Abstract
The linear complexicy profile was introduced by Rueppel [7], [8, Ch. 4] as a cool for the assessment of keystream sequences with respect to randomness and unpredictability properties. In the following let F be an arbitrary field. We recall that a sequence of elements of F is called a kth-order linear feedback shift register (LFSR) sequence if it satisfies a kth-order linear recursion with constant coefficients from F. The zero sequence O,O,... is viewed as an LFSR sequence of order 0. Now let S be an arbitrary sequence s1,s2,... of elements of F. For a positive integer n the (local) linear complexity Ln(S) is defined as the least k such that s1,s2,...,sn form the first n terms of a kth-order LFSR sequence. The sequence L1(S),L2(S),... of integers is called the linear complexity profile (LCP) of S. For basic facts about the LCP see [4], [7], [8, Ch. 4].
Chapter PDF
References
U. Krengel: Ergodic Theorems, de Gruyter, Berlin, 1985.
M. Loève: Probability Theory, 3rd ed., Van Nostrand, New York, 1963.
H. Niederreiter: Continued fractions for formal power series, pseudorandom numbers, and linear complexity of sequences, Contributions to General Algebra 5 (Proc. Salzburg Conf., 1986), pp. 221–233, Teubner, Stuttgart, 1987.
H. Niederreiter: Sequences with almost perfect linear complexity profile, Advances in Cryptology — EUROCRYPT’ 87 (D. Chaum and W. L. Price, eds.), Lecture Notes in Computer Science, Vol. 304, pp. 37–51, Springer, Berlin, 1988.
H. Niederreiter: The probabilistic theory of linear complexity, Advances in Cryptology — EUROCRYPT’ 88 (C. G. Günther, ed.), Lecture Notes in Computer Science, Vol. 330, pp. 191–209, Springer, Berlin, 1988.
F. Piper: Stream ciphers, Elektrotechnik und Maschinenbau 104, 564–568 (1987).
R. A. Rueppel: Linear complexity and random sequences, Advances in Cryptology — EUROCRYPT’ 85 (F. Pichler, ed.), Lecture Notes in Computer Science, Vol. 219, pp. 167–188, Springer, Berlin, 1986.
R. A. Rueppel: Analysis and Design of Stream Ciphers, Springer, Berlin, 1986.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Niederreiter, H. (1990). Keystream Sequences with a Good Linear Complexity Profile for Every Starting Point. In: Quisquater, JJ., Vandewalle, J. (eds) Advances in Cryptology — EUROCRYPT ’89. EUROCRYPT 1989. Lecture Notes in Computer Science, vol 434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46885-4_50
Download citation
DOI: https://doi.org/10.1007/3-540-46885-4_50
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-53433-4
Online ISBN: 978-3-540-46885-1
eBook Packages: Springer Book Archive