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A new concept of compound symbolic chaotic series is proposed. According to the kneading pair series in symbolic dynamics, by compounding a pseudo-random series with sub-series on condition of kneading rules we obtain a new symbolic chaotic series which is then transformed into a pseudo-random binary number (PRN) series. The length of the new PRN series elongates at a speed of geometric procession with iteration number. Theoretical and experimental analyses both prove that the above algorithm provides an effective PRN generator. To apply the algorithm to digital secure communication, a new cellular automata is established. With the automata, the data expansion is avoided, the encryption is finished quickly, the obvious avalanche effect can be produced, and thus the security is improved.
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Keywords:
- compound symbolic chaotic series /
- symbolic dynamics /
- pseudo-random series /
- cellular automata
[1] Wang F L 2010 Chin. Phys. B 19 0605151
[2] Sheng L Y, Xiao Y Y, Sheng Z 2008 Acta Phys. Sin 57 4007(in Chinese)[盛利元、肖燕予、盛 喆 2008 57 4007]
[3] Ping P, Zhao X L, Zhang H, Liu F Y 2008 Acta Phys. Sin. 57 6188(in Chinese) [平 萍、赵学龙、张 宏、刘凤玉 2008 57 6188]
[4] Zhang X, Ren W, Tang D N, Tang G N 2010 Acta Phys. Sin. 59 5281(in Chinese) [张 旭、任 卫、唐冬妮、唐国宁 2010 57 5281]
[5] Liu Y Z, Lin C S, Li X C, Liu H P, Wang Z L 2011 Acta Phys. Sin. 60 030502(in Chinese) [刘扬正、林长圣、李心朝、刘海鹏、王忠林 2011 60 030502]
[6] Guan Z H, David J H, Shen X M 2004 International Conference on Control, Automation, Robotics and Vision, Kunming China 320
[7] Sun F Y, Lu Z W 2011 Acta Phys. Sin. 60 040503(in Chinese) [孙福艳、吕宗旺 2011 60 040503]
[8] Sun F Y, Liu S T 2008 Chaos, Solitons & Fractals 38 631
[9] Sun F Y, Liu S T 2009 Chaos, Solitons & Fractals 41 2216
[10] Sánchez S, Criado R, Vega C 2005 Math. & Coput. Model. 42 809
[11] Wang L, Wang F P, Wang Z J 2006 Acta Phys. Sin. 55 3964 (in Chinese) [王 蕾、汪芙平、王赞基 2006 55 3964]
[12] Almeida J, Peralta S D, Romera M 2005 Physica D 200 124
[13] Zhang R, Xu Z Y, Yang Y Q 2011 Acta Phys. Sin. 60 010515(in Chinese) [张 荣、徐振源、杨永清 2011 60 010515]
[14] Gutowitz H 1994 Method and Apparantus for Encryption, Decryption and Authentication Using Dynamical Systems USA: 5, 395, 589
[15] Li K P, Gao Z Y 2005 Chin. Phys. 14 930
[16] Qian Y S, Shi P J,Zeng Q, Ma C X, Lin F, Sun P, Wang H L 2010 Chin. Phys. B 19 048201
[17] Zhang X, Ren W, Tang D N, Tang G N 2010 Acta Phys. Sin. 59 5281(in Cinese) [张 旭、任 卫、唐冬妮、唐国宁 2010 57 5281]
[18] Wang F L 2010 Advances in Difference Equations Doi:10.1155/2010/985982 Article ID 985982
[19] Zheng Y, Zhang X D 2010 Chin. Phys. B 19 010505
[20] Sheng L Y, Cao L L, Sun K H, Jiang W 2005 Acta Phys. Sin. 54 4031(in Chinese)[盛利元、曹莉凌、孙克辉、闻 姜 2005 54 4031]
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[1] Wang F L 2010 Chin. Phys. B 19 0605151
[2] Sheng L Y, Xiao Y Y, Sheng Z 2008 Acta Phys. Sin 57 4007(in Chinese)[盛利元、肖燕予、盛 喆 2008 57 4007]
[3] Ping P, Zhao X L, Zhang H, Liu F Y 2008 Acta Phys. Sin. 57 6188(in Chinese) [平 萍、赵学龙、张 宏、刘凤玉 2008 57 6188]
[4] Zhang X, Ren W, Tang D N, Tang G N 2010 Acta Phys. Sin. 59 5281(in Chinese) [张 旭、任 卫、唐冬妮、唐国宁 2010 57 5281]
[5] Liu Y Z, Lin C S, Li X C, Liu H P, Wang Z L 2011 Acta Phys. Sin. 60 030502(in Chinese) [刘扬正、林长圣、李心朝、刘海鹏、王忠林 2011 60 030502]
[6] Guan Z H, David J H, Shen X M 2004 International Conference on Control, Automation, Robotics and Vision, Kunming China 320
[7] Sun F Y, Lu Z W 2011 Acta Phys. Sin. 60 040503(in Chinese) [孙福艳、吕宗旺 2011 60 040503]
[8] Sun F Y, Liu S T 2008 Chaos, Solitons & Fractals 38 631
[9] Sun F Y, Liu S T 2009 Chaos, Solitons & Fractals 41 2216
[10] Sánchez S, Criado R, Vega C 2005 Math. & Coput. Model. 42 809
[11] Wang L, Wang F P, Wang Z J 2006 Acta Phys. Sin. 55 3964 (in Chinese) [王 蕾、汪芙平、王赞基 2006 55 3964]
[12] Almeida J, Peralta S D, Romera M 2005 Physica D 200 124
[13] Zhang R, Xu Z Y, Yang Y Q 2011 Acta Phys. Sin. 60 010515(in Chinese) [张 荣、徐振源、杨永清 2011 60 010515]
[14] Gutowitz H 1994 Method and Apparantus for Encryption, Decryption and Authentication Using Dynamical Systems USA: 5, 395, 589
[15] Li K P, Gao Z Y 2005 Chin. Phys. 14 930
[16] Qian Y S, Shi P J,Zeng Q, Ma C X, Lin F, Sun P, Wang H L 2010 Chin. Phys. B 19 048201
[17] Zhang X, Ren W, Tang D N, Tang G N 2010 Acta Phys. Sin. 59 5281(in Cinese) [张 旭、任 卫、唐冬妮、唐国宁 2010 57 5281]
[18] Wang F L 2010 Advances in Difference Equations Doi:10.1155/2010/985982 Article ID 985982
[19] Zheng Y, Zhang X D 2010 Chin. Phys. B 19 010505
[20] Sheng L Y, Cao L L, Sun K H, Jiang W 2005 Acta Phys. Sin. 54 4031(in Chinese)[盛利元、曹莉凌、孙克辉、闻 姜 2005 54 4031]
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