On the properties of substitution blocks on the base of a modified additive generator and on the base of the block cipher nash

Here, we present two algorithms for computing substitution blocks (S-boxes) of the size 16 x 16 bits. The first one is based on a modified additive generator, the second - on the lightweight block cipher NASH. For both algorithms, we give the numerical values for some cryptographic properties of S-boxes produced by them, namely for differential probability, for linear probability, for nonlinearity order of coordinate functions and their linear combinations and compare them with the similar values related to S-boxes of some known block ciphers (AES, Kuznechik and others). Also, we show that the running time of these algorithms is 3.5-5 times more than the running time needed to compute the same S-boxes in the table form.

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