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The Cryptographic Properties of Von Neumann Cellular Automata

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Abstract (2. Language): 
In this paper it is shown that two-dimensional cellular automata with Von Neumann neighborhoods are not suitable for cryptographic purposes. This result is obtained after analyzing the most important cryptographic properties of boolean functions defining their local transition rules
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REFERENCES

References: 

[1] I. Damgard, A design principle for hash functions, in Advances in Cryptology: Proc. of
Crypto’89 (G. Brassard, Ed.), Lect. Notes Comput. Sci. 435: 416-427 1990.
[2] J.H. Evertse, Linear structures in block ciphers, in Advances in Cryptology, Proc. of Eurocrypt’
87 (D. Chaum, W. L. Price, Eds.), Lect. Notes Comput. Sci. 304: 249–266 1988.
[3] A. Fúster, P. Caballero, On the Use of Cellular Automata in Symmetric Cryptography.
Acta Appl. Math. 93, 2: 215–236, 2006.
[4] X. Lai, Higher order derivatives and differential cryptanalysis, in Communications and
Cryptology, Kluwer Academic Publishers, p. 227-233. 1994.
[5] L.R. Knudsen, Truncated and higher order differentials, in Proc. of 2nd FSE (B. Preneel,
Ed.), Lect. Notes Comput. Sci. 1008: 196–211. 1995.
[6] B. Martin, A Walsh exploration of elementary CA rules. J. Cellular Automata 3, 2: 145–
156. 2008.
[7] A. Martín del Rey, J. Pereira Mateus, G. Rodríguez Sánchez, A secret sharing scheme
based on cellular automata. Appl. Math. Comput. 170: 1356-1364. 2005.
[8] A. Martín del Rey, A. Queiruga Dios, G. Rodríguez Sánchez, A (2,n)-secret sharing
scheme based on linear cellular automata. Int. J. Mod. Phys. C 19, 10: 1529-1535. 2008.
[9] A. J. Menezes, P. C. van Oorschot, S. A. Vanstone, Handbook of Applied Cryptography,
CRC Press, Boca Raton, FL, 1997.
[10] M. Mukherjee, N. Ganguly, P.P. Chaudhuri, Cellular automata based authentication. in
Proc. of ACRI 2002 (S. Bandini, B. Chopard, M. Tomassini, Eds.), Lect. Notes Comput. Sci.
2493: 259-269. 2002.
[11] B. Preneel, W. Van Leekwijck, L. Van Linden, R. Govaerts, J. Vandevalle, Propagation
characteristic of boolean functions. in Advances in Cryptology, Proc. of Eurocrypt’90 (I.B.
Damgard, Ed.), Lect. Notes Comput. Sci. 473: 161–173. 1991.
[12] R.A. Rueppel, and O.J. Staffelbach, Products of linear recurring sequences with maximum
complexity. IEEE Trans. Inform. Theory 33, 1: 124–131. 1987.
[13] A.F. Webster, S.E. Tavares, On the design of S-boxes. in Advances in Cryptology, Proc. of
Crypto’85 (H. C. Williams, Ed.), Lect. Notes Comput. Sci. 219: 523–534. 1985.
[14] S. Wolfram, A New Kind of Science. Wolfram Media Inc., Champaing, IL, 2002.
[15] G.Z. Xiao, J.L. Massey, A spectral characterization of correlation-immune combining
functions, IEEE Trans. Inform. Theory 34, 3: 569–571. 1988.

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