Abstract
Non-linear functions are very essential in different crypto primitives as they increase the security of the cipher designs. On the other hand, maximum length sequences help to prevent repeatability of a pseudorandom generator. Linear functions such as LFSR and linear cellular automata are used to generate maximum length sequences. However linear maximum length sequences are not secure. So there is a necessity of a construction that can provide both non-linearity and maximum length sequence for optimized cipher designs. In this work, we propose an algorithm for synthesizing a maximum length non-linear cellular automata to fulfill the requirement. Extensive experimentation on the proposed scheme shows that the construction achieves high non-linearity. Moreover, we have implemented and tested the design in Xilinx Spartan-3 FPGA platform and the hardware overhead is shown to be nominal.
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Cattell, K., Muzio, J.C.: Synthesis of one-dimensional linear hybrid cellular automata. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 15, 325–335 (1996)
Meier, W., Staffelbach, O.: Analysis of pseudo random sequences generated by cellular automata. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 186–199. Springer, Heidelberg (1991)
Daemen, J., Rijmen, V.: The Design of Rijndael. Springer (2002)
Hell, M., Johansson, T., Meier, W.: Grain: a stream cipher for constrained environments. Int. J. Wire. Mob. Comput. 2, 86–93 (2007)
Bertoni, G., Daemen, J., Peeters, M., Assche, G.V.: The keccak sha-3 submission. Submission to NIST (Round 3) (2011)
Fredricksen, H.: A survey of full length nonlinear shift register cycle algorithms. SIAM Review 24(2), 195–221 (1982)
Dubrova, E.: A scalable method for constructing galois nlfsrs with period 2n − 1 using cross-join pairs. IEEE Transactions on Information Theory 59, 703–709 (2013)
Das, S., Roy Chowdhury, D.: Generating cryptographically suitable non-linear maximum length cellular automata. In: Bandini, S., Manzoni, S., Umeo, H., Vizzari, G. (eds.) ACRI 2010. LNCS, vol. 6350, pp. 241–250. Springer, Heidelberg (2010)
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Ghosh, S., Sengupta, A., Saha, D., Chowdhury, D.R. (2014). A Scalable Method for Constructing Non-linear Cellular Automata with Period 2n − 1. In: Wąs, J., Sirakoulis, G.C., Bandini, S. (eds) Cellular Automata. ACRI 2014. Lecture Notes in Computer Science, vol 8751. Springer, Cham. https://doi.org/10.1007/978-3-319-11520-7_8
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DOI: https://doi.org/10.1007/978-3-319-11520-7_8
Publisher Name: Springer, Cham
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