Abstract
We apply the algebraic attacks on stream ciphers with memories to the summation generator. For a summation generator that uses n LFSRs, an algebraic equation relating the key stream bits and LFSR output bits can be made to be of degree less than or equal to \(^{\lceil\log_2 n \rceil}\) using ⌈log2 n ⌉ + 1 consecutive key stream bits. This is much lower than the upper bound given by previous general results. We also show that the techniques of [6,2] can be applied to summation generators using 2k LFSRs to reduce the effective degree of the algebraic equation.
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Lee, D.H., Kim, J., Hong, J., Han, J.W., Moon, D. (2004). Algebraic Attacks on Summation Generators. In: Roy, B., Meier, W. (eds) Fast Software Encryption. FSE 2004. Lecture Notes in Computer Science, vol 3017. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25937-4_3
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DOI: https://doi.org/10.1007/978-3-540-25937-4_3
Publisher Name: Springer, Berlin, Heidelberg
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