Substitution of characters in q-ary m-sequences
- 157 Downloads
This paper discusses a simple way of increasing the linear complexity of maximal length q-ary sequences. This is attained by using character substitution tables. The achievable maximum of increase is determined and it is shown that a portion of about 1/e of all substitution tables share this maximum. The mean value and the variance of the linear complexity is derived for the sequence's output by randomly chosen substitutions. The special case of permutations as substitutions are investigated, as well. At the end of the paper we propose an extension of the notion of linear complexity.
Unable to display preview. Download preview PDF.
- Zierler, N., "Linear recurring sequences", J.SIAM, Vol.7, 1959.Google Scholar
- Golomb, S. W., Shift-Register Sequences. San Francisco: Holden Day, 1967.Google Scholar
- Massey, J.L., "Shift-Register Synthesis and BCH Decoding", IEEE Trans. Inform. Theory, Vol. IT-15, Jan. 1969. 4.Google Scholar
- Key, E.L., "An analysis of the structure and complexity of nonlinear binary sequence generators", IEEE Trans. Inform. Theory, IT-22, No. 6., Nov. 1976.Google Scholar
- L. Brynielson, "On the Linear Complexity of Combined Shift Register Sequences", Advances in Cryptology — Eurocrypt '85, Lecture Notes in Computer Science, No. 219, Springer, 1985.Google Scholar
- Simon, M.K., Omura, J.K., Scholtz, R.A., Levitt, B.K., Spread Spectrum Communications, Vol 1., Ch.5., Computer Science Press, 1985.Google Scholar
- Rueppel, R.A., New Approaches to Stream Ciphers. Communication and Control Series of Engineering, Springer Verlag, 1986.Google Scholar
- T. Siegenthaler, Methoden für den Entwurf von Stream Cipher-Systemen, Doctoral Thesis, ETH Zürich, 1986Google Scholar