Cryptanalytic invertibility of two-argument functions

Tests of cryptanalytic invertibility of all possible types for functions g : D₁ x D₂ D are proposed. Let G_a = {g(a,x₂) : x₂ G D₂} for any a G D₁. Then: 1) function g is invertible with respect to the variable x₁ of the type VV iff Va, b G D₁ (a = b G_a П G_b = 0); 2) function g is invertible with respect to the variable x₁ of the type V3 iff there exists a mapping such that the mapping a g(a, ^(a)) is injective; 3) function g is invertible with respect to the variable x₂ of the type 3V iff |Ga| = |D2| for some value a G D1. Algorithms for constructing a recovering function and generating invertible functions are formulated; some estimates of the number of invertible functions are given.

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