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Theory and Applications of Cellular Automata in Cryptography
December 1994 (vol. 43 no. 12)
pp. 1346-1357

This paper deals with the theory and application of Cellular Automata (CA) for a class of block ciphers and stream ciphers. Based on CA state transitions certain fundamental transformations are defined which are block ciphering functions of the proposed enciphering scheme, These fundamental transformations are found to generate the simple (alternating) group of even permutations which in turn is a subgroup of the permutation group, These functions are implemented with a class of programmable cellular automata (PCA) built around rules 51, 153, and 195. Further, high quality pseudorandom pattern generators built around rule 90 and 150 programmable cellular automata with a rule selector (i.e., combining function) has been proposed as running key generators in stream ciphers, Both the schemes provide better security against different types of attacks. With a simple, regular, modular and cascadable structure of CA, hardware implementation of such schemes idealy suit VLSI implementation.

[1] S. Wolfram, "Statistical mechanics of cellular automata,"Rev. Mod. Physics, vol. 55, no. 3, pp. 601-644, 1983.
[2] A. K. Das, A. Ganguly, A. Dasgupta, S. Bhawmik, and P. Pal Chaudhuri, "Efficient characterization of cellular automata,"IEE Proc., vol. 137, Pt. E, no. 1, pp. 81-87, Jan. 1990.
[3] A. K. Das, S. Saha, A. Roy Chowdhury, S. Misra, and P. Pal Chaudhuri, "Signature analyzer based on additive-cellular automata," inProc. 20th Fault Tolerant Computing Syst., pp. 265-272, U.K., June 1990.
[4] W. Pries, A. Thanailakis, and H. C. Card, "Group properties of cellular automata and VLSI applications,"IEEE Trans. Comput., vol. C-35, pp. 1013-1024, Dec. 1986.
[5] O. Martin, A. M. Odlyzko, and S. Wolfram, "Algebraic properties of cellular automata,"Commun. Math. Phys.vol. 93, pp. 219, 1984.
[6] D.E. Denning,Cryptography and Data Security, Addison-Wesley Publishing Co., Reading, Mass., 1982.
[7] I. N. Herstein,Topics In Algebra, New Delhi, India: Vikas Publishing House Pvt. Ltd, 1976.
[8] D. Welsh,Codes and Cryptography. Oxford, UK: Oxford Univ. Press, 1988
[9] J. Seberry and J. Pieprzyk,Cryptography: An Introduction to Computer Security. Australia: Prentice Hall of Australia, 1989.
[10] A. Salomma,Public-Key Cryptography. Berlin Heidelberg: Springer-Verlag, 1990.
[11] W. Meier and O. Steffelbach, "Correlation properties of combiners with memory in stream ciphers," inProc. Advances in Cryptology-EUROCRYPT'90, Springer-Verlag, 1990, pp. 204-213.
[12] J. Pieprzyk and X. M. Zhang, "Permutation generators of alternating groups," inProc. Advances in Cryptology-AUSCRYPT '90, Springer-Verlag, 1990, pp. 237-244.
[13] T. Siegenthaler, "Correlation-Immunity of Nonlinear Combining Functions for Cryptographic Applications,"IEEE Trans. Information Theory, Vol. IT-31, No. 5, Sept. 1984, pp. 776-780.
[14] T. Siegenthaler, "Decrypting a class of stream ciphers using ciphertext only,"IEEE Trans. Comput., vol. C-34, no. 1, pp. 81-85, Jan. 1985.
[15] P. H. Bardell, "Analysis of cellular automata used as pseudorandom pattern generators," inProc. Int. Test Conf., 1990, pp. 762-768.
[16] A. K. Das and P. Pal Chaudhuri, "Vector space theoretic analysis of additive cellular automata and its application pseudo-exhaustive test pattern generation,"IEEE Trans. Comput., vol. 42, no. 3, pp. 340-352, Mar. 1993.
[17] D. Roy Chawdhury, I. Sengupta, S. Basu, and P. Pal Chaudhuri, "Cellular automata based error correcting codes (CAECC),"IEEE Trans. Comput., vol. 43, no. 6, pp. 759-764, June 1994.
[18] D. E. Knuth,The Art of Computer Programming, Vol. 2, Seminumerical Algorithms. Reading, MA: Addison-Wesley, 1981.
[19] S. Even and O. Goldreich, "DES-like functions can generate the alternating group,"IEEE Trans. Inform. Theory, vol. IT-29, no. 6, pp. 863-865, Nov. 1983.
[20] P. D. Hortensius, R. D. Mcleod, W. Pries, D. M. Miller, and H. C. Card, "Cellular automata based pseudorandom number generators for built-in self-test,"IEEE Trans. Comput.-Aided Design, vol. 8, no 8, pp. 842-59, Aug. 1989.
[21] Ph. Tsalides, T. A. York, and A. Thanailakis, "Pseudorandom number generators for VLSI systems based on linear cellular automata," inIEEE Proc. E. Comput. Digit. Tech, vol. 138, no. 4, 1991, pp. 241-249.
[22] Ph. Tsalides, "Cellular automata based built-in self test structures for VLSI systems,"Electron. Lett., vol. 26, no. 17, pp. 1350-1352, 1990.
[23] T. K. York, Ph. Tsalides, B. Srisuchinwong, P. J. Hicks, and A. Thanailakis, "Design and VLSI implementation of a mod- 127 multiplier using cellular automaton-based data compression techniques," inIEEE Proc. E. Comput. Digit. Tech., vol. 138, no. 5, 1991, pp. 351-356.
[24] P. Tzionas, Ph. Tsalides, and A. Thanailakis, "Design and VLSI implementation of a pattern classifier using pseudo @ D cellular automata,"IEE Proc. G, vol. 139, no. 6, pp. 661-668, Dec. 1992.
[25] B. Srisuchinwong, Ph. Tsalides, T. A. York, P. J. Hicks, and A. Thanailakis, "VLSI implementation of mod-pmultipliers using homomorphisms and hybrid cellular automata,"IEE Proc. E, vol. 139. no. 6, pp. 486-490, Nov. 1992.
[26] S. Wolfram, "Cryptography with cellular automata," inAdvances in Cryptology-Crypto'85(Springer-Verlag Lecture Notes in Computer Science 218). 1986. pp. 429-432.

Index Terms:
cellular automata; cryptography; VLSI; random number generation; cellular automata; cryptography; block ciphers; stream ciphers; CA state transitions; fundamental transformations; programmable cellular automata; pseudorandom pattern generators; VLSI implementation.
Citation:
S. Nandi, B.K. Kar, P. Pal Chaudhuri, "Theory and Applications of Cellular Automata in Cryptography," IEEE Transactions on Computers, vol. 43, no. 12, pp. 1346-1357, Dec. 1994, doi:10.1109/12.338094
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