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Pseudorandom sequences are very important in the field of cryptography. The characteristics such as non-linearity and random-like behaviours make chaotic systems suited to generate pseudorandom sequences. However, most of chaos-based pseudorandom number generators have a typical shortcoming. That is, the finite precision in all processors may cause the chaotic systems to degenerate into a periodic function or a fixed point. To overcome this shortcoming, a hyperchaos-based generator is proposed. First, a new hyperchaotic system with bigger Lyapunov exponent is constructed. Then the self-shrinking generator, which is superior to many other linear feedback shift register-based generators, is used to perturb the hyperchaotic sequences to decrease the period degeneration and improve the performance of the sequences. The proposed generator is named as hyperchaos with self-shrinking perturbance generator (H-SSP generator). The analysis results show that the H-SSP generator has better performance.
References
-
-
1)
-
14. Yang, T.: ‘A survey of chaotic secure communication systems’, Int. J. Comput. Cogn., 2004, 2, (2), pp. 81–130.
-
2)
-
3)
-
33. Cai, G.L., Tan, Z.M., Zhou, W.H., et al: ‘Dynamical analysis of a new chaotic system and its chaotic control’, Acta Phys. Sin., 2007, 56, (11), pp. 6230–6237.
-
4)
-
12. Kocarev, L.: ‘Chaos-based cryptography: a brief overview’, IEEE Circuits Syst. Mag., 2001, 1, (3), pp. 6–21.
-
5)
-
1. Kapitaniak, T., Chua, L.O., Zhong, G.Q.: ‘Experimental hyperchaos in coupled Chua's circuits’, IEEE Trans. Circuits I, 1994, 41, (7), pp. 499–503.
-
6)
-
35. Kaplan, J.L., Yorke, J.A.: ‘Functional differential equations and approximation of fixed points’ (Springer-Verlag, 1979, 1st edn.).
-
7)
-
30. Matsumoto, T., Chua, L.O., Kobayashi, K.: ‘Hyperchaos: laboratory experiment and numerical confirmation’, IEEE Trans. Circuits I, 1986, 33, (11), pp. 1143–1147.
-
8)
-
18. Wang, K., Pei, W.J., Xia, H.S., et al: ‘Pseudo-random number generator based on asymptotic deterministic randomness’, Phys. Lett. A, 2008, 372, pp. 4388–4394.
-
9)
-
37. Li, S.J., Mou, X.Q., Cai, Y.L.: ‘Pseudo-random bit generator based on couple chaotic systems and its applications in stream-cipher cryptography’. INDOCRYPT, Berlin, 2001 (, 2247), p. 316.
-
10)
-
41. Cover, T.M., Thomas, J.A.: ‘Elements of information theory’ (John Wiley & Sons Inc., Hoboken, 2006, 2nd edn.).
-
11)
-
7. Pareek, N.K., Patidar, V., Sud, K.K.: ‘Discrete chaotic cryptography using external key’, Phys. Lett. A, 2003, 309, (1–2), pp. 75–82.
-
12)
-
36. Sang, T., Wang, R.L., Yan, Y.X.: ‘Perturbance-based algorithm to expand cycle length of chaotic key stream’, Electron. Lett., 1998, 34, (9), pp. 873–874.
-
13)
-
29. Rössler, O.E.: ‘An equation for hyperchaos’, Phys. Lett. A, 1979, 71, (2–3), pp. 155–157.
-
14)
-
23. Özkaynaka, F., Yavuz, S.: ‘Security problems for a pseudorandom sequence generator based on the Chen chaotic system’, Comput. Phys. Commun., 2013, 184, (9), pp. 2178–2181.
-
15)
-
6. Swathy, P.S., Thamilmaran, K.: ‘Hyperchaos in SC-CNN based modified canonical Chua's circuit’, Nonlinear Dyn., 2014, 78, (4), pp. 2639–2650.
-
16)
-
16. Dachselt, F., Kelber, K., Vandewalle, J., et al: ‘Chaotic versus classical stream ciphers – a comparative study’. Proc. Int. Symp. Circuits and Systems, Monterey, CA, June 1998, vol. 4, pp. 518–521.
-
17)
-
13. Dachselt, F., Schwarz, W.: ‘Chaos and cryptography’, IEEE Trans. Circuits I, 2001, 48, (12), pp. 1498–1509.
-
18)
-
5. Hu, G.S.: ‘Hyperchaos of higher order and its circuit implementation’, Int. J. Circuits Theory Appl., 2011, 39, (1), pp. 79–89.
-
19)
-
15. Sankpal, P.R., Vijaya, P.A.: ‘Image encryption using chaotic maps: a survey’. Fifth Int. Conf. Signal and Image Processing, Jeju Island, South Korea, July 2014, pp. 102–107.
-
20)
-
42. James, F.: ‘Chaos and randomness’, Chaos Soliton Fractals, 1995, 6, pp. 221–226.
-
21)
-
26. Qi, G.Y., Van Wyk, M.A., Van Wyk, B.J., et al: ‘On a new hyperchaotic system’, Phys. Lett. A, 2008, 372, pp. 124–136.
-
22)
-
3. Ogorzalek, M.J.: ‘Taming chaos – part I: synchronization’, IEEE Trans. Circuits I, 1993, 40, (10), pp. 693–699.
-
23)
-
17. Millerioux, G., Maria Amigo, J., Daafouz, J.: ‘A connection between chaotic and conventional cryptography’, IEEE Trans. Circuits I, 2008, 55, (6), pp. 1695–1703.
-
24)
-
47. Jeng, F.G., Huang, W.L., Chen, T.H.: ‘Cryptanalysis and improvement of two hyper-chaos- based image encryption schemes’, Signal Process., Image, 2015, 34, pp. 45–51.
