Network Synchronization of MACM Circuits and Its Application to Secure Communications
Abstract
:1. Introduction
2. Brief Review on Synchronization of Complex Networks
2.1. Synchronization of Complex Network
2.2. Star Coupled Networks
2.3. Synchronization Analysis Based on Master Stability Function Approach
3. MACM Circuit like Node
4. Star Network Synchronization of MACM’s Circuits
4.1. Synchronization Analysis Based on Master Stability Function Approach and Its Simulation
4.2. Star Network Electronic Circuit Synchronization
5. Application to Image Encryption
- 1.
- Binary string. The 8-bit gray-scale digital image with pixels are placed row-by-row in a binary string with bits.
- 2.
- Synchronization of star network. We used a coupling constant of between the master and slave MACM systems; different initial conditions are used for each MACM system (see Table 1); the control parameters are the same in all MACM systems, i.e., , and . After 50 time units (transient time), the star network is synchronized as shown in Figure 16.
- 3.
- Extended plain binary data. Since synchronization is achieved after a transient time and to avoid data loss in the receptors, the plain binary string is mounted over 400 time units for each bit producing an extended plain binary data of . As an example, Figure 16a–d show the first two bytes of the plain image transmitted, which are defined as 1010010010100011 with a length of 6400 time units (dashed line).
- 4.
- Switching parameter d of master MACM. The parameter d of the master node is switched between and , for 0 and 1 in the extended plain binary data, respectively. During this time, the absolute synchronization error is determined in , , , and , which are shown in Figure 16a–d with a blue line. Since initial conditions are considerably different at the start communication, the error is bigger in the first time units.
- 5.
- Processing the error. The recovered binary string in the receptor is calculated with the sum of the last 100 data in each error signal considering windows of 400 data; if the sum is greater than 0.7, a bit of 1 is defined for such window or bit of 0 in other case. Figure 16e–h presents the first recovered binary string in each slave MACM system (receptor).
- 6.
- Image construction. The digital image is constructed using the recovered binary string and the inverse process of step 1; the string is separated into 8-bit segments and assigned to rows and columns to form the corresponding digital image. Figure 16i–l present the difference between the plain image and recovered image at the bit level (first 8000 bits) for slaves 2–5, respectively.
5.1. Security Analysis
5.1.1. Histograms
5.1.2. Statistics of Histogram
5.1.3. Structural Similarity Index
5.1.4. Correlation Analysis
5.1.5. Information Entropy
5.1.6. Decryption Error Test
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
3D | Three-dimensional |
MACM | Méndez–Arellano–Cruz–Martínez |
IC | Integrated circuit |
OA | Operational amplifier |
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Initial | Master 1 | Slave 2 | Slave 3 | Slave 4 | Slave 5 |
---|---|---|---|---|---|
Condition | MACM | MACM | MACM | MACM | MACM |
−4.0 | 2.0 | 2.5 | −4.5 | 2.2 | |
−4.0 | 2.0 | 2.5 | −4.5 | 2.2 | |
−3.0 | 4.0 | 4.5 | −3.5 | 4.2 |
Component or IC | Value or Description |
---|---|
C1, C2, C3, C4, C5, C6, C7, C8, C9, C10, C11, C12, C13, C14, C15 | 10 nF |
R1, R25, R38, R51, R64 | 500 k |
R2, R37, R63 | 47 k |
R3, R4, R7, R8, R12, R13, R14, R15, R19, R20, R23, R26, R27, R28, R32, R33, R36, R39, R40, R41, R45, R46, R49, R52, R53, R54, R58, R59, R62, R66, R66, R67, R68, R69, R70, R71, R72, R73, R74, R75, R76, R77, R78, R79, R80, R81, R82, R83, R84, R85, R86, R87 R88, R89, R90, R91, R92, R93 | 10 k |
R5, R9, R11, R17, R18, R22, R31, R30, R35, R43, R44, R48, R56, R57, R61, R94, R95, R96, R97 | 1 M |
R6, R21, R34, R47, R60 | 2 M |
R10, R16, R42 | 94 k |
R24 | 47.5 k |
R50 | 48 k |
R29 | 94.5 k |
R55 | 95 k |
U1, U4, U5, U6, U8, U9, U12, U13, U15, U16 | Analog-multiplier AD633 |
U2, U3, U7, U10, U11, U14, U17, U18, U19 | OA TL084 |
Plain | Encrypted | Image in | Image in | Image in | Image in | |
---|---|---|---|---|---|---|
Image | Image | Slave 2 | Slave 3 | Slave 4 | Slave 5 | |
with | 3713.12 | 101.04 | 3711.78 | 3711.78 | 3711.78 | 3.71178 |
with | 60.93 | 10.05 | 60.92 | 60.92 | 60.92 | 60.92 |
Plain | Encrypted | Image in | Image in | Image in | Image in | |
Image | Image | Slave 2 | Slave 3 | Slave 4 | Slave 5 | |
with | 3713.12 | 101.04 | 96.91 | 96.87 | 96.91 | 96.93 |
with | 60.93 | 10.05 | 9.84 | 9.84 | 9.84 | 9.84 |
P | E | with | with |
---|---|---|---|
Plain image | Plain image | 1 | 1 |
Plain image | Encrypted image | 0.0030 | 0.0030 |
Plain image | Image in slave 2 | 0.9998 | 0.0135 |
Plain image | Image in slave 3 | 0.9998 | 0.0134 |
Plain image | Image in slave 4 | 0.9998 | 0.0135 |
Plain image | Image in slave 5 | 0.9998 | 0.0134 |
Coupling | Plain | Encrypted | Image in | Image in | Image in | Image in |
---|---|---|---|---|---|---|
Constant | Image | Image | Slave 2 | Slave 3 | Slave 4 | Slave 5 |
0.8757 | 0.1255 | 0.8520 | 0.8520 | 0.8520 | 0.8520 | |
0.8758 | 0.1256 | 0.1060 | 0.0957 | 0.1060 | 0.0957 |
Coupling | Plain | Encrypted | Image in | Image in | Image in | Image in |
---|---|---|---|---|---|---|
Constant | Image | Image | Slave 2 | Slave 3 | Slave 4 | Slave 5 |
7.5250 | 7.9903 | 7.5253 | 7.5253 | 7.5253 | 7.5253 | |
7.5250 | 7.9903 | 7.9910 | 7.9910 | 7.9910 | 7.9910 |
P | D | (%) with | (%) with |
---|---|---|---|
Plain image | Encrypted image | 99.5688 | 99.5688 |
Plain image | Image in slave 2 | 0.0044 | 99.6488 |
Plain image | Image in slave 3 | 0.0044 | 99.6488 |
Plain image | Image in slave 4 | 0.0044 | 99.6488 |
Plain image | Image in slave 5 | 0.0044 | 99.6488 |
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Méndez-Ramírez, R.; Arellano-Delgado, A.; Murillo-Escobar, M.Á. Network Synchronization of MACM Circuits and Its Application to Secure Communications. Entropy 2023, 25, 688. https://doi.org/10.3390/e25040688
Méndez-Ramírez R, Arellano-Delgado A, Murillo-Escobar MÁ. Network Synchronization of MACM Circuits and Its Application to Secure Communications. Entropy. 2023; 25(4):688. https://doi.org/10.3390/e25040688
Chicago/Turabian StyleMéndez-Ramírez, Rodrigo, Adrian Arellano-Delgado, and Miguel Ángel Murillo-Escobar. 2023. "Network Synchronization of MACM Circuits and Its Application to Secure Communications" Entropy 25, no. 4: 688. https://doi.org/10.3390/e25040688