Finite Precision Logistic Map between Computational Efficiency and Accuracy with Encryption Applications
Chaotic systems appear in many applications such as pseudo-random number generation, text encryption, and secure image transfer. Numerical solutions of these systems using digital software or hardware inevitably deviate from the expected analytical solutions. Chaotic orbits produced using finite pre...
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Online Access: | http://dx.doi.org/10.1155/2017/8692046 |
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doaj-e191500a6a63440bb282ec3f0491fe852020-11-25T01:05:57ZengHindawi-WileyComplexity1076-27871099-05262017-01-01201710.1155/2017/86920468692046Finite Precision Logistic Map between Computational Efficiency and Accuracy with Encryption ApplicationsWafaa S. Sayed0Ahmed G. Radwan1Ahmed A. Rezk2Hossam A. H. Fahmy3Engineering Mathematics and Physics Department, Faculty of Engineering, Cairo University, Giza 12613, EgyptEngineering Mathematics and Physics Department, Faculty of Engineering, Cairo University, Giza 12613, EgyptNanoelectronics Integrated Systems Center, Nile University, Cairo 12588, EgyptElectronics and Communication Engineering Department, Faculty of Engineering, Cairo University, Giza 12613, EgyptChaotic systems appear in many applications such as pseudo-random number generation, text encryption, and secure image transfer. Numerical solutions of these systems using digital software or hardware inevitably deviate from the expected analytical solutions. Chaotic orbits produced using finite precision systems do not exhibit the infinite period expected under the assumptions of infinite simulation time and precision. In this paper, digital implementation of the generalized logistic map with signed parameter is considered. We present a fixed-point hardware realization of a Pseudo-Random Number Generator using the logistic map that experiences a trade-off between computational efficiency and accuracy. Several introduced factors such as the used precision, the order of execution of the operations, parameter, and initial point values affect the properties of the finite precision map. For positive and negative parameter cases, the studied properties include bifurcation points, output range, maximum Lyapunov exponent, and period length. The performance of the finite precision logistic map is compared in the two cases. A basic stream cipher system is realized to evaluate the system performance for encryption applications for different bus sizes regarding the encryption key size, hardware requirements, maximum clock frequency, NIST and correlation, histogram, entropy, and Mean Absolute Error analyses of encrypted images.http://dx.doi.org/10.1155/2017/8692046 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Wafaa S. Sayed Ahmed G. Radwan Ahmed A. Rezk Hossam A. H. Fahmy |
spellingShingle |
Wafaa S. Sayed Ahmed G. Radwan Ahmed A. Rezk Hossam A. H. Fahmy Finite Precision Logistic Map between Computational Efficiency and Accuracy with Encryption Applications Complexity |
author_facet |
Wafaa S. Sayed Ahmed G. Radwan Ahmed A. Rezk Hossam A. H. Fahmy |
author_sort |
Wafaa S. Sayed |
title |
Finite Precision Logistic Map between Computational Efficiency and Accuracy with Encryption Applications |
title_short |
Finite Precision Logistic Map between Computational Efficiency and Accuracy with Encryption Applications |
title_full |
Finite Precision Logistic Map between Computational Efficiency and Accuracy with Encryption Applications |
title_fullStr |
Finite Precision Logistic Map between Computational Efficiency and Accuracy with Encryption Applications |
title_full_unstemmed |
Finite Precision Logistic Map between Computational Efficiency and Accuracy with Encryption Applications |
title_sort |
finite precision logistic map between computational efficiency and accuracy with encryption applications |
publisher |
Hindawi-Wiley |
series |
Complexity |
issn |
1076-2787 1099-0526 |
publishDate |
2017-01-01 |
description |
Chaotic systems appear in many applications such as pseudo-random number generation, text encryption, and secure image transfer. Numerical solutions of these systems using digital software or hardware inevitably deviate from the expected analytical solutions. Chaotic orbits produced using finite precision systems do not exhibit the infinite period expected under the assumptions of infinite simulation time and precision. In this paper, digital implementation of the generalized logistic map with signed parameter is considered. We present a fixed-point hardware realization of a Pseudo-Random Number Generator using the logistic map that experiences a trade-off between computational efficiency and accuracy. Several introduced factors such as the used precision, the order of execution of the operations, parameter, and initial point values affect the properties of the finite precision map. For positive and negative parameter cases, the studied properties include bifurcation points, output range, maximum Lyapunov exponent, and period length. The performance of the finite precision logistic map is compared in the two cases. A basic stream cipher system is realized to evaluate the system performance for encryption applications for different bus sizes regarding the encryption key size, hardware requirements, maximum clock frequency, NIST and correlation, histogram, entropy, and Mean Absolute Error analyses of encrypted images. |
url |
http://dx.doi.org/10.1155/2017/8692046 |
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