Abstract
Linear cryptanalysis and linear approximation methods in general are among the most important cryptanalysis methods of symmetric ciphers and their components. Recently, these methods have been extended to efficiently exploit multiple linear approximations simultaneously. It is known that high nonlinearity of Boolean functions and S-boxes is a desirable property and that the bent functions offer the strongest resistance against cryptanalysis using single linear approximations. The goal of this paper is to investigate to which extent resistance against the multidimensional extension of the linear cryptanalysis method can be achieved. For this purpose some common highly nonlinear Boolean functions as well as a basic LFSR based key stream generator using a nonlinear filter function are investigated.
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Acknowledgements
We thank Gregor Leander for noticing a problem in the original version of Theorem 4.3 and for proposing a new elegant solution. We also thank Anne Canteaut for her comments and suggestion to investigate plateaued filter functions. Last but least we thank the anonymous referees for their insightful comments and help in improving the presentation of the paper. Financial support from Matine project number 776 is gratefully acknowledged.
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Preliminary version appeared in the proceedings of BFCA’08 International Workshop on Boolean Functions: Cryptography and Applications.
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Hermelin, M., Nyberg, K. Multidimensional linear distinguishing attacks and Boolean functions. Cryptogr. Commun. 4, 47–64 (2012). https://doi.org/10.1007/s12095-011-0053-3
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DOI: https://doi.org/10.1007/s12095-011-0053-3
Keywords
- Linear approximation
- Multidimensional linear approximation
- Distinguishing attack
- Boolean function
- Filter generator