Analyses of Reconfigurable Chaotic Systems and their Cryptographic S-box Design Applications

Year 2023, Volume: 5 Issue: 3, 219 - 232, 30.11.2023

Mangal Deep Gupta Rajeev Kumar Chauhan Vipin Kumar Upaddhyay

Abstract

This manuscript includes the design and evaluation of the new four 16×16 S-boxes for subbyte operation in image encryption applications and estimates their strength using the following parameters: Dynamic Distance, BIC non-linearity, Bijective, Non-linearity, Strict Avalanche Criterion (SAC), and Balanced criterion. The S-box matrix is designed by a new reconfigurable 3D-Chaotic PRNG. This PRNG is designed using four different 3D chaotic systems i.e. Lorenz, Chen, Lu, and Pehlivan's chaotic systems. This reconfigurable architecture of PRNG exploits the ODEs of these four attractors that fit all four chaotic systems in a single circuit. The first part of this manuscript is focused to develop hardware-efficient VLSI architecture. To demonstrate the hardware performance, the PRNG circuit is implemented in Virtex-5 (XC5VLX50T) FPGA. A performance comparison of proposed and existing PRNGs (in terms of timing performance, area constraint, power dissipation and statistical testing) has been presented in this work. The PRNG generates the 24-bit random number at 96.438-MHz. The area of FPGA is occupied by only 16.66 %, 1.08%, 0.33%, and 1.15% of the available DSP blocks, slice LUTs, slice registers and slices respectively. The designed S-boxes using reconfigurable PRNG fulfill the following criteria: Dynamic Distance, BIC non-linearity, Bijective, Non-linearity, Strict Avalanche Criterion (SAC), and Balanced criterion.

Keywords

Cryptography, Chaotic System, PRNG, Operating frequency, NIST Tests, S-Boxes, FPGA

