Abstract
The linear-complexity profile measures the extent to which the initial segments of a keystream sequence can be simulated by linear feedback shift-register sequences. To provide a benchmark for the assessment of keystream sequences, a probabilistic theory of the linear-complexity profile of random sequences is needed. For sequences of elements of a finite field we show probabilistic results that can be derived by a combinatorial method.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
F. G.Gustavson, Analysis of the Berlekamp-Massey linear feedback shift-register synthesis algorithm, IBM J. Res. Develop., vol. 20, 1976, pp. 204–212.
M.Loève, Probability Theory, 3rd edn., Van Nostrand, New York, 1963.
H.Niederreiter, Sequences with almost perfect linear complexity profile, Advances in Cryptology—EUROCRYPT '87, Lecture Notes in Computer Science, Vol. 304, Springer-Verlag, Berlin, 1988, pp. 37–51.
H.Niederreiter, The probabilistic theory of linear complexity, Advances in Cryptology —EUROCRYPT '88, Lecture Notes in Computer Science, Vol. 330, Springer-Verlag, Berlin, 1988, pp. 191–209.
R. A.Rueppel, Linear complexity and random sequences, Advances in Cryptology—EURO-CRYPT '85, Lecture Notes in Computer Science, Vol. 219, Springer-Verlag, Berlin, 1986, pp. 167–188.
R. A.Rueppel, Analysis and Design of Stream Ciphers, Springer-Verlag, Berlin, 1986.
B. Smeets, The linear complexity profile and experimental results on a randomness test of sequences over the field F q , Preprint, University of Lund, September 1988.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Niederreiter, H. A combinatorial approach to probabilistic results on the linear-complexity profile of random sequences. J. Cryptology 2, 105–112 (1990). https://doi.org/10.1007/BF00204450
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00204450