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Cryptographic PRNG Based on Combination of LFSR and Chaotic Logistic Map
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Applied Mathematics·Volume 02 (2011)·Pages 1531–1534·Published 5 December 2011·DOI10.4236/am.2011.212217
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Abstract
The random sequence generated by linear feedback shift register can’t meet the demand of unpredictability for secure paradigms. A combination logistic chaotic equation improves the linear property of LFSR and constructs a novel random sequence generator with longer period and complex architecture. We present the detailed result of the statistical testing on generated bit sequences, done by very strict tests of randomness: the NIST suite tests, to detect the specific characteristic expected of truly random sequences. The results of NIST’s statistical tests show that our proposed method for generating random numbers has more efficient performance.
KeywordsRandom Bit GeneratorCombinationChaoticLogistic EquationsLFSRNIST Suite Tests
- R. C. Fair?eld, R. L. Mortenson and K. B. Coulthart, “An LSI Random Number Generator (RNG),” Advances in Cryptography: Proceeding of Cryptography 84, Vol. 196, 1984, pp. 203-230.
- S. Callegari, R. Rovatti and G. Setti, “Embeddable ADC-Based True Random Number Generator for Cryptographic Applications Exploiting Nonlinear Signal Processing and Chaos,” Signal Processing IEEE Transactions, Vol. 53, No. 2, 2005, pp. 793-805. doi:10.1109/TSP.2004.839924
- K. Tsoi, K. Leung and P. Leong, “Compact FPGA-Based True and Pseudo Random Number Generators,” Proceedings of IEEE Symposium on Field-Programmable Custom Computing Machines (FCCM), 9-11 April 2003, pp. 51-61.
- H. Zhang, Y. Wang, B. Wang and X. Wu, “Evolutionary Random Sequence Generators Based on LFSR,” Wuhan University Journal of Natural Sciences, Vol. 12, No. 1, 2007, pp. 75-78.
- T. Stojanovski, J. Pil and L. Kocarev, “Chaos-Based Random Number Generators. Part II: Practical Realization,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, Vol. 48, No. 3, 2001, pp. 382-385. doi:10.1109/81.915396
- M. Sharaf, H. A. K. Mansour and H. H. Zayed, “A Complex Linear Feedback Shift Register Design for the A5 Key Stream Generator,” Proceedings of the Twenty-Second National Radio Science Conference (NRSC 2005), Cairo, 15-17 March 2005, pp. 395-402. doi:10.1109/NRSC.2005.194024
- L. C. Reese, W. M. Isenhower and S.-T. Wang. “Analysis and Design of Shallow and Deep Foundations,” John Wiley & Sons, New York, 2006.
- L. Y. Deng and Y. C. Chu, “Combining Random Number Generators,” Proceedings of the 23rd Conference on Winter Simulation, 1991, pp. 1043-1046.
- A. Reese, “Random Number Generators in Genetic Algorithms for Unconstrained and Constrained Optimization,” Nonlinear Analysis, Vol. 71, 2009, pp. 679-692. doi:10.1016/j.na.2008.11.084
- M. Babaei and M. Ramyar, “Improved Performance of LFSR’s System with Discrete Chaotic Iterations,” Word Applied Science Journal (ISI), Vol. 13, No. 7, 2011, pp. 1720-1725.
- NIST Special Publication 800-22, Statistical Test Suite for Random and Pseudo Random Number Generators for Cryptographic Applications, Available at http://www.nist.gov