FAULT TOLERANCE AND DETECTION IN CHAOTIC COMPUTERS

2007 ◽  
Vol 17 (06) ◽  
pp. 1955-1968 ◽  
Author(s):  
MOHAMMAD R. JAHED-MOTLAGH ◽  
BEHNAM KIA ◽  
WILLIAM L. DITTO ◽  
SUDESHNA SINHA
Keyword(s):  
Chaotic Systems ◽  
Chaotic Maps ◽  
Structural Testing ◽  
Testing Time ◽  
Computing Device ◽  
One Dimensional ◽  
Testing Method ◽  
Higher Dimensional ◽  
Parameter Variations ◽  
Logic Blocks

We introduce a structural testing method for a dynamics based computing device. Our scheme detects different physical defects, manifesting themselves as parameter variations in the chaotic system at the core of the logic blocks. Since this testing method exploits the dynamical properties of chaotic systems to detect damaged logic blocks, the damaged elements can be detected by very few testing inputs, leading to very low testing time. Further the method does not entail dedicated or extra hardware for testing. Specifically, we demonstrate the method on one-dimensional unimodal chaotic maps. Some ideas for testing higher dimensional maps and flows are also presented.

GENERATION OF PSEUDO-CHAOTIC SEQUENCES

1994 ◽  
Vol 04 (03) ◽  
pp. 709-713 ◽  
Author(s):  
T. KILIAS
Keyword(s):  
Discrete Time ◽  
Spectral Properties ◽  
Chaotic Systems ◽  
Chaotic Maps ◽  
Maximum Length ◽  
Shift Register ◽  
One Dimensional ◽  
Chaotic Sequences ◽  
Random Signals

This paper deals with the spectral properties of pseudo-random signals generated in maximum-length shift registers. It is shown that infinitely long registers are comparable in behavior with one-dimensional discrete-time chaotic maps. Therefore the theory, results and tools developed for chaotic systems can be applied to the design of the spectral properties of maximum-length shift register sequences.

scholarly journals Cryptanalysis and Improvement of a Block Cipher Based on Multiple Chaotic Systems

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Jun He ◽  
Haifeng Qian ◽  
Yuan Zhou ◽  
Zhibin Li
Keyword(s):  
Chaotic Systems ◽  
Block Cipher ◽  
Chaotic Maps ◽  
Encryption Algorithm ◽  
Secret Key ◽  
Random Sequences ◽  
One Dimensional ◽  
Multiple Chaotic Systems

Wang and Yu proposed a block cipher scheme based on dynamic sequences generated by multiple chaotic systems, which overcomes the problem of periodical degradation on random sequences due to computational precision. Their scheme has a feature that a plaintext is encrypted by a keystream created from several one-dimensional chaotic maps. However, this feature results in some weaknesses of the encryption algorithm. We show three kinds of attacks in this paper, through which one can recover the plaintext from a given ciphertext without the secret key. We also present an improvement on their scheme, which prevents the three attacks mentioned above. Security of the enhanced cipher is presented and analyzed, which shows that our improved scheme is secure under the current attacks.

scholarly journals A Novel S-Box Dynamic Design Based on Nonlinear-Transform of 1D Chaotic Maps

Electronics ◽  
2021 ◽  
Vol 10 (11) ◽  
pp. 1313
Author(s):  
Wenhao Yan ◽  
Qun Ding
Keyword(s):  
Chaotic Systems ◽  
Chaotic Maps ◽  
Chaotic Map ◽  
Logistic Map ◽  
Sample Entropy ◽  
One Dimension ◽  
Linear Combinations ◽  
Dynamic Design ◽  
Construction Methods ◽  
Low Dimensional

In this paper, a method to enhance the dynamic characteristics of one-dimension (1D) chaotic maps is first presented. Linear combinations and nonlinear transform based on existing chaotic systems (LNECS) are introduced. Then, a numerical chaotic map (LCLS), based on Logistic map and Sine map, is given. Through the analysis of a bifurcation diagram, Lyapunov exponent (LE), and Sample entropy (SE), we can see that CLS has overcome the shortcomings of a low-dimensional chaotic system and can be used in the field of cryptology. In addition, the construction of eight functions is designed to obtain an S-box. Finally, five security criteria of the S-box are shown, which indicate the S-box based on the proposed in this paper has strong encryption characteristics. The research of this paper is helpful for the development of cryptography study such as dynamic construction methods based on chaotic systems.

scholarly journals Higher Dimensional Holonomy Map for Rules Submanifolds in Graded Manifolds

2020 ◽  
Vol 8 (1) ◽  
pp. 68-91
Author(s):  
Gianmarco Giovannardi
Keyword(s):  
Characteristic Direction ◽  
Fixed Degree ◽  
One Dimensional ◽  
First Order ◽  
Natural Choice ◽  
Higher Dimensional ◽  
Graded Manifold ◽  
The One ◽  
Graded Manifolds ◽  
Holonomy Map

