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This article is cited in 1 scientific paper (total in 1 paper)
Mathematical Methods of Cryptography
Cryptanalytic invertibility of two-argument functions
N. Yu. Berdnikova, I. A. Pankratova Tomsk State University
Abstract:
Tests of cryptanalytic invertibility of all possible types for functions $g: D_1\times D_2\to D$ are proposed. Let $G_a=\{g(a,x_2): x_2\in D_2\}$ for any $a\in D_1$. Then: 1) function $g$ is invertible with respect to the variable $x_1$ of the type $\forall\forall$
iff $\forall a, b\in D_1$ ($a\ne b\Rightarrow G_a\cap G_b=\varnothing$); 2) function $g$ is invertible with respect to the variable $x_1$ of the type $\forall\exists$ iff there exists a mapping $\varphi$ such that the mapping $a\mapsto g(a, \varphi(a))$ is injective; 3) function $g$ is invertible with respect to the variable $x_2$ of the type $\exists\forall$ iff $|G_a|=|D_2|$ for some value $a\in D_1$. Algorithms for constructing a recovering function and generating invertible functions are formulated; some estimates of the number of invertible
functions are given.
Keywords:
cryptanalytic invertibility, invertibility test, recovering function.
Citation:
N. Yu. Berdnikova, I. A. Pankratova, “Cryptanalytic invertibility of two-argument functions”, Prikl. Diskr. Mat. Suppl., 2021, no. 14, 67–71
Linking options:
https://www.mathnet.ru/eng/pdma564 https://www.mathnet.ru/eng/pdma/y2021/i14/p67
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Abstract page: | 137 | Full-text PDF : | 63 | References: | 23 |
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