On the Bit-Slice representations of some nonlinear bijective transformations

We study how to obtain efficient Bit-Slice representations in some classes of nonlinear bijective transformations having almost optimal cryptographic properties. For some 8-bit instances belonging to these classes, we determine (by combining analytical methods with a open source tool) its low gate count logic circuit representations through binary logic operations $\mathtt{AND, XOR, OR}$ and $\mathtt{NOT}$. In particular, for the S-Box used in the Russian cryptographic standard GOST R 34.12-2015 "Kuznyechik”, we derive a Bit-Slice implementation which consume a total of 176 binary logical operations. The new representation requires 51 Boolean operations less than in previously known one (that need 227 bitwise logical operations, see, for example, [1]).