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An improved one-dimensional cellular automata is designed in which the key space is large with pseudo random series on a shift map and perturbed terms and thus data expansion is avoided. Random triggering rules are involved. There is no complex computation, but a large amount of information can be processed every time. The stream cipher generated by the automata is proved to be of ideal randomness and avalanche effect with rapid dispersion velocity of errors. Empirical results show that the stream cipher is perfectly random both globally and locally. The chi-square test(confidence 95%) on a set of stream cipher with a length of 24000 and its 400 time iterations shows that the passing rates of frequencies and series are above 95% and 100%, respectively. To test the sensitivity of the data, 1 bit is changed at any position of the key stream and the average variation rate of total bits is 49.99%, ranging from 49% to 51% (theoretical value is 50%), and variance is 1.193 ·10－5, which means that the automata is a good encryption technique.
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Keywords:
- secure communication /
- cellular automata /
- pseudo-random series
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[2] 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]
[3] 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]
[4] Ding J X, Huang H J 2010 Acta Phys. Sin. 59 3093 (in Chinese) [丁建勋、 黄海军 2010 59 3093]
[5] Qian Y S, Wang H L, Wang C L 2008 Acta Phys. Sin. 57 2115 (in Chinese) [钱勇生、 汪海龙、 王春雷 2008 57 2115]
[6] Wang L, Zhou S H, Yuan J, Ren Y, Shan X M 2007 Acta Phys. Sin. 56 36 (in Chinese) [王 磊、 周淑华、 袁 坚、 任 勇、 山秀明 2007 56 36]
[7] Li K P, Gao Z Y 2005 Chin. Phys. 14 930
[8] Qian Y S, Shi P J, Zeng Q, Ma C X, Lin F, Sun P, Wang H L 2010 Chin. Phys. B 19 048201
[9] Borcherds P H, Mccauley G P 1993 Chaos Soliton. Fract. 3 451
[10] Wang Fulai 2010 Advances in Difference Equations Doi:10.1155/2010/985982 Article ID 985982
[11] Liang H, Lui Q H, Bai F S 2005 Comput. Math. Appl. 49 331
[12] Sobol I M, Levitan Y L 1999 Comput. Math. Applic. 37 33
[13] Wang F L 2010 Chin. Phys. B 19 090505
[14] Hou W, Feng G L, Deng W J, Li J P 2006 Acta Phys. Sin. 57 37 (in Chinese) [侯 威、 封国林、 董文杰、 李建平 2006 55 2663]
[15] Cao Y H, Tung W W, Gao J B Protopopescu V A, Hively L M 2004 Phys . Rev. E 70 217
[16] Wang F L 2010 Chin Phys. B 19 0605151
[17] 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]
[18] Wichmann B A, Hill I D 2006 Comput. Stat. Data Anal. 51 1614
[19] Snchez S, Criado R, Vega C 2005 Math. Coput. Model. 42 809
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[1] Gutowitz H A 1994 Method and Apparantus for Encryption, Decryption and Authentication Using Dynamical Systems USA Patent: 5-395-589
[2] 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]
[3] 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]
[4] Ding J X, Huang H J 2010 Acta Phys. Sin. 59 3093 (in Chinese) [丁建勋、 黄海军 2010 59 3093]
[5] Qian Y S, Wang H L, Wang C L 2008 Acta Phys. Sin. 57 2115 (in Chinese) [钱勇生、 汪海龙、 王春雷 2008 57 2115]
[6] Wang L, Zhou S H, Yuan J, Ren Y, Shan X M 2007 Acta Phys. Sin. 56 36 (in Chinese) [王 磊、 周淑华、 袁 坚、 任 勇、 山秀明 2007 56 36]
[7] Li K P, Gao Z Y 2005 Chin. Phys. 14 930
[8] Qian Y S, Shi P J, Zeng Q, Ma C X, Lin F, Sun P, Wang H L 2010 Chin. Phys. B 19 048201
[9] Borcherds P H, Mccauley G P 1993 Chaos Soliton. Fract. 3 451
[10] Wang Fulai 2010 Advances in Difference Equations Doi:10.1155/2010/985982 Article ID 985982
[11] Liang H, Lui Q H, Bai F S 2005 Comput. Math. Appl. 49 331
[12] Sobol I M, Levitan Y L 1999 Comput. Math. Applic. 37 33
[13] Wang F L 2010 Chin. Phys. B 19 090505
[14] Hou W, Feng G L, Deng W J, Li J P 2006 Acta Phys. Sin. 57 37 (in Chinese) [侯 威、 封国林、 董文杰、 李建平 2006 55 2663]
[15] Cao Y H, Tung W W, Gao J B Protopopescu V A, Hively L M 2004 Phys . Rev. E 70 217
[16] Wang F L 2010 Chin Phys. B 19 0605151
[17] 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]
[18] Wichmann B A, Hill I D 2006 Comput. Stat. Data Anal. 51 1614
[19] Snchez S, Criado R, Vega C 2005 Math. Coput. Model. 42 809
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