-
25)
-
44. Persohn, K.J., Povinelli, R.J.: ‘Analyzing logistic map pseudorandom number generators for periodicity induced by finite precision floating-point representation’, Chaos Soliton Fractals, 2012, 45, (3), pp. 238–245.
-
26)
-
43. Sheng, L.Y., Xiao, Y.Y., Sheng, Z.: ‘A universal algorithm for transforming chaotic sequences into uniform pseudo-random sequences’, Acta Phys. Sin., 2008, 57, (7), pp. 4007–4013.
-
27)
-
11. Li, J.H., Liu, H.: ‘Colour image encryption based on advanced encryption standard algorithm with two-dimensional chaotic map’, IET Inf. Sec., 2013, 7, (4), pp. 265–270.
-
28)
-
21. Wang, X.Y., Qin, X.: ‘A new pseudo-random number generator based on CML and chaotic iteration’, Nonlinear Dyn., 2012, 70, (2), pp. 1589–1592.
-
29)
-
2. Pecora, L.M., Carroll, T.L.: ‘Synchronization in chaotic systems’, 1990, 64, (8), pp. 821–824.
-
30)
-
34. Lu, K.: ‘Chaos dynamics’ (Shanghai Translation Publishing House, Shanghai, 1990, 1st edn.).
-
31)
-
10. Barakat, L.M., Mansingka, A.S., Radwan, A.G.: ‘Hardware stream cipher with controllable chaos generator for colour image encryption’, IET Image Process., 2014, 8, (1), pp. 33–43.
-
32)
-
48. Özkaynak, F., Özer, A.B., Yavuz, S.: ‘Cryptanalysis of a novel image encryption scheme based on improved hyperchaotic sequences’, Opt. Commun., 2012, 285, (24), pp. 4946–4948.
-
33)
-
32. Liu, M.H., Feng, J.C., Tse, C.K.: ‘A new hyperchaotic system and its circuit implementation’, Int. J. Bifurcation Chaos, 2010, 20, (4), pp. 1201–1208.
-
34)
-
28. Meier, W., Staffelbach, O.: ‘The self-shrinking generator’. Advances in Cryptology – EUROCRYPT ’94. Workshop on the Theory and Application of Cryptographic Techniques, Perugia, Italy, May 1994, pp. 205–214.
-
35)
-
22. Hu, H.P., Liu, L.F., Ding, N.D.: ‘Pseudorandom sequence generator based on the Chen chaotic system’, Comput. Phys. Commun., 2013, 184, (3), pp. 765–768.
-
36)
-
31. Li, Y.X., Tang, W.K.S., Chen, G.R.: ‘Generating hyperchaos via state feedback control’, Int. J. Bifurcation Chaos, 2005, 15, (10), pp. 3367–3375.
-
37)
-
49. Zhang, Y.S., Wen, W.Y., Su, M.T., et al: ‘Cryptanalyzing a novel image fusion encryption algorithm based on DNA sequence operation and hyper-chaotic system’, Opt. – Int. J. Light Electron Opt., 2014, 125, (4), pp. 1562–1564.
-
38)
-
25. Qi, G.Y., Sandra, B.M.: ‘Hyper-chaos encryption using convolutional masking and model free unmasking’, Chin. Phys. B., 2014, 23, (5), p. 050507.
-
39)
-
50. Xie, T., Liu, Y.S., Tang, J.: ‘Breaking a novel image fusion encryption algorithm based on DNA sequence operation and hyper-chaotic system’, Opt. – Int. J. Light Electron Opt., 2014, 125, (24), pp. 7166–7169.
-
40)
-
24. Wang, J.Z., Chen, Z.Q., Yuan, Z.Z.: ‘The generation of a hyperchaotic system based on a three-dimensional autonomous chaotic system’, Chin. Phys., 2006, 15, (6), pp. 1216–1225.
-
41)
-
19. Li, H.J., Zhang, J.S.: ‘A novel chaotic stream cipher and its application to palmprint template protection’, Chin. Phys. B, 2010, 19, (4), p. 040505.
-
42)
-
8. Chen, G.R., Mao, Y.B., Chui, C.K.: ‘A symmetric image encryption scheme based on 3D chaotic cat maps’, Chaos Soliton Fractals, 2004, 21, (3), pp. 749–761.
-
43)
-
44)
-
20. Wang, F.L.: ‘A new pseudo-random number generator and application to digital secure communication scheme based on compound symbolic chaos’, Acta Phys. Sin., 2011, 60, (11), p. 110517.
-
45)
-
4. Wu, G.C., Baleanu, D.: ‘Chaos synchronization of the discrete fractional logistic map’, Signal Process., 2014, 102, pp. 96–99.
-
46)
-
40. Tong, X.J., Cui, M.G.: ‘Feedback image encryption algorithm with compound chaotic stream cipher based on perturbation’, Sci. China Inf. Sci., 2010, 53, (1), pp. 191–202.
-
47)
-
46. Rhouma, R., Belghith, S.: ‘Cryptanalysis of a new image encryption algorithm based on hyper-chaos’, Phys. Lett. A., 2008, 372, (38), pp. 5973–5978.
-
48)
-
27. Zhu, C.X.: ‘A novel image encryption scheme based on improved hyperchaotic sequences’, Opt. Commun., 2012, 285, (1), pp. 29–37.
-
49)
-
9. Kanso, A.: ‘Self-shrinking chaotic stream ciphers’, Commun. Nonlinear Sci. Numer. Simul., 2011, 16, (2), pp. 822–836.
-
50)
-
39. Wu, X.J., Bai, C.X., Kan, H.B.: ‘A new color image cryptosystem via hyperchaos synchronization’, Commun. Nonlinear Sci. Numer. Simul., 2014, 19, (6), pp. 1884–1897.
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