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In this paper, a class of topologically conjugated maps of tent map is established, and the sampling rule is proved to generate the independently and uniformly distributed key streams. One example is given to show that the established chaotic system does not converge into zero in each parameter due to its nonlinear characteristic. Another example with different initial values and lengths of sequence is illustrated, in which the chaotic key stream generated by the proposed theorem is independently and uniformly distributed chaotic system and can successfully satisfy the randomness requirements in Federal Information Processing Standard 140-2(FIPS PUB 140-2) and National Institute of Standards and Technology Special Publication 800-22 (NIST SP800-22) test. The result in this paper can provide the theoretical foundation and more selections of systems to generate independently and uniformly distributed chaotic key stream.
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Keywords:
- independent and identically distributed /
- chaotic system /
- tent map /
- topologically conjugate
[1] Hu H P, Liu S H, Wang Z X, Wu X G 2004 Chin. J. Comput. 27 408 (in Chinese) [胡汉平, 刘双红, 王祖喜, 吴晓刚 2004计算机学报 27 408]
[2] Xiang F, Qiu S S 2008 Acta Phys. Sin. 57 6132 (in Chinese) [向菲, 丘水生 2008 物理学报 57 6132]
[3] Hao B L 1995 Starting with Parabola: An Introduction to Chaotic Dynamics (Shanghai: Shanghai Scientific and Technological Education Publishing House) pp12-15 (in Chinese) [郝柏林 1995 从抛物线谈起––混沌动力学引论(上海: 上海科技教育出版社) 第12–15页]
[4] Alvarez G, Li S 2006 Int. J. Bifurcat. Chaos 16 2129
[5] Lian S G, Sun J S, Wang J W, Wang Z Q 2007 Chaos, Solitons and Fractals 34 851
[6] Phatak S, Rao S 1995 Phys. Rev. E 51 3670
[7] Kanso A, Smaoui N 2009 Chaos, Solitons and Fractals 40 2557
[8] Kocarev L, Jakimoski G 2003 IEEE Trans. CAS-I 50 123
[9] Li J B, Zeng Y C, Chen S B, Chen J S 2011 Acta Phys. Sin. 60 060508 (in Chinese) [ 李家标, 曾以成, 陈仕必, 陈家胜2011 物理学报 60 060508]
[10] Sun F Y, L Z W 2011 Acta Phys. Sin. 60 040503 (in Chinese) [孙福艳, 吕宗旺2011 物理学报 60 040503]
[11] Luo S J, Qiu S S, Luo K Q 2003 Acta Phys. Sin. 52 1871 (in Chinese) [罗松江, 丘水生, 骆开庆 2003 物理学报 52 1871]
[12] Luca A, Vlad A 2005 In Proc. IEEE Int. Symposium on Signals, Circuits and Systems (ISSCS 2005) Iasi, Romania, July 14-15, 2005 p227
[13] Luca A, Vlad A, Badea B, Frunzete M 2009 In Proc. IEEE Int. Symposium on Signals, Circuits and Systems (ISSCS 2009) Iasi, Romania, July 9-10, 2009 p1
[14] Luca A, Ilyas A, Vlad A 2011 In Proc. IEEE Int. Symposium on Signals, Circuits and Systems (ISSCS 2011) Bucharest, Romania, June 30-July 1, 2001 p1
[15] Liu X B, Zhao D A, Zhu Z Y 2006 J. Jiangsu Univ. Sci. Technol. (Natural Science Edition) 20 4 (in Chinese) [刘新波, 赵德安, 朱志宇2006 江苏科技大学学报(自然科学版) 20 4]
[16] Pincus S M 1991 In Proc. of the National Academy of Sciences of the United States of America 88 2297
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[1] Hu H P, Liu S H, Wang Z X, Wu X G 2004 Chin. J. Comput. 27 408 (in Chinese) [胡汉平, 刘双红, 王祖喜, 吴晓刚 2004计算机学报 27 408]
[2] Xiang F, Qiu S S 2008 Acta Phys. Sin. 57 6132 (in Chinese) [向菲, 丘水生 2008 物理学报 57 6132]
[3] Hao B L 1995 Starting with Parabola: An Introduction to Chaotic Dynamics (Shanghai: Shanghai Scientific and Technological Education Publishing House) pp12-15 (in Chinese) [郝柏林 1995 从抛物线谈起––混沌动力学引论(上海: 上海科技教育出版社) 第12–15页]
[4] Alvarez G, Li S 2006 Int. J. Bifurcat. Chaos 16 2129
[5] Lian S G, Sun J S, Wang J W, Wang Z Q 2007 Chaos, Solitons and Fractals 34 851
[6] Phatak S, Rao S 1995 Phys. Rev. E 51 3670
[7] Kanso A, Smaoui N 2009 Chaos, Solitons and Fractals 40 2557
[8] Kocarev L, Jakimoski G 2003 IEEE Trans. CAS-I 50 123
[9] Li J B, Zeng Y C, Chen S B, Chen J S 2011 Acta Phys. Sin. 60 060508 (in Chinese) [ 李家标, 曾以成, 陈仕必, 陈家胜2011 物理学报 60 060508]
[10] Sun F Y, L Z W 2011 Acta Phys. Sin. 60 040503 (in Chinese) [孙福艳, 吕宗旺2011 物理学报 60 040503]
[11] Luo S J, Qiu S S, Luo K Q 2003 Acta Phys. Sin. 52 1871 (in Chinese) [罗松江, 丘水生, 骆开庆 2003 物理学报 52 1871]
[12] Luca A, Vlad A 2005 In Proc. IEEE Int. Symposium on Signals, Circuits and Systems (ISSCS 2005) Iasi, Romania, July 14-15, 2005 p227
[13] Luca A, Vlad A, Badea B, Frunzete M 2009 In Proc. IEEE Int. Symposium on Signals, Circuits and Systems (ISSCS 2009) Iasi, Romania, July 9-10, 2009 p1
[14] Luca A, Ilyas A, Vlad A 2011 In Proc. IEEE Int. Symposium on Signals, Circuits and Systems (ISSCS 2011) Bucharest, Romania, June 30-July 1, 2001 p1
[15] Liu X B, Zhao D A, Zhu Z Y 2006 J. Jiangsu Univ. Sci. Technol. (Natural Science Edition) 20 4 (in Chinese) [刘新波, 赵德安, 朱志宇2006 江苏科技大学学报(自然科学版) 20 4]
[16] Pincus S M 1991 In Proc. of the National Academy of Sciences of the United States of America 88 2297
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