This paper presents a new multioutput and high throughput pseudorandom number generator. The scheme is to make the homogenized Logistic chaotic sequence as unified hyperchaotic system parameter. So the unified hyperchaos can transfer in different chaotic systems and the output can be more complex with the changing of homogenized Logistic chaotic output. Through processing the unified hyperchaotic 4-way outputs, the output will be extended to 26 channels. In addition, the generated pseudorandom sequences have all passed NIST SP800-22 standard test and DIEHARD test. The system is designed in Verilog HDL and experimentally verified on a Xilinx Spartan 6 FPGA for a maximum throughput of 16.91？Gbits/s for the native chaotic output and 13.49？Gbits/s for the resulting pseudorandom number generators. 1. Introduction Pseudorandom number (PN) is the 01 sequence which has the randomness similar to noise. It has been widely used in digital communication, cryptography, computer games, and numerical computation [1–3]. Chaos is the phenomenon which shows very complex nonlinear dynamic characteristics in a deterministic system. And it has excellent properties such as nonperiodicity, broad bandwidth, and sensitivity to initial value [4, 5]. So Chaos and PN have a natural link. And compared to other PN sequences like m sequences, and so forth, the PN sequence generated by chaotic system has advantages like larger key space, longer cycle, and so forth. Currently, researches of chaotic pseudorandom number generator (PRNG) are more focused on the digital implementation of low dimensional chaos such as Logistic chaos, Tent chaos, and Lorenz chaos. While these algorithms have significant advantages in some respects, like simpler construction, fewer resources consuming, and faster computing speed, they also have the fatal weakness that cannot be ignored to PRNG like smaller secret key space, periodic problem, and relatively lower throughput. Therefore, implementing a PRNG based on higher-order chaos equations seems more advantage because the hyperchaos has multiple positive Lyapunov exponent and more controllable parameters and the output of system will have more complex randomness. The hyperchaotic encryption signal is harder to decode than low dimensional encryption signal [6]. And hyperchaos can provide multiple outputs, improve the throughput, and process multiple target signal [7, 8]. In 2002, Lu et al. proposed the unified chaos that can make Lorenz chaos, Lu chaos, and Chen chaos into a unified chaotic system and realize continued transition from one to another [9]. In
References
[1]
Q. Rong and Y. Fang, “Pseudo random sequence generator based on variable structure chaos,” Modern Electronics Technique, vol. 35, no. 11, pp. 64–67, 2012.
[2]
H. P. Ren, The design of chaotic key system based on FPGA [M.S. dissertation], Dalian Maritime University, Ganjingzi, China, 2011.
[3]
P. Dabal and R. Pelka, “FPGA implementation of chaotic pseudo-random bit generators,” in Proceedings of the 19th International Conference on Mixed Design of Integrated Circuits and Systems (MIXDES '12), pp. 260–264, Warsaw, Poland, May 2012.
[4]
P. Li, Z. Li, W. A. Halang, and G. Chen, “A multiple pseudorandom-bit generator based on a spatiotemporal chaotic map,” Physics Letters A, vol. 349, no. 6, pp. 467–473, 2006.
[5]
K. Wang, W. Pei, H. Xia, and Y. Cheung, “Pseudo-random number generator based on asymptotic deterministic randomness,” Physics Letters A, vol. 372, no. 24, pp. 4388–4394, 2008.
[6]
H. Wang, L. Cheng, and J.-H. Peng, “Application of hyperchaos to encrypting digital signals,” Journal of Northeast Normal University (Natural Science Edition), vol. 32, no. 2, pp. 31–35, 2000.
[7]
A. S. Mansingka, M. Affan Zidan, M. L. Barakat, A. G. Radwan, and K. N. Salama, “Fully digital jerk-based chaotic oscillators for high throughput pseudo-random number generators up to 8.77 Gbits/s,” Microelectronics Journal, vol. 44, no. 9, pp. 744–752, 2013.
[8]
F. Jin-Qing, “Several advances in chaos-based communication and research of information security associated with networks,” Journal of Systems Engineering, vol. 25, no. 6, pp. 725–741, 2010.
[9]
J. H. Lu, G. R. Chen, and D. Z. Cheng, “Bridge the gap between the Lorenz system and the Chen system,” International Journal of Bifurcation and Chaos, vol. 12, no. 12, pp. 2917–2926, 2002.
[10]
C. Ma and X. Wang, “Bridge between the hyperchaotic Lorenz system and the hyperchaotic Chen system,” International Journal of Modern Physics B, vol. 25, no. 5, pp. 711–721, 2011.
[11]
S. Li-Yuan, X. Yan-Yu, and Z. Sheng, “How homogenize Chaos-based Pseudo-random sequences,” in Proceedings of the International Conference on Computer Science and Software Engineering (CSSE '08), pp. 793–796, December 2008.
[12]
A. Rukhin, J. Soto, M. Smid et al., “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Special Publication 800-22, 2010.
[13]
M. A. Zidan, A. G. Radwan, and K. N. Salama, “The effect of numerical techniques on differential equation based chaotic generators,” in Proceedings of the 23rd International Conference on Microelectronics (ICM '11), pp. 1–4, Hammamet, Tunisia, December 2011.
[14]
A. Pande and J. Zambreno, “A chaotic encryption scheme for real-time embedded systems: design and implementation,” Telecommunication Systems, vol. 52, no. 2, pp. 551–561, 2013.
[15]
L. Wang, W. Liu, H. Shi, and J. M. Zurada, “Cellular neural networks with transient chaos,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 54, no. 5, pp. 440–444, 2007.
[16]
B. Zhang, Performance analysis and optimization of chaotic PN sequence [M.S. thesis], Hangzhou Dianzi University, Jianggan, China, 2009.
[17]
M. L. Barakat, A. S. Mansingka, A. G. Radwan, and K. N. Salama, “Generalized hardware post-processing technique for chaos-based pseudorandom number generators,” ETRI Journal, vol. 35, no. 3, pp. 448–458, 2013.
[18]
S. Chen, T. Hwang, and W. Lin, “Randomness enhancement using digitalized modified logistic map,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 57, no. 12, pp. 996–1000, 2010.
[19]
C.-Y. Li, T.-Y. Chang, and C.-C. Huang, “A nonlinear PRNG using digitized logistic map with self-reseeding method,” in Proceedings of the International Symposium on VLSI Design, Automation and Test (VLSI-DAT '10), pp. 108–111, April 2010.
[20]
S.- L. Chen, T. Hwang, S.-M. Chang, and W.-W. Lin, “A fast digital chaotic generator for secure communication,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 20, no. 12, pp. 3969–3987, 2010.
