thus this new development in image encryption methods may provide an alternative to chaos dependent image encryption.

New video encryption schemes based on chaotic maps

Two new encryption algorithms for secure video transmission are proposed in this paper. The two algorithms employ different types of chaotic maps to generate the keystream for encrypting the video frames. Both algorithms involve a substitution step and a permutation step to achieve confusion and diffusion requirements. For efficient transmission, the video file is compressed before being encrypted. In the basic implementation of both algorithms, MPEG-2 standard is used for compression. However, the algorithms are shown to be compliant with other compression techniques. In the permutation step, the effect of the block size used in the shuffling process is examined. Smaller blocks result in increasing the processing time, while reducing both the correlation between adjacent pixels and the peak-signal-to noise ratio of an encrypted frame. The use of a Feistel structure is investigated to enhance security and its negative impact on the encryption time is demonstrated. The experimental results of the two proposed schemes confirm that they represent different tradeoffs between security and computational efficiency. Both schemes are sensitive to slight variations in the encryption key as apparent from the obtained differential measures. The conducted comparative study shows the competitiveness of the proposed schemes to existing schemes in literature.

Scale invariant digital image encryption using 3D modular chaotic map

Cryptography techniques are used to preserve the privacy and integrity of image media. Most proposed cryptographic images methods based on chaotic maps are dependent upon image sizes and most of them worked on square images. Tackling this problem, a scale invariant gray level image encryption method is proposed by means of 3D modular chaotic map. Initially, a 2D image with desirable size M × N is converted into a 3D image with m sub-images by size n × n. Optimizing the calculation, the parameters m and n should be appropriately selected. Having diffusion and confusion properties, two steps of 3D substitution and a 3D permutation step are used. In the 3D substitution steps, the pixels value of sub-images will be changed using the XOR operators and the circular shift. In the permutation step the pixels position of sub-images will be changed using 3D modular chaotic map, In this case, the m sub-images are divided into $$ k=\left\lceil \frac{m}{n}\right\rceil $$ equal size windows which each window has n sub-images with size n × n, and the 3D modular chaotic map is performed on any window with independent parameters. Depending upon the value of m, the number of windows is greater than or equal to 1; for k > 1, the last two windows may overlap to perform 3D chaotic map operation. Accelerating the proposed encryption method, the 3D chaotic map operations on windows can be implemented in parallel. The proposed method, in comparison with other methods of image encryption, improves the statistical parameters of cryptographic analysis, key space, and speed.

Treatment Effect Validation via a Permutation Test in Stata

In this paper we describe the testing procedure for assessing the statistical significance of treatment effect under the experimental conditions of baseline imbalance across covariates and attrition from the survey, using the permutation tests proposed by Freedman and Lane (1983) and Romano and Wolf (2016). We discuss the testing procedure for these hypotheses based on a linear regression model and introduce the new Stata command [R] permtest for the implementation of the permutation test in Stata. Moreover, we investigate the finite-sample performance as well as the statistical validity of the test with a Monte Carlo simulation study in which we examine the empirical size and power properties under the conditions of baseline imbalance and attrition for a fixed number of permutation steps.

General Confidentiality and Utility Metrics for Privacy-Preserving Data Publishing Based on the Permutation Model

Anonymization for privacy-preserving data publishing, also known as statistical disclosure control (SDC), can be viewed under the lens of the permutation model. According to this model, any SDC method for individual data records is functionally equivalent to a permutation step plus a noise addition step, where the noise added is marginal, in the sense that it does not alter ranks. Here, we propose metrics to quantify the data confidentiality and utility achieved by SDC methods based on the permutation model. We distinguish two privacy notions: in our work, anonymity refers to subjects and hence mainly to protection against record re-identification, whereas confidentiality refers to the protection afforded to attribute values against attribute disclosure. Thus, our confidentiality metrics are useful even if using a privacy model ensuring an anonymity level ex ante . The utility metric is a general-purpose metric that can be conveniently traded off against the confidentiality metrics, because all of them are bounded between 0 and 1. As an application, we compare the utility-confidentiality trade-offs achieved by several anonymization approaches, including privacy models ( $k$ k -anonymity and $\epsilon$ e -differential privacy) as well as SDC methods (additive noise, multiplicative noise and synthetic data) used without privacy models.

