Abstract
Most current symmetric cryptographic algorithms (symmetric ciphers and hash functions) are considered to be relatively secure against attacks by quantum computers. Here we propose an adaptive color double-image encryption scheme based on autonomous ODE chaotic system and SHA-512. The double-image is diffused firstly by chaotic sequences with bitwise exclusive or operation, and an algorithm is designed to transform two 512-bit hash values into two S-Boxes, to substitute for the pixels of diffused double-image respectively. In each encryption process, the initial values of chaotic system are from random signal, they are true random numbers. Simulation results demonstrate that the scheme is suitable and effective for color double-image encryption.
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References
Bernstein DJ (2010a) Grover vs. mceliece. Post-Quantum Cryptography. Springer, Berlin, p 73–80
Bernstein DJ (2010b) Grover vs. mceliece. International Workshop on Post-Quantum Cryptography. Springer, Berlin, p 73–80
Bernstein DJ, Hopwood D, Hülsing A, et al. (2015) SPHINCS: practical stateless hash-based signatures. Advances in Cryptology--EUROCRYPT 2015. Springer, Berlin, p 368–397
Cafagna D, Grassi G (2012) On the simplest fractional-order memristor-based chaotic system. Nonlinear Dynamics 70(2):1185–1197
Chen J, Zhu Z, Fu C et al (2015) A fast chaos-based image encryption scheme with a dynamic state variables selection mechanism. Commun Nonlinear Sci Numer Simul 20(3):846–860
De Feo L, Jao D, Plût J (2014) Towards quantum-resistant cryptosystems from super singular elliptic curve isogenies. J Math Cryptol 8(3):209–247
Delfs C, Galbraith S D. (2013) Computing isogenies between super singular elliptic curves over Fp arXiv preprint arXiv: 1310.7789
Hussain I, Gondal MA (2014) An algorithm to generating inverse S-box for Rijndael encryption standard. 3D Res 5(4):1–5
Hussain I, Shah T, Gondal MA (2012) Image encryption algorithm based on PGL(2,GF(28)) S-boxes and TD-ERCS chaotic sequence. Nonlinear Dynamics 70(1):181–187
Hussain I, Shah T, Gondal MA (2013) Application of S-box and chaotic map for image encryption. Math Comput Model 57(9):2576–2579
Hussain I, Azam NA, Shah T (2014) Stego optical encryption based on chaotic S-box transformation. Opt Laser Technol 61:50–56
Liu H, Wang X (2011) Color image encryption using spatial bit-level permutation and high-dimension chaotic system. Opt Commun 284(16–17):3895–3903
Liu H, Wang X (2013) Triple-image encryption scheme based on one-time key stream generated by chaos and plain images. J Syst Softw 86(3):826–834
Liu G, Li J, Liu H (2014) Chaos-based color pathological image encryption scheme using one-time keys. Comput Biol Med 45:111–117
Liu Y, Pang S, Chen D (2013) An unusual chaotic system and its control. Math Comput Model 57(9):2473–2493
Liu H, Kadir A, Gong P (2015) A fast color image encryption scheme using one-time S-boxes based on complex chaotic system and random environmental noise. Opt Commun 338:340–347
Nyberg K (1991) Perfect nonlinear S-boxes. Advances in Cryptology—EUROCRYPT’91. Springer, Berlin, p 378–386
Radhakrishnan SV, Subramanian S (2013) An analytical approach to s-box generation. Comput Electr Eng 39(3):1006–1015
Seyedzadeh SM, Mirzakuchaki S (2012) A fast color image encryption algorithm based on coupled two-dimensional piecewise chaotic map. Signal Process 92(5):1202–1215
Sui L, Duan K, Liang J et al (2014a) Asymmetric double-image encryption based on cascaded discrete fractional random transform and logistic maps. Opt Express 22(9):10605–10621
Sui L, Lu H, Wang Z et al (2014b) Double-image encryption using discrete fractional random transform and logistic maps. Opt Lasers Eng 56:1–12
Wang Y, Wong KW, Li C et al (2012) A novel method to design S-box based on chaotic map and genetic algorithm. Phys Lett A 376(6):827–833
Wang Y, Lei P, Wong KW (2015) A method for constructing Bijective S-box with high nonlinearity based on chaos and optimization. Int J Bifurcation Chaos 25(10):1550127
Wu X, Kan H, Kurths J (2015) A new color image encryption scheme based on DNA sequences and multiple improved 1D chaotic maps. Appl Soft Comput 37:24–39
Xiao D, Zhang YS (2014) Self-adaptive permutation and combined global diffusion for chaotic color image encryption. AEU Int J Electron Commun 68(4):361–368
Xu Y. DCT domain image encryption algorithm based on Lorenz chaotic system. 2014, 556: 5168–5171.
Ye G (2014) A block image encryption algorithm based on wave transmission and chaotic systems. Nonlinear Dynamics 75(3):417–427
Zhang X, Zhao Z, Wang J (2014) Chaotic image encryption based on circular substitution box and key stream buffer. Signal Process Image Commun 29(8):902–913
Zhou G, Zhang D, Liu Y et al (2015a) A novel image encryption algorithm based on chaos and line map. Neurocomputing 169:150–157
Zhou Y, Ionescu C, Machado JAT (2015b) Fractional dynamics and its applications. Nonlinear Dynamics 80(4):1661–1664
Acknowledgements
This research is supported by the National Natural Science Foundation of China (No: 61363082, 61662073), the Natural Science Foundation of Shandong Province (No: ZR2015FM019), and the Natural Science Foundation of Weifang (No. 2014ZJ1060).
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Liu, H., Kadir, A., Sun, X. et al. Chaos based adaptive double-image encryption scheme using hash function and S-boxes. Multimed Tools Appl 77, 1391–1407 (2018). https://doi.org/10.1007/s11042-016-4288-z
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DOI: https://doi.org/10.1007/s11042-016-4288-z