Abstract
Siegenthaler has shown how cross-correlation techniques can be applied to identify pseudo random generators consisting of linear feedback shift registers and a scrambling function [7]. These techniques may allow to attack one register in such a generator at a time. The original algorithm needs O(R2rN) operations to identify one register. (r denotes the length of the register examined, R the number of primitive polynomials of degree r. and N the minimal number of bits one has to observe). Employing Walsh-Hadamard transform this analysis can be done in O(R(r22+N)) operations [8].
We show that there exists a trade-off between the dimension of the Hadamard matrix and the number of bits required to compute the cross correlation coefficients. The complexity of this attack is O(R(r2r−σ+2σN)). The integer σ can be selected so that the cost of the attack is minimized. The MSR-generator will serve as an example to demonstrate our algorithm.
Furthermore we examine the correlation immunity of the S-boxes used in the DES.
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Keywords
- Cross Correlation
- Stream Cipher
- Cross Correlation Analysis
- Hadamard Matrix
- Linear Feedback Shift Register
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.
Literature
K.G. Beauchamp, “Applications of Walsh and Related Functions”, Academic Press, 1984
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T. Beth, “Verfahren der Schnellen Fourier-Transformation”, Teubner, Stuttgart. 1984
E.F. Brickell, J.H. Moore, M.R. Purtill, “Structures in the S-Boxes of the DES (extended abstract)”, Springer, LNCS 263, pp.3–8, 1987
A.G. Konheim, “Cryptography, a Primer”, Wiley, New York, 1981
R.A. Rueppel, “Analysis and Design of Stream Ciphers”, Springer, Heidelberg. 1986
T. Siegenthaler, “Decrypting a Class of Stream Ciphers Using Ciphertext Only”, IEEE Trans.Comp.,Vol. C-34. No.1, pp.81–85, 1985
Guo-Zhen Xiao. J.L. Massey, “A Spectral Approach to Correlation-Immune Combining Functions”, to appear
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© 1988 Springer-Verlag Berlin Heidelberg
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Mund, S., Gollmann, D., Beth, T. (1988). Some Remarks on The Cross Correlation Analysis of Pseudo Random Generators. In: Chaum, D., Price, W.L. (eds) Advances in Cryptology — EUROCRYPT’ 87. EUROCRYPT 1987. Lecture Notes in Computer Science, vol 304. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-39118-5_4
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DOI: https://doi.org/10.1007/3-540-39118-5_4
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