Supporting Institution

NA

Project Number

NA

References

• Ahmad, M. and E. A. Alsolami, 2020 Evolving dynamic s-boxes using fractional-order hopfield neural network based scheme. Entropy 22.
• Akgul, A., C. Arslan, and B. Arıcıo˘glu, 2019 Design of an interface for random number generators based on integer and fractional order chaotic systems. volume 1, pp. 1–18.
• Alawida, M., A. Samsudin, and J. S. Teh, 2020 Enhanced digital chaotic maps based on bit reversal with applications in random bit generators. Inf. Sci. 512: 1155–1169.
• Alçın, M., ˙I. Pehlivan, and ˙I. Koyuncu, 2016 Hardware design and implementation of a novel ann-based chaotic generator in fpga. Optik 127: 5500–5505.
• Alhadawi, H. S., D. Lambi´c, M. F. B. Zolkipli, and M. Ahmad, 2020 Globalized firefly algorithm and chaos for designing substitution box. J. Inf. Secur. Appl. 55: 102671.
• Artu˘ger, F., 2023 A new s-box generator algorithm based on 3d chaotic maps and whale optimization algorithm. Wireless Personal Communications 131: 1–19.
• Artu˘ger, F. and F. Özkaynak, 2022a A method for generation of substitution box based on random selection. Egyptian Informatics Journal 23: 127–135.
• Artu˘ger, F. and F. Özkaynak, 2022b Sbox-cga: substitution box generator based on chaos and genetic algorithm. Neural Computing and Applications 34: 1–9.
• Cassal-Quiroga, B. B. and E. Campos-Cantón, 2020 Generation of dynamical s-boxes for block ciphers via extended logistic map. Mathematical Problems in Engineering 2020: 1–12.
• ElSafty, A. H., M. F. Tolba, L. A. Said, A. H. Madian, and A. G. Radwan, 2021 Analog integrated circuits and signal processing. Hardware realization of a secure and enhanced s-box based speech encryption engine 106: 385–397.
• G. Di Patrizio Stanchieri, E. P., A. De Marcellis and M. Faccio, 2019 A true random number generator architecture based on a reduced number of fpga primitives. AEU - Inte. J. Electron. Commun. 105.
• Garcia-Bosque, M., A. Pérez-Resa, C. Sánchez-Azqueta, C. Aldea, and S. Celma, 2019 Chaos-based bitwise dynamical pseudorandom number generator on fpga. IEEE Transactions on Instrumentation and Measurement 68: 291–293.
• Garcia-Bosque, M., A. Pérez-Resa, C. Sánchez-Azqueta, C. Aldea, and S. Celma, 2018 A new technique for improving the security of chaos based cryptosystems. In 2018 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5.
• Garipcan, A. M. and E. Erdem, 2020 A trng using chaotic entropy pool as a post-processing technique: analysis, design and fpga implementation. Analog Integr. Circuits Signal Process. 103: 391– 410.
• Gupta, M. and R. Chauhan, 2020 Efficient hardware implementation of pseudo-random bit generator using dual-clcg method. Journal of Circuits, Systems and Computers 30.
• Gupta, M. D. and R. K. Chauhan, 2021 Secure image encryption scheme using 4d-hyperchaotic systems based reconfigurable pseudo-random number generator and s-box. Integr. 81: 137– 159.
• Gupta, M. D. and R. K. Chauhan, 2022 “hardware efficient pseudorandom number generator using chen chaotic system on fpga. J. Circuits, Syst. Comput. 31: 2250043.
• H. S. Alhadawi, S. M. I., M. F. Zolkipli and D. Lambi, 2019 Designing a pseudorandom bit generator based on lfsrs and a discrete chaotic map. Cryptologia 43: 190–210.
• Ishfaq, F., 2018 A MATLAB Tool for the Analysis of Cryptographic Properties of S-boxes. MATLAB Tool for the Analysis of Cryptographic Properties of S-boxes.
• Khan, H., M. M. Hazzazi, S. S. Jamal, I. Hussain, and M. Khan, 2022 New color image encryption technique based on three-dimensional logistic map and grey wolf optimization based generated substitution boxes. Multimedia Tools and Applications 82: 1–22.
• Khan, M., T. Shah, and S. I. Batool, 2016 Construction of s-box based on chaotic boolean functions and its application in image encryption. Neural Computing and Applications 27: 677–685.
• Lambi´c, D. and M. Nikolic, 2019 New pseudo-random number generator based on improved discrete-space chaotic map. Filomat 33: pp. 2257–2268.
• Li, Q. and X. S. Yang, 2010 simple method for finding topological horseshoes. A simple method for finding topological horseshoes 20: 467–478.
• Li, S., X. Mou, and C. Yuanlong, 2001 Pseudo-random bit generator based on couple chaotic systems and its applications in stream-cipher cryptography. In International Conference on Cryptology in India.
• Lorenz, E. N., 1963 Deterministic nonperiodic flow. Journal of the Atmospheric Sciences 20: 130–141.
• Lu, J. and G. Chen, 2002 A new chaotic attractor coined. Int. J. Bifurc. Chaos 12: 659–661.
• L’Ecuyer, P., 2012 Random number generation. in Handbook of Computational Statistics .
• Pande, A. and J. Zambreno, 2013 A chaotic encryption scheme for real-time embedded systems: design and implementation. Telecommunication Systems 52: 551–561.
• Pehlivan, I. and Y. Uyaro˘glu, 2010 A new chaotic attractor from general lorenz system family and its electronic experimental implementation. Turkish Journal of Electrical Engineering and Computer Sciences 18: 171–184.
• Pehlivan, I. and Y. Uyaroglu, 2012 A new 3d chaotic system with ˇ golden proportion equilibria: Analysis and electronic circuit realization. Comput. Electr. Eng 38: 285–317.
• Rezk, A. A., A. H. Madian, A. G. Radwan, and A. M. Soliman, 2019 Reconfigurable chaotic pseudo random number generator based on fpga. AEU - International Journal of Electronics and Communications .
• Rezk, A. A., A. H. Madian, A. G. Radwan, and A. M. Soliman, 2020 Multiplierless chaotic pseudo random number generators. Aeu-international Journal of Electronics and Communications 113: 152947.
• Rukhin, A. L., J. Soto, J. Nechvatal, M. E. Smid, and E. B. Barker, 2000 A statistical test suite for random and pseudorandom number generators for cryptographic applications. volume 2, pp. 1–8.
• T. Zhou, G. C. and S. Celikovský, 2005 Lnikov chaos in the gener- ˇ alized lorenz canonical form of dynamical systems,. Nonlinear Dyn. 39: 319–334.
• Tang, G., X. Liao, and Y. Chen, 2005 A novel method for designing s-boxes based on chaotic maps. Chaos Solitons & Fractals 23: 413–419.
• Wang, X., Ü. Çavusoglu, S. Kaçar, A. Akgul, V.-T. Pham, et al., 2019 S-box based image encryption application using a chaotic system without equilibrium. Applied Sciences 9: 4.
• Wang, Y., Z. Liu, J. Ma, and a. H. He, 2016 pseudorandom number generator based on piecewise logistic map. Nonlinear Dyn. 83: 2373–2391.
• Wang, Y., K. wo Wong, X. Liao, and T. Xiang, 2009 A block cipher with dynamic s-boxes based on tent map. Communications in Nonlinear Science and Numerical Simulation 14: 3089–3099.
• Wolf, A., J. B. Swift, H. L. Swinney, and J. A. Vastano, 1985 A new 3d chaotic system with golden proportion equilibria: Analysis and electronic circuit realization. Phys. D Nonlinear Phenom. 16: 285–317.
• X. Y. Wang, R. L., L. Yang and A. Kadir, 2010 A chaotic image encryption algorithm based on perceptron model. Nonlinear Dyn. 62: 615–621.
• Xu, W., J. Feng, and H. Rong, 2009 Melnikov’s method for a general nonlinear vibro-impact oscillator. Nonlinear Anal. Theory, Methods Appl. 71: 418–426.
• Zahid, A. H., A. M. Iliyasu, M. Ahmad, M. M. U. Shaban, M. J. Arshad, et al., 2021 A novel construction of dynamic s-box with high nonlinearity using heuristic evolution. IEEE Access 9: 67797–67812.
• Zamli, K. Z., F. Din, H. S. Alhadawi, S. Khalid, H. Alsolai, et al., 2023 Exploiting an elitist barnacles mating optimizer implementation for substitution box optimization. ICT Express 9: 619–627.
• Zhao, Y., C. Gao, J. Liu, and S. Dong, 2019 A self-perturbed pseudorandom sequence generator based on hyperchaos. volume 4, p. 100023.
• Zidan, M. A., A. G. Radwan, and K. N. Salama, 2011 The effect of numerical techniques on differential equation based chaotic generators. ICM 2011 Proceeding pp. 1–4.
• Çavusoglu, Ü., S. Kaçar, I. Pehlivan, and A. Zengin, 2017 Secure image encryption algorithm design using a novel chaos based s-box. Chaos Solitons & Fractals 95: 92–101.
• Ü. Çavusoglu, A. A. S. J., S. Panahi and S. Kaçar, 2019 A new chaotic system with hidden attractor and its engineering applications: analog circuit realization and image encryption