On characteristics of local primitive matrices and digraphs

For local primitive n-vertex digraphs and matrices of order n, the following new characteristics are introduced: a matex is defined as a matrix (7^) of order n, where 7^ = (i,j)-expT, 1 ^ i,j ^ n; k, r-exporadius exrd_k,_rГ is defined as min 7/ _J, where 7/ _J = max Y_i7-; k, r-expocenter is defined as a set I x J, where / xJ:|/|=fc,|J |=r (i,j)e/xJ |I| = k, | J| = r, 7/,_J = exrd_k,_rГ. An approach to build the perfect s-boxes of order k x r using introduced characteristics is proposed. This approach is based on iterations of n-dimensional Boolean vectors set transformations with n > max(k,r). An exemplification of the function construction for perfect s-boxes of order k x r is presented.

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