Linear Span analysis of a set of periodic sequence generators
An algorithm for computing lower bounds on the global linear complexity of nonlinearly filtered PN-sequences is presented. Unlike the existing methods, the algorithm here presented is based on the realization of bit wise logic operations. The numerical results obtained are valid for any nonlinear function with a unique term of maximum order and for any maximal-length LFSR. To illustrate the power of this technique, we give some high lower bounds that confirm Rueppel's conclusion about the exponential growth of the linear complexity in filter generators.
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- 1.A. Fúster-Sabater and P. Caballero-Gil, ‘On the Linear Complexity of Nonlinearly Filtered PN-Sequences', Advances in Cryptology-ASIACRYPT'94, Lecture Notes in Computer Science Vol. 917, Springer-Verlag.Google Scholar
- 3.D.E. Knuth, ‘The Art of Computer Programming, Vol. 2: Seminumerical Algorithms', Addison-Wesley, 1981.Google Scholar
- 6.J.L. Massey and S. Serconek, ‘A Fourier Transform Approach to the Linear Complexity of Nonlinearly Filtered Sequences', Advances in Cryptology-CRYPTO'94, Lecture Notes in Computer Science Vol. 839, pp. 332–340, Springer-Verlag, 1994.Google Scholar
- 7.K.G. Paterson, ‘New Lower Bounds on the Linear Complexity of Nonlinearly Filtered m-Sequences', submitted to IEEE Transactions on Information Theory, 1995.Google Scholar
- 8.R.A. Rueppel, ‘Analysis and Design of Stream Ciphers', Springer-Verlag, New York, 1986.Google Scholar
- 9.G.J. Simmons (ed.), ‘Contemporary Cryptology: The Science of Information Integrity', IEEE Press, 1991.Google Scholar