Permutation Phase Research Articles

An improved Logistic chaotic map and self-adaptive model for image encryption

An image encryption scheme provides the means for securely transmitting images over public channels. In this paper, I proposed an efficient permutation-diffusion image encryption scheme based on an improved Logistic chaotic map (ILCM) and self-adaptive model. The permutation phase permuted the addresses of the image pixel using thefirst chaotic sequence generated by ILCM, created the parameter which was related to the number of 0's in the bit-planes of the plain-image. Since this different plain-image had different parameter for permutation even just only a bit is changed in the plain-image. The diffusion phase then altered the pixel values of the permuted image with combined space-bit-plane exchange and XOR operation with the second chaotic sequence generated by ILCM. Simulations and performance evaluations showed that the ILCM with larger chaotic ranges and better chaotic behaviors compare with the Logistic chaotic map (LCM). Numerical experiments also showed that our proposed self-adaptive method can considerably enhance the cryptosystem resistance against known/chosen-plaintext and differential attacks. Theoretical analysis and computer experiments confirmed that the new algorithm was secure and reliable, with high potential to be adopted for network security and secure communications.

Wiretapping Strategies for Artificial Noise Assisted Communication in MU-MIMO wiretap channel

We investigate the opposite of artificial noise (AN)-assisted communication in multiple-input–multiple-output (MIMO) wiretap channels for the multiuser case by taking the side of the eavesdropper. We first define a framework for an AN-assisted multiuser multiple-input–multiple-output (MU-MIMO) system, for which eavesdropping methods are proposed with and without knowledge of legitimate users’ channel state information (CSI). The proposed method without CSI is based on a modified joint approximate diagonalization of eigen-matrices algorithm, which eliminates permutation indetermination and phase ambiguity, as well as the minimum description length algorithm, which blindly estimates the number of secret data sources. Simulation results show that both proposed methods can intercept information effectively. In addition, the proposed method without legitimate users’ CSI performs well in terms of robustness and computational complexity.

Novel permutation measures for image encryption algorithms

This paper proposes two measures for the evaluation of permutation techniques used in image encryption. First, a general mathematical framework for describing the permutation phase used in image encryption is presented. Using this framework, six different permutation techniques, based on chaotic and non-chaotic generators, are described. The two new measures are, then, introduced to evaluate the effectiveness of permutation techniques. These measures are (1) Percentage of Adjacent Pixels Count (PAPC) and (2) Distance Between Adjacent Pixels (DBAP). The proposed measures are used to evaluate and compare the six permutation techniques in different scenarios. The permutation techniques are applied on several standard images and the resulting scrambled images are analyzed. Moreover, the new measures are used to compare the permutation algorithms on different matrix sizes irrespective of the actual parameters used in each algorithm. The analysis results show that the proposed measures are good indicators of the effectiveness of the permutation technique.

A novel image encryption scheme based on substitution-permutation network and chaos

In this paper, a novel image encryption approach based on permutation-substitution (SP) network and chaotic systems is proposed. It consists of four cryptographic phases: diffusion, substitution, diffusion and permutation. Firstly, a diffusion phase is proposed based on new chaotic map. Then, a substitution phase based on strong S-boxes followed by a diffusion phase based on chaotic logistic map are presented which will, in turn, significantly increase the encryption performance. Finally, a block permutation phase is accomplished by a permutation function to enhance the statistical performance of the proposed encryption approach. Conducted experiments based on various types of differential and statistical analyses show that the proposed encryption approach has high security, sensitivity and speed compared to previous approaches

Color image encryption scheme using CML and DNA sequence operations

In this paper, an encryption algorithm for color images using chaotic system and DNA (Deoxyribonucleic acid) sequence operations is proposed. Three components for the color plain image is employed to construct a matrix, then perform confusion operation on the pixels matrix generated by the spatiotemporal chaos system, i.e., CML (coupled map lattice). DNA encoding rules, and decoding rules are introduced in the permutation phase. The extended Hamming distance is proposed to generate new initial values for CML iteration combining color plain image. Permute the rows and columns of the DNA matrix and then get the color cipher image from this matrix. Theoretical analysis and experimental results prove the cryptosystem secure and practical, and it is suitable for encrypting color images of any size.

