Secret Communication Systems Using Chaotic Wave Equations with Neural Network Boundary Conditions
In a secret communication system using chaotic synchronization, the communication information is embedded in a signal that behaves as chaos and is sent to the receiver to retrieve the information. In a previous study, a chaotic synchronous system was developed by integrating the wave equation with t...
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doaj-39498a02f77940948cd132f67b950a752021-07-23T13:39:50ZengMDPI AGEntropy1099-43002021-07-012390490410.3390/e23070904Secret Communication Systems Using Chaotic Wave Equations with Neural Network Boundary ConditionsYuhan Chen0Hideki Sano1Masashi Wakaiki2Takaharu Yaguchi3Graduate School of System Informatics, Kobe University, Kobe 657-8501, JapanGraduate School of System Informatics, Kobe University, Kobe 657-8501, JapanGraduate School of System Informatics, Kobe University, Kobe 657-8501, JapanGraduate School of System Informatics, Kobe University, Kobe 657-8501, JapanIn a secret communication system using chaotic synchronization, the communication information is embedded in a signal that behaves as chaos and is sent to the receiver to retrieve the information. In a previous study, a chaotic synchronous system was developed by integrating the wave equation with the van der Pol boundary condition, of which the number of the parameters are only three, which is not enough for security. In this study, we replace the nonlinear boundary condition with an artificial neural network, thereby making the transmitted information difficult to leak. The neural network is divided into two parts; the first half is used as the left boundary condition of the wave equation and the second half is used as that on the right boundary, thus replacing the original nonlinear boundary condition. We also show the results for both monochrome and color images and evaluate the security performance. In particular, it is shown that the encrypted images are almost identical regardless of the input images. The learning performance of the neural network is also investigated. The calculated Lyapunov exponent shows that the learned neural network causes some chaotic vibration effect. The information in the original image is completely invisible when viewed through the image obtained after being concealed by the proposed system. Some security tests are also performed. The proposed method is designed in such a way that the transmitted images are encrypted into almost identical images of waves, thereby preventing the retrieval of information from the original image. The numerical results show that the encrypted images are certainly almost identical, which supports the security of the proposed method. Some security tests are also performed. The proposed method is designed in such a way that the transmitted images are encrypted into almost identical images of waves, thereby preventing the retrieval of information from the original image. The numerical results show that the encrypted images are certainly almost identical, which supports the security of the proposed method.https://www.mdpi.com/1099-4300/23/7/904chaotic synchronizationsecret communication systemvan der Pol boundary conditiondeep learning |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Yuhan Chen Hideki Sano Masashi Wakaiki Takaharu Yaguchi |
spellingShingle |
Yuhan Chen Hideki Sano Masashi Wakaiki Takaharu Yaguchi Secret Communication Systems Using Chaotic Wave Equations with Neural Network Boundary Conditions Entropy chaotic synchronization secret communication system van der Pol boundary condition deep learning |
author_facet |
Yuhan Chen Hideki Sano Masashi Wakaiki Takaharu Yaguchi |
author_sort |
Yuhan Chen |
title |
Secret Communication Systems Using Chaotic Wave Equations with Neural Network Boundary Conditions |
title_short |
Secret Communication Systems Using Chaotic Wave Equations with Neural Network Boundary Conditions |
title_full |
Secret Communication Systems Using Chaotic Wave Equations with Neural Network Boundary Conditions |
title_fullStr |
Secret Communication Systems Using Chaotic Wave Equations with Neural Network Boundary Conditions |
title_full_unstemmed |
Secret Communication Systems Using Chaotic Wave Equations with Neural Network Boundary Conditions |
title_sort |
secret communication systems using chaotic wave equations with neural network boundary conditions |
publisher |
MDPI AG |
series |
Entropy |
issn |
1099-4300 |
publishDate |
2021-07-01 |
description |
In a secret communication system using chaotic synchronization, the communication information is embedded in a signal that behaves as chaos and is sent to the receiver to retrieve the information. In a previous study, a chaotic synchronous system was developed by integrating the wave equation with the van der Pol boundary condition, of which the number of the parameters are only three, which is not enough for security. In this study, we replace the nonlinear boundary condition with an artificial neural network, thereby making the transmitted information difficult to leak. The neural network is divided into two parts; the first half is used as the left boundary condition of the wave equation and the second half is used as that on the right boundary, thus replacing the original nonlinear boundary condition. We also show the results for both monochrome and color images and evaluate the security performance. In particular, it is shown that the encrypted images are almost identical regardless of the input images. The learning performance of the neural network is also investigated. The calculated Lyapunov exponent shows that the learned neural network causes some chaotic vibration effect. The information in the original image is completely invisible when viewed through the image obtained after being concealed by the proposed system. Some security tests are also performed. The proposed method is designed in such a way that the transmitted images are encrypted into almost identical images of waves, thereby preventing the retrieval of information from the original image. The numerical results show that the encrypted images are certainly almost identical, which supports the security of the proposed method. Some security tests are also performed. The proposed method is designed in such a way that the transmitted images are encrypted into almost identical images of waves, thereby preventing the retrieval of information from the original image. The numerical results show that the encrypted images are certainly almost identical, which supports the security of the proposed method. |
topic |
chaotic synchronization secret communication system van der Pol boundary condition deep learning |
url |
https://www.mdpi.com/1099-4300/23/7/904 |
work_keys_str_mv |
AT yuhanchen secretcommunicationsystemsusingchaoticwaveequationswithneuralnetworkboundaryconditions AT hidekisano secretcommunicationsystemsusingchaoticwaveequationswithneuralnetworkboundaryconditions AT masashiwakaiki secretcommunicationsystemsusingchaoticwaveequationswithneuralnetworkboundaryconditions AT takaharuyaguchi secretcommunicationsystemsusingchaoticwaveequationswithneuralnetworkboundaryconditions |
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1721288438527819776 |