A three-dimensional chaotic map and their applications to digital audio security

In this paper, an effective framework for chaotic encryption based on a three-dimensional logistic map is presented together with secure hash algorithm-3 (SHA-3) and electrocardiograph (ECG) signal. Following the analysis of the drawbacks, namely, fixed key and low sensitivity, of some current algorithms, this work tries to solve these two problems and includes two contributions: (1) removal of the phenomenon of summation invariance in a plain-image, for which SHA-3 is proposed to calculate the hash value for the plain-image, with the results being employed to influence the initial keys for chaotic map; (2) resolution of the problem of fixed key by using an ECG signal, that can be different for different subjects or different for same subject at different times. The Wolf algorithm is employed to produce all the control parameters and initial keys in the proposed encryption method. It is believed that combining with the classical architecture of permutation-diffusion, the summation invariance in the plain-image and shortcoming of a fixed key will be avoided in our algorithm. Furthermore, the experimental results and security analysis show that the proposed encryption algorithm can achieve confidentiality.

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Analysis of trigonometric chaotic sequence by proposing an index-based bit level scrambling image encryption

Modern Physics Letters B ◽

10.1142/s0217984921504066 ◽

2021 ◽

pp. 2150406

Author(s):

Wanbo Yu ◽

Hao Wang

Keyword(s):

Chaotic Map ◽

Three Dimensional ◽

Correlation Coefficients ◽

Chaotic Sequence ◽

Binary Number ◽

Encryption Scheme ◽

Binary Matrix ◽

Binary Images ◽

Average Value ◽

Research Fields

Chaotic map is applied to numerous research fields, such as encryption of data and information. In this paper, a novel bit-level scrambling encryption based on three-dimensional trigonometric chaotic sequence is proposed. This encryption is operated on grayscale images because pixel value of which is between 0 and 255, which can be converted into 8-bit binary number, then each image can be converted into eight binary images. Combine binary images a three-dimensional matrix as input, which have three index values width, height, and page. Generate three numbers by the chaotic sequence to locate the value of the matrix need to be changed. After the value is located, change its value 0 to 1 or 1 to 0, this is the basic encryption scheme. This paper makes a three-dimensional binary matrix with 32 images to test the encryption scheme, and get average value of images’ number of pixel change rate at 0.9603, unified averaged change intensity at 31.27%, information entropy at 7.9891, also the histograms. And correlation coefficients of each pixel from three directions are small. There are comparisons with other encryptions too. The key space of this encryption is more than 10[Formula: see text].

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A New Two-Dimensional Mutual Coupled Logistic Map and Its Application for Pseudorandom Number Generator

Mathematical Problems in Engineering ◽

10.1155/2019/7685359 ◽

2019 ◽

Vol 2019 ◽

pp. 1-10 ◽

Cited By ~ 2

Author(s):

Xuan Huang ◽

Lingfeng Liu ◽

Xiangjun Li ◽

Minrong Yu ◽

Zijie Wu

Keyword(s):

Statistical Tests ◽

Chaotic Map ◽

Logistic Map ◽

Security Analysis ◽

Three Dimensional ◽

Pseudorandom Number ◽

Pseudorandom Number Generator ◽

Number Generator ◽

Two Dimensional ◽

Practical Applications

Given that the sequences generated by logistic map are unsecure with a number of weaknesses, including its relatively small key space, uneven distribution, and vulnerability to attack by phase space reconstruction, this paper proposes a new two-dimensional mutual coupled logistic map, which can overcome these weaknesses. Our two-dimensional chaotic map model is simpler than the recently proposed three-dimensional coupled logistic map, whereas the sequence generated by our system is more complex. Furthermore, a new kind of pseudorandom number generator (PRNG) based on the mutual coupled logistic maps is proposed for application. Both statistical tests and security analysis show that our proposed PRNG has good randomness and that it can resist all kinds of attacks. The algorithm speed analysis indicates that PRNG is valuable to practical applications.

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SOLVABLE THREE-DIMENSIONAL RATIONAL CHAOTIC MAP DEFINED BY JACOBIAN ELLIPTIC FUNCTIONS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127407019500 ◽

2007 ◽

Vol 17 (10) ◽

pp. 3645-3650 ◽

Cited By ~ 2

Author(s):

ASUKA ONO ◽

TOHRU KOHDA

Keyword(s):

Communication Systems ◽

Chaotic Map ◽

Three Dimensional ◽

Sufficient Conditions ◽

Random Variables ◽

Space Curve ◽

Random Vectors ◽

Rational Map ◽

Binary Function ◽

Jacobian Elliptic Functions

Cryptanalysis needs a lot of pseudo-random numbers. In particular, a sequence of independent and identically distributed (i.i.d.) binary random variables plays an important role in modern digital communication systems. Sufficient conditions have been recently provided for a class of ergodic maps of an interval onto itself: R1 → R1 and its associated binary function to generate a sequence of i.i.d. random variables. In order to get more i.i.d. binary random vectors, Jacobian elliptic Chebyshev rational map, its derivative and second derivative which define a Jacobian elliptic space curve have been introduced. Using duplication formula gives three-dimensional real-valued sequences on the space curve onto itself: R3 → R3. This also defines three projective onto mappings, represented in the form of rational functions of xn, yn, zn. These maps generate a three-dimensional sequence of i.i.d. random vectors.

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Cryptanalysis of hybrid secure image encryption based on Julia set fractals and three-dimensional Lorenz chaotic map

Mathematics and Computers in Simulation ◽

10.1016/j.matcom.2021.06.008 ◽

2021 ◽

Author(s):

Noor Munir ◽

Majid Khan ◽

Sajjad Shaukat Jamal ◽

Mohammad Mazyad Hazzazi ◽

Iqtadar Hussain

Keyword(s):

Image Encryption ◽

Julia Set ◽

Chaotic Map ◽

Three Dimensional

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A Symmetric Image Encryption Algorithm Based on a Coupled Logistic–Bernoulli Map and Cellular Automata Diffusion Strategy

Entropy ◽

10.3390/e21050504 ◽

2019 ◽

Vol 21 (5) ◽

pp. 504 ◽

Cited By ~ 9

Author(s):

Wei Zhang ◽

Zhiliang Zhu ◽

Hai Yu

Keyword(s):

Cellular Automata ◽

Image Encryption ◽

High Efficiency ◽

Chaotic Map ◽

Logistic Map ◽

Three Dimensional ◽

Encryption Algorithm ◽

Original Structure ◽

One Dimensional ◽

Image Encryption Algorithm

In this paper, the properties of the classical confusion–substitution structure and some recently proposed pseudorandom number generators using one-dimensional chaotic maps are investigated. To solve the low security problem of the original structure, a new bit-level cellular automata strategy is used to improve the sensitivity to the cryptosystem. We find that the new evolution effects among different generations of cells in cellular automata can significantly improve the diffusion effect. After this, a new one-dimensional chaotic map is proposed, which is constructed by coupling the logistic map and the Bernoulli map (LBM). The new map exhibits a much better random behavior and is more efficient than comparable ones. Due to the favorable properties of the new map and cellular automata algorithm, we propose a new image-encryption algorithm in which three-dimensional bit-level permutation with LBM is employed in the confusion phase. Simulations are carried out, and the results demonstrate the superior security and high efficiency of the proposed scheme.

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