Cache vs. Key-Dependency: Side Channeling an Implementation of Pilsung

Over the past two decades, cache attacks have been identified as a threat to the security of cipher implementations. These attacks recover secret information by combining observations of the victim cache accesses with the knowledge of the internal structure of the cipher. So far, cache attacks have been applied to ciphers that have fixed state transformations, leaving open the question of whether using secret, key-dependent transformations enhances the security against such attacks. In this paper we investigate this question. We look at an implementation of the North Korean cipher Pilsung, as reverse-engineered by Kryptos Logic. Like AES, Pilsung is a permutation-substitution cipher, but unlike AES, both the substitution and the permutation steps in Pilsung depend on the key, and are not known to the attacker. We analyze Pilsung and design a cache-based attack. We improve the state of the art by developing techniques for reversing secret-dependent transformations. Our attack, which requires an average of eight minutes on a typical laptop computer, demonstrates that secret transformations do not necessarily protect ciphers against side channel attacks.

The Effect of Interstitial Nitrogen Addition on the Structural Properties of Supercells of NdFe12-x Ti x

We investigated the effect of nitrogenation on $3 \times 3 \times 2$ supercell structures of NdFe12- x Ti x from $x = 0.028$ to $x = 1.56$ (~0.2Ti at. % to ~12Ti at. %). We used the molecular dynamics and Boltzmann probabilities to permeate titanium into NdFe12- x Ti x across the investigated range, before nitrogenating the minimum energy structures that resulted at each permutation step. By comparison of the nitrogenated and base structures, we found that the cohesive energy gains caused by nitrogenation are mainly due to a large asymmetry introduced into the $c$ lattice parameter and the efficacy of nitrogenation decreases with increasing titanium at. %.

Minimum Breakpoint Set Determination for Directional Overcurrent Relay Coordination in Large-Scale Power Networks via Matrix Computations

Determination of the minimum breakpoint set (MBPS) is essential for optimum coordination of directional protection relays. However, in modern large-scale power networks, this task poses serious difficulties and becomes time consuming. This paper addresses such deficiencies and proposes a numerically efficient algorithm. Despite being derived from graph theory, the proposed algorithm functions via a series of matrix computations, that is, reduction, permutation, and LU factorization of the branch to bus incidence matrix of a given network. At first, parallel branches are united via the reduction step. Then, branches and buses are reset to form spanning trees of the network via the permutation step. Finally, MBPS is determined via the LU factorization step. Experimental results obtained by implementing the proposed algorithm in various test systems are presented to illustrate its computational performance.

197 Functional SNP associated with birth weight in independent populations identified with a permutation step added to GBLUP-GWAS

197 Functional SNP associated with birth weight in independent populations identified with a permutation step added to GBLUP-GWAS

Image encryption using a synchronous permutation-diffusion technique

In the past decade, the interest on digital images security has been increased among scientists. A synchronous permutation and diffusion technique is designed in order to protect gray-level image content while sending it through internet. To implement the proposed method, two-dimensional plain-image is converted to one dimension. Afterward, in order to reduce the sending process time, permutation and diffusion steps for any pixel are performed in the same time. The permutation step uses chaotic map and deoxyribonucleic acid (DNA) to permute a pixel, while diffusion employs DNA sequence and DNA operator to encrypt the pixel. Experimental results and extensive security analyses have been conducted to demonstrate the feasibility and validity of this proposed image encryption method.