AbstractThe deformability condition for submanifolds of fixed degree immersed in a graded manifold can be expressed as a system of first order PDEs. In the particular but important case of ruled submanifolds, we introduce a natural choice of coordinates, which allows to deeply simplify the formal expression of the system, and to reduce it to a system of ODEs along a characteristic direction. We introduce a notion of higher dimensional holonomy map in analogy with the one-dimensional case [29], and we provide a characterization for singularities as well as a deformability criterion.

scholarly journals Classification of one-dimensional superattracting germs in positive characteristic

2014 ◽  
Vol 35 (7) ◽  
pp. 2242-2268 ◽  
Author(s):  
MATTEO RUGGIERO
Keyword(s):  
Positive Characteristic ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
One Dimensional ◽  
Higher Dimensional ◽  
Dimensional Version

We give a classification of superattracting germs in dimension $1$ over a complete normed algebraically closed field $\mathbb{K}$ of positive characteristic up to conjugacy. In particular, we show that formal and analytic classifications coincide for these germs. We also give a higher-dimensional version of some of these results.

A WEIGHTED CHAOTIC BLOCK ENCRYPTION ALGORITHM USING MULTIPLE ONE-DIMENSIONAL CHAOTIC MAPS

2011 ◽  
Vol 25 (29) ◽  
pp. 3987-3996
Author(s):  
XING-YUAN WANG ◽  
XIAO-JUAN WANG
Keyword(s):  
Chaotic Maps ◽  
Encryption Algorithm ◽  
One Dimensional ◽  
Chaotic Iterations ◽  
Block Encryption

This paper proposes a new block encryption algorithm. The chaotic trajectories are computed by weighting. Then the result is used to mask the plaintext. Multiple blocks of plaintext are encrypted at the same time and this decreases the chaotic iterations. So the encryption speed is improved to some extent. The proposed algorithm is flexible. When the number of weights is increased, the number of the encrypted plaintext block at the same time is increased and the encryption speed is improved. The simulation result shows that the proposed algorithm has fast encryption speed and fine security.

Test Data Generation and Selection Using Levy Flight-Based Firefly Algorithm

2021 ◽  
Vol 9 (2) ◽  
pp. 18-34
Author(s):  
Abhishek Pandey ◽  
Soumya Banerjee
Keyword(s):  
Test Data ◽  
Firefly Algorithm ◽  
Optimization Problem ◽  
Structural Testing ◽  
Software Test ◽  
Testing Time ◽  
Test Data Generation ◽  
Data Generation ◽  
Test Suite Optimization ◽  
Test Optimization

This article discusses the application of an improved version of the firefly algorithm for the test suite optimization problem. Software test optimization refers to optimizing test data generation and selection for structural testing criteria for white box testing. This will subsequently reduce the two most costly activities performed during testing: time and cost. Recently, various search-based approaches proved very interesting results for the software test optimization problem. Also, due to no free lunch theorem, scientists are continuously searching for more efficient and convergent methods for the optimization problem. In this paper, firefly algorithm is modified in a way that local search ability is improved. Levy flights are incorporated into the firefly algorithm. This modified algorithm is applied to the software test optimization problem. This is the first application of Levy-based firefly algorithm for software test optimization. Results are shown and compared with some existing metaheuristic approaches.

Discrete-Time Memristor Model for Enhancing Chaotic Complexity and Application in Secure Communication

2022 ◽  
Author(s):  
Wenhao Yan ◽  
Zijing Jiang ◽  
Qun Ding
Keyword(s):  
Fixed Points ◽  
Discrete Time ◽  
Dynamic Characteristics ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Two Dimensional ◽  
Initial State ◽  
One Dimensional ◽  
Backward Euler ◽  
Short Period

Abstract The physical implementation of continuoustime memristor makes it widely used in chaotic circuits, whereas discrete-time memristor has not received much attention. In this paper, the backward-Euler method is used to discretize TiO2 memristor model, and the discretized model also meets the three fingerprinter characteristics of the generalized memristor. The short period phenomenon and uneven output distribution of one-dimensional chaotic systems affect their applications in some fields, so it is necessary to improve the dynamic characteristics of one-dimensional chaotic systems. In this paper, a two-dimensional discrete-time memristor model is obtained by linear coupling the proposed TiO2 memristor model and one-dimensional chaotic systems. Since the two-dimensional model has infinite fixed points, the stability of these fixed points depends on the coupling parameters and the initial state of the discrete TiO2 memristor model. Furthermore, the dynamic characteristics of one-dimensional chaotic systems can be enhanced by the proposed method. Finally, we apply the generated chaotic sequence to secure communication.

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