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Correlation properties of combiners with memory in stream ciphers

✍ Scribed by Willi Meier; Othmar Staffelbach

Publisher: Springer
Year: 1992
Tongue: English
Weight: 923 KB
Volume: 5
Category: Article
ISSN: 0933-2790
DOI: 10.1007/bf00191322

No coin nor oath required. For personal study only.

✦ Synopsis

For pseudo-random generators where one or several LFSRs are combined by a memoryless function, it is known that the output sequences are correlated to certain LFSR-sequences whose correlation coefficients c~ satisfy the equation ~c 2 = 1. In this paper it is proved that a corresponding result also holds for generators whose LFSRs are connected to a combiner with memory.

If correlation probabilities are conditioned on side information, e.g., on known output digits, it is shown that new or stronger correlations may occur. This is exemplified for the summation cipher with only two LFSRs where such correlations can be exploited in a known plaintext attack. A cryptanalytic algorithm is given which is shown to be successful for LFSRs of considerable length and with arbitrary feedback connection.

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