Abstract
A systematic approach to the design of running-key generators in stream cipher systems is proposed using a new class of nonlinear functions based on integer arithmetic operations. This approach is applicable to both feedforward- and feedback-types running-key generators. Most practical nonlinear functions that use only one addition and one multiplication are fully analyzed. Cryptographic properties, such as 0-1 balance, linear complexity, and correlation, of the key-sequence generated by this scheme are examined and several important criteria for determining the parameters of such generators are derived. This approach will prove valuable in designing running-key generators.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
H. Beker and F. Piper, Cipher Systems: The Protection of Communications, Wiley Interscience, New York, 1982.
H. Fredricksen, A Survey of Full Length Nonlinear Shift Register Cycle Algorithms, SIAM Review, Vol. 24, pp. 195–221 (1982).
S.W. Golomb, Shift Register Sequences, Holden-Day, San Francisco, Calif., 1967.
G.H. Hardy and E.M. Wright, An Introduction to the Theory of Numbers, 5th ed.,Oxford University Press, Oxford, 1983.
E.L. Key, An Analysis of the Structure and Complexity of Nonlinear Binary Sequences Generators, IEEE Transactions on Information Theory, Vol. IT-22, pp.732–736 (1976).
D.E. Knuth, The Art of Computer Programming: Vol.2, Seminumerical Algorithms, 2nd ed., Addison-Wesley, 1981.
H. Niederreiter, Quasi-Monte Carlo Methods and Pseudorandom Numbers, Bull. Amer. Math. Soc., Vol.84, pp.957–1041 (1978).
R.A. Rueppel, Analysis and Resign of Stream Ciphers, Springer-Verlag, Berlin, 1986.
T. Siegenthaler, Decrypting A Class of Stream Ciphers Using Cipher-texts Only, IEEE Transactions on Computers, Vol.C-34, pp.81–85 (1985).
M.K. Simon, J.K. Omura, R.A. Scholtz, and B.K. Levitt, Spread Spectrum Communications, vol. 1, Computer Science Press, Maryland, 1985.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1988 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tezuka, S. (1988). A New Class of Nonlinear Functions for Running-key Generators. In: Barstow, D., et al. Advances in Cryptology — EUROCRYPT ’88. EUROCRYPT 1988. Lecture Notes in Computer Science, vol 330. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45961-8_29
Download citation
DOI: https://doi.org/10.1007/3-540-45961-8_29
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50251-7
Online ISBN: 978-3-540-45961-3
eBook Packages: Springer Book Archive