Enhanced Audio Cryptosystem Using Multiple Secret Keys and Permutations in Time and Transform Domains

This paper presents an enhanced audio speech cryptosystem based on three enhancements for permutation and substitution of speech segments using multiple secret keys and permutations in time and transform domains. The first enhancement method is based on repeating the first and last permutation steps in both encryption/decryption procedures for several times to enhance the security level. The second and third enhancement methods are based on adding two additional secret keys generated from the original key besides the utilized three keys. This adds another security layer for the modified developed audio cryptosystem. Simulation experiments demonstrated that these modifications enhance the security level and quality for the audio cryptosystem compared with a recent audio cryptosystem.

GSA-Lightning: ultra-fast permutation-based gene set analysis.

The computational speed of many gene set analysis methods can be slow due to the computationally demanding permutation step. This article introduces GSA-Lightning, a fast implementation of permutation-based gene set analysis. GSA-Lightning achieves significant speedup compared with existing methods, particularly when the number of gene sets and permutations are large. The GSA-Lightning R package is available on Github at https://github.com/billyhw/GSALightning and on R Bioconductor. The package also contains a comprehensive user's guide with a step-by-step tutorial vignette. weidong.tian@fudan.edu.cn Supplementary data are available at Bioinformatics online.

이질적인 중도절단분포 하에서 생존분포의 동일성 검정법 비교연구

세 개 이상의 집단에 대한 생존분포의 비교를 위해 가중 로그순위 검정법(Weighted Logrank test)과 그의 특별한 경우인 로그순위 검정법(Logrank test)이 널리 쓰인다. 그러나 이 방법은 근사적인 분포를 이용한 방법이므로 표본 크기가 작은 경우에는 유효하지 못할 수 있으며, 각 집단의 중도절단 분포가 동일하다는 가정 또한 충족되어야 하기 때문에 이 가정이 충족되지 못할 경우에도 검정법의 유효성을 장담할 수 없다. 표본 크기가 작은 경우에 대한 대안으로, 분포에 대한 가정이 없이 관찰된 자료만으로 검정통계량의 분포를 추정하고 그 분포를 이용해 검정하는 순열 검정법(Permutation test)이 제안되었으나, 순열 검정법 또한 각 집단의 중도절단 분포가 동일하다는 가정이 충족되어야 한다. 따라서 순열 검정법을 향상시킨 순열-대치 검정법(Permutation-Imputation test)이 대안이 될 수 있는데, 이는 대치 단계(Imputation step)에서 귀무가설 하에서의 생존확률이 집단에 의존하지 않도록 자료를 조정한 후 순열 검정 단계(Permutation step)를 통해 검정하는 방법이다. 본 논문에서는 근사적 방법, 순열 검정법, 순열-대치 검정법을 로그순위 검정법과 가중 로그순위 검정법의 한 형태인 Prentice-Wilcoxon 검정법에 적용해 각 검정법의 유효성과 검정력을 비교하였다. The Weighted Logrank test and its special case, Logrank test are widely used to compare survival distributions; however, these methods are inappropriate when the sample size is small or censoring distributions are not equal since they use test statistics from approximate distributions. A permutation test can be an alternative for small sample cases; however, this should be used only when censoring distributions are equal. To handle cases with small sample size and unequal censoring distributions, the permutation-imputation method was developed to compare two survival distributions. In this paper, approximate method, permutation method and permutation-imputation method were compared using a Logrank test and Prentice-Wilcoxon test for three or more survival distributions comparison.

Chaos-based image encryption with total shuffling and bidirectional diffusion

This paper proposes a chaos-based image encryption method with permutation–diffusion architecture, in which a spatiotemporal chaotic system modeled by coupled map lattices is used to generate random sequences. In the permutation step, the permutation is generated of the same size as the plain image, which shuffles the positions of image pixels totally. In order to effectively generate this large permutation, we present a fast method to construct permutation by combining several small permutations, where small permutations are directly generated by a chaotic system. In the diffusion step, bidirectional diffusion is used to diffuse each pixel to all other pixels of the image. A key stream buffer is utilized to cache the random numbers generated by the chaotic system, and each pixel is ciphered by a random number chosen from the key stream buffer according to its previous pixel. The experimental results and analysis by using several security measures show that the proposed image encryption scheme has high security and efficiency.