Abstract
Boolean functions with large algebraic immunity resist algebraic attacks to a certain degree, but they may not resist fast algebraic attacks (FAA’s). It is necessary to study the resistance of Boolean functions against FAA’s. In this paper, we localize the optimal resistance of Boolean functions against FAA’s and introduce the concept of e-fast algebraic immunity (e-FAI) for n-variable Boolean functions against FAA’s, where e is a positive integer and \(1 \leq e<\lceil\frac{n}{2}\rceil\). We give the sufficient and necessary condition of e-FAI. With e-FAI the problem of deciding the resistance of an n-variable Boolean function against FAA’s can be converted into the problem of observing the properties of one given matrix. An algorithm for deciding e-FAI and the optimal resistance against FAA’s is also described.
Keywords
- stream ciphers
- algebraic attacks
- fast algebraic attacks
- Boolean functions
- algebraic immunity
This work is supported by Funds of Key Lab of Fujian Province University Network Security and Cryptology (2011008) and National Natural Science Foundations of China (Grant No. 61070168, 10971246, 61003244, 60803135).
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Du, Y., Zhang, F., Liu, M. (2012). On the Resistance of Boolean Functions against Fast Algebraic Attacks. In: Kim, H. (eds) Information Security and Cryptology - ICISC 2011. ICISC 2011. Lecture Notes in Computer Science, vol 7259. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31912-9_18
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DOI: https://doi.org/10.1007/978-3-642-31912-9_18
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