Origin of Randomness on Chaos Neural Network
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 conta
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Faculty of Education, Iwate University, Ueda, Morioka, Iwate 020-8550, Japan {hitoaki,e0112007}@iwate-u.ac.jp 2 Technical Division, Iwate University, Morioka, Japan [email protected] 3 Super-Computing and Information Sciences Center, Iwate University, Morioka, Japan [email protected]
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. Keywords: Chaos
Pseudo-random number Chaos neural network Cipher
1 Introduction Cipher for consumer use has been important as the Internet community has developed; for protection of personal information and privacy, for prevention against information leakage and so on. We have continuously studied on the chaos neural network (CNN) that consists of conventional artificial neurons and generates chaotic outputs [1–3]. Recently, we have reported a high-speed (more than 300 Gbps with GPGPU) and highly secure novel pseudo-random number generator based on CNN. In particular, the period of the pseudo-random number (PRN) series is more than 109726 ( 232308) [4]. A period of theoretical chaos is generally infinite, but it is not true in computer generated chaos. The time series from CNN is chaotic but also eventually periodic. The CNN pseudo-random number generator (CNN-PRNG) is expected to apply to a high-speed and highly secure stream cipher [4, 5]. In this paper, we have investigated properties of chaos time series and corresponding PRNs, and proposed a mechanism of random number generation, and then a hypothesis on the origin of randomness. Improved methods of random number generation also have been proposed, according to the hypothesis.
© Springer International Publishing Switzerland 2016 H. Fujita et al. (Eds.): IEA/AIE 2016, LNAI 9799, pp. 587–598, 2016. DOI: 10.1007/978-3-319-42007-3_51
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2 Deterministic Chaos as Pseudo-random Number Generator Pseudo-random number generators (PRNGs) based on chaotic time series have been reported so far. Chaotic time series, however, do not always show uniform distribution, and adjacent PRNs show a strong correlation (or determinism). As for the time series from a logistic map some improved methods have proposed as follows: (i) direct transformation of the series to uniform PRN series [6, 7] (ii) using a threshold the series transform to uniform 1 bit binary number [8, 9] (iii) a part of a mantissa is extracted from the series as uniform PRN [10]. The correlation should be reduced by some other method as to (i), (ii). While, (iii) is also useful method of reducing the correlation [4, 5, 10]. These methods (i–iii), however, the origin of randomness is still un
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