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A novel true random number generator based on mouse movement and a one-dimensional chaotic map. (English) Zbl 1264.65007

Summary: We propose a novel true random number generator using mouse movement and a one-dimensional chaotic map. We utilize the \(x\)-coordinate of the mouse movement to be the length of an iteration segment of our TRNs and the \(y\)-coordinate to be the initial value of this iteration segment. And, when it iterates, we perturb the parameter with the real value produced by the TRNG itself. And we find that the TRNG we proposed conquers several flaws of some former mouse-based TRNGs. At last we take experiments and test the randomness of our algorithm with the NIST statistical test suite; results illustrate that our TRNG is suitable to produce true random numbers (TRNs) on universal personal computers (PCs).

MSC:

65C10 Random number generation in numerical analysis
37N35 Dynamical systems in control
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[1] D. E. Knuth, The Art of Computer Programming. Vol. 2: Seminumerical Algorithms, Addison-Wesley, Reading, Mass, USA, 2nd edition, 1981. · Zbl 0477.65002
[2] G. Jakimoski and L. Kocarev, “Chaos and cryptography: block encryption ciphers based on chaotic maps,” IEEE Transactions on Circuits and Systems. I, vol. 48, no. 2, pp. 163-169, 2001. · Zbl 0998.94016 · doi:10.1109/81.904880
[3] R. L. Rivest, A. Shamir, and L. Adleman, “A method for obtaining digital signatures and public-key cryptosystems,” Communications of the Association for Computing Machinery, vol. 21, no. 2, pp. 120-126, 1978. · Zbl 0368.94005 · doi:10.1145/359340.359342
[4] B. Wang, Q. Wu, and Y. Hu, “A knapsack-based probabilistic encryption scheme,” Information Sciences, vol. 177, no. 19, pp. 3981-3994, 2007. · Zbl 1142.94361 · doi:10.1016/j.ins.2007.03.010
[5] F. Cao and Z. Cao, “A secure identity-based proxy multi-signature scheme,” Information Sciences, vol. 179, no. 3, pp. 292-302, 2009. · Zbl 1156.94337 · doi:10.1016/j.ins.2008.05.039
[6] D. Xiao, X. Liao, and S. Deng, “A novel key agreement protocol based on chaotic maps,” Information Sciences, vol. 177, no. 4, pp. 1136-1142, 2007. · Zbl 05127742 · doi:10.1016/j.ins.2006.07.026
[7] D. Xiao, X. Liao, and S. Deng, “Using time-stamp to improve the security of a chaotic maps-based key agreement protocol,” Information Sciences, vol. 178, no. 6, pp. 1598-1602, 2008. · Zbl 1131.94017 · doi:10.1016/j.ins.2007.11.001
[8] C. Tokunaga, D. Blaauw, and T. Mudge, “True random number generator with a metastability-based quality control,” IEEE Journal of Solid-State Circuits, vol. 43, no. 1, pp. 78-85, 2008.
[9] M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanonuovo, “A high-speed oscillator-based truly random number source for cryptographic applications on a smart card IC,” IEEE Transactions on Computers, vol. 52, no. 4, pp. 403-409, 2003. · doi:10.1109/TC.2003.1190581
[10] D. Davis, R. Ihaka, and P. Fenstermacher, “Cryptographic randomness from air turbulence in disk drives,” Advances in Cryptology, vol. 839, pp. 114-120, 1994. · Zbl 0939.94521
[11] W. T. Holman, J. Alvin Connelly, and A. B. Dowlatabadi, “An integrated analog/digital random noise source,” IEEE Transactions on Circuits and Systems I, vol. 44, no. 6, pp. 521-528, 1997.
[12] Y. Hu, X. Liao, K. W. Wong, and Q. Zhou, “A true random number generator based on mouse movement and chaotic cryptography,” Chaos, Solitons and Fractals, vol. 40, no. 5, pp. 2286-2293, 2009. · doi:10.1016/j.chaos.2007.10.022
[13] Q. Zhou, X. Liao, K.-W. Wong, Y. Hu, and D. Xiao, “True random number generator based on mouse movement and chaotic hash function,” Information Sciences, vol. 179, no. 19, pp. 3442-3450, 2009. · Zbl 05610263 · doi:10.1016/j.ins.2009.06.005
[14] J. M. Aguirregabiria, “Robust chaos with variable Lyapunov exponent in smooth one-dimensional maps,” Chaos, Solitons and Fractals, vol. 42, no. 4, pp. 2531-2539, 2009. · Zbl 1198.93004 · doi:10.1016/j.chaos.2009.03.196
[15] Z. Hong and L. Xieting, “Generating chaotic secure sequences with desired statistical properties and high security,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 7, no. 1, pp. 205-213, 1997. · Zbl 0884.94013 · doi:10.1142/S0218127497000145
[16] P. Li, Z. Li, S. Fettinger, Y. Mao, and W. A. Halang, “Application of chaos-based pseudo-random-bit generators in internet-based online payments,” Studies in Computational Intelligence, vol. 37, pp. 667-685, 2007. · doi:10.1007/978-3-540-37017-8_31
[17] C. Ling and S. G. Sun, “4-phase spreading sequences by chaotic maps for CDMA,” Journal of China Institute of Communications, vol. 19, no. 3, pp. 40-44, 1998.
[18] T. Kohda and A. Tsuneda, “Statistics of chaotic binary sequences,” IEEE Transactions on Information Theory, vol. 43, no. 1, pp. 104-112, 1997. · Zbl 0871.94021 · doi:10.1109/18.567654
[19] NIST, “A statistical test suite for random and pseudo-random number generators for cryptographic applications,” 2010, http://csrc.nist.gov/publications/nistpubs/800-22-rev1a/SP800-22rev1a.pdf.
[20] “NIST Special Publication 800-22,” 2001, http://csrc.nist.gov/rng/rng2.html.
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