Abstract
We have proposed a hypothesis on the origin of randomness in the chaos time series of a chaos neural network (CNN) according to empirical results. An improved pseudo-random number generator (PRNG) has been proposed on the basis of the hypothesis and contamination mechanisms. PRNG has been implemented also with the fixed-point arithmetic (Q5.26). The result is expected to apply to embedded systems; for example the application of protecting personal information in smartphone and other mobile devices.
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References
Yoshida, H., Yoneki, K., Tsunekawa, Y., Miura, M.: Chaos neural network. In: Proceedings of Papers, ISPACS 1996, vol. l of 3, pp. 16.1.1–16.1.5 (1996)
Yoshida, H., Nihei, Y., Nakanishi, T.: Comparative study on structurally different chaos neural networks. In: Proceedings of Papers, ISITA 2004, pp. 1046–1050 (2004)
Nihei, Y., Nakanishi, T., Yoshida, H.: Time series analysis for chaos neural network. Tech. Rep. IEICE 104, 7–10 (2004)
Yoshida, H., Murakami, T., Liu, Z.: High-speed and highly secure pseudo-random number generator based on chaos neural network. In: Proceedings of Papers, ICSSE 2015, pp. 224–237 (2015)
Kawamura, S., Yoshida, H., Miura, M., Abe, M.: Implementation of uniform pseudo random number generator and application to stream cipher based on chaos neural network. In: Proceedings of Papers, ICFS 2002, R-18, pp. 4–9 (2002)
Ulam, S.M., von Neumann, J.: On combination of stochastic deterministic processes. Bull. AMS 53, 1120 (1947)
Phatak, S.C., Rao, S.S.: Logistic map: a possible random-number generator. Phys. Rev. E 51(4), 3670–3678 (1995)
Kohda, T., Ogata, E.: Bernoulli trials and chaotic trajectories in the logistic map. IEICE Trans. Fundam. J68-A(2), 146–152 (1985)
Kozak, J.J., Musho, M.K., Hartlee, M.D.: Chaos, periodic chaos, and the random-walk problem. Phys. Rev. Lett. 49, 1801–1804 (1982)
Watanabe, H., Kanada, Y.: Pseudorandom Numbers generator using logistic map. In: Proceedings of the 53th National Convention of IPSJ, pp. 65–66 (1996)
Yoshida, H., Murakami, T.: Japan patent JP5504501B (2014)
Komori, T., Yi, H., Nakanishi, T., Murakami, T., Yoshida, H.: Behavior analysis of chaos neural network with simplification of nonlinear function. Tech. Rep. IEICE 109, 53–58 (2009)
Soto, J., Bassham, L.: Randomness Testing of the Advanced Encryption Standard Finalist Candidates. National Institute of Standards and Technology (NIST) (2000)
Rukhin, A., Soto, J., Nechvatal, J., Smid, M., Barker, E., Leigh, S., Levenson, M., Vangel, M., Banks, D., Heckert, A., Dray, J., Vo, S.: A statistical test suite for random and pseudorandom number generators for cryptographic applications, NIST SP800-22 rev.1a, Accessed July 2015 (sts-2.1.1). Lawrence E. Bassham III (2015)
Yoshida, H., Murakami, T., Kawamura, S.: Study on testing for randomness of pseudo-random number sequence with NIST SP800-22 rev. la. Tech. Rep. IEICE 110, 13–18 (2012)
Yoshida, H., Ohira, O., Taira, H., Nakanishi, T.: Fractal analysis of chaos neural network outputs in transient state and steady state. In: Proceedings of Papers, NOLTA 2006, pp. 103–106 (2006)
Horai, S., Yamada, T., Aihara, K.: Determinism analysis with Iso-directional recurrence plots. IEEE Trans. – Inst. Electr. Eng. Jpn. C122, 141–147 (2002)
Coron, J.-S., Naccache, D.: An accurate evaluation of Maurer’s Universal test. In: Tavares, S., Meijer, H. (eds.) SAC 1998. LNCS, vol. 1556, pp. 57–71. Springer, Heidelberg (1999)
Okutomi, H., Nakamura, K., Aihara, K.: A study on rational judgement method of randomness property using NIST randomness test (NIST SP.800-22). IEICE Trans. Fundam. J93-A(1), 11–22 (2010)
Lasota, A., Mackey, M.C.: Probabilistic Properties of Deterministic Systems. Cambridge University Press, Cambridge (1985)
Aihara, K. (ed.): Basics and Application of Chaos Time Series Analysis. Sangyo Tosho, Tokyo (2000)
Thompson, J.M.T., Stewart, H.B.: Nonlinear Dynamics and Chaos: Geometrical Methods for Engineers and Scientists. Wiley, Chichester (1986)
Murakami, T., Kawamura, S., Yoshida, H.: Prediction of periods on chaos time series: dependence on precision of chaos neural network outputs. Tech. Rep. IEICE 107, 21–26 (2008)
Acknowledgements
The calculations in this study have performed with the SGI UV-100 and the GPGPU computers in Iwate University Super-Computing and Information Sciences Center (ISIC). Special thanks to Mr. Mitsuaki SASAKI for help with experiments.
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Yoshida, H., Murakami, T., Inao, T., Kawamura, S. (2016). Origin of Randomness on Chaos Neural Network. In: Fujita, H., Ali, M., Selamat, A., Sasaki, J., Kurematsu, M. (eds) Trends in Applied Knowledge-Based Systems and Data Science. IEA/AIE 2016. Lecture Notes in Computer Science(), vol 9799. Springer, Cham. https://doi.org/10.1007/978-3-319-42007-3_51
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