I`m on searching of any method of building system equations for S-boxes. Firstly, I just cannot undestand exact meaning of "system equations", is it anf for each input (I know how to make it using Sage, maybe someone can help you make it using Magma)? If not, please, maybe you have any articles or can a little bit describe algorithm.
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$\begingroup$ Possible help crypto.stackexchange.com/questions/22944/… $\endgroup$ – hardyrama May 11 '19 at 18:13
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$\begingroup$ this eprint.iacr.org/2015/589.pdf explains how to generate Multivariate Quadratic Equation Systems $\endgroup$ – hardyrama May 11 '19 at 18:42
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$\begingroup$ eprint.iacr.org/2015/589.pdf -- useful for S-boxes, which has description like AES, but if it has only table, not $\endgroup$ – Mixi May 11 '19 at 19:38
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$\begingroup$ It's a system, i.e., a set of simultaneous equations. See the excellent comments. $\endgroup$ – kodlu May 12 '19 at 1:28