Reusing the permutation matrix dynamically for efficient image cryptographic algorithm

In traditional type of chaotic image ciphers with the architecture of permutation–diffusion, one-dimensional chaotic map is always employed for generating key stream in the diffusion procedure. However, the workloads derived from the iteration-then-quantization of the key stream generation operations severely downgrade the overall encryption efficiency of such cryptosystems. In this paper, we demonstrate how to obtain the diffusion key stream from the permutation matrix, which is produced and preserved in the permutation phase. No extra chaotic iteration and quantization is required in the diffusion procedure, the operation efficiency is thus improved. A complete cryptosystem is built using Bake map for image permutation. Simulations and security analyses have been carried out and the results illustrate the superior security and high efficiency of the proposed scheme.

An authenticated image encryption scheme based on chaotic maps and memory cellular automata

This paper introduces a new image encryption scheme based on chaotic maps, cellular automata and permutation–diffusion architecture. In the permutation phase, a piecewise linear chaotic map is utilized to confuse the plain-image and in the diffusion phase, we employ the Logistic map as well as a reversible memory cellular automata to obtain an efficient and secure cryptosystem. The proposed method admits advantages such as highly secure diffusion mechanism, computational efficiency and ease of implementation. A novel property of the proposed scheme is its authentication ability which can detect whether the image is tampered during the transmission or not. This is particularly important in applications where image data or part of it contains highly sensitive information. Results of various analyses manifest high security of this new method and its capability for practical image encryption.

Chaotic Image Encryption Design Using Tompkins‐Paige Algorithm

In this paper, we have presented a new permutation‐substitution image encryption architecture using chaotic maps and Tompkins‐Paige algorithm. The proposed encryption system includes two major parts, chaotic pixels permutation and chaotic pixels substitution. A logistic map is used to generate a bit sequence, which is used to generate pseudorandom numbers in Tompkins‐Paige algorithm, in 2D permutation phase. Pixel substitution phase includes two process, the tent pseudorandom image (TPRI) generator and modulo addition operation. All parts of the proposed chaotic encryption system are simulated. Uniformity of the histogram of the proposed encrypted image is justified using the chi‐square test, which is less than χ2(255, 0.05). The vertical, horizontal, and diagonal correlation coefficients, as well as their average and RMS values for the proposed encrypted image are calculated that is about 13% less than previous researches. To quantify the difference between the encrypted image and the corresponding plain‐image, three measures are used. These are MAE, NPCR, and UACI, which are improved in our proposed system considerably. NPCR of our proposed system is exactly the ideal value of this criterion. The key space of our proposed method is large enough to protect the system against any Brute‐force and statistical attacks.

The input/output complexity of sorting and related problems

We provide tight upper and lower bounds, up to a constant factor, for the number of inputs and outputs (I/OS) between internal memory and secondary storage required for five sorting-related problems: sorting, the fast Fourier transform (FFT), permutation networks, permuting, and matrix transposition. The bounds hold both in the worst case and in the average case, and in several situations the constant factors match. Secondary storage is modeled as a magnetic disk capable of transferring P blocks each containing B records in a single time unit; the records in each block must be input from or output to B contiguous locations on the disk. We give two optimal algorithms for the problems, which are variants of merge sorting and distribution sorting. In particular we show for P = 1 that the standard merge sorting algorithm is an optimal external sorting method, up to a constant factor in the number of I/Os. Our sorting algorithms use the same number of I/Os as does the permutation phase of key sorting, except when the internal memory size is extremely small, thus affirming the popular adage that key sorting is not faster. We also give a simpler and more direct derivation of Hong and Kung's lower bound for the FFT for the special case B = P = O(1).

Cabibbo angle II

When permutation symmetry and phase invariance are assumed, the mass matrices for two generations take a unique form. The expressions for the masses of various quarks found earlier are used in the mass matrices to determine the Cabibbo angle. This angle is found to be 13° 11′. It is very close to the experimental value.