Abstract
Algebraic attack studies ciphers from the point of view of solving equations. It is important to measure the security of block ciphers how many linearly independent bi-affine or quadratic equations they satisfy. As the S-box is the main nonlinear part of block ciphers, it really makes sense to get the number of linearly independent bi-affine and quadratic equations that an S-box satisfies to analyse the security of block ciphers. The article answers this question for two S-boxes based on APN power functions, and shows how to find out the equations by two toy examples. The techniques can be generalized to other S-boxes constructed by power functions. According to these conclusions, we can estimate the safety of such kind of block ciphers.
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Xie, J., Cao, W., Wang, T. (2009). Quadratic Equations from a Kind of S-boxes. In: Youm, H.Y., Yung, M. (eds) Information Security Applications. WISA 2009. Lecture Notes in Computer Science, vol 5932. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10838-9_18
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DOI: https://doi.org/10.1007/978-3-642-10838-9_18
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