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This article is cited in 1 scientific paper (total in 1 paper)
Multidimensional spectral criterion for testing hypotheses on random permutations
O. V. Denisov LLC «Innovative Telecommunication Technologies», Moscow
Abstract:
Let $N$ random identically distributed pairs $(x,y)\in\mathbb{X}^2$ are observed, where $x$ has the uniform distribution on the finite set $\mathbb{X}$. We test the hypothesis that the matrix $Q=\|\mathsf{P}\{y=b\mid x=a\}\|_{a,b\in\mathbb{X}}$ equals $\|\frac1{|\mathbb{X}|}\|$ against the hypothesis $Q=\mathbb{P}^R$, where doubly stochastic matrix $\mathbb{P}$ and degree $R$ are known. A multidimensional tests based on eigenvectors of $\mathbb{P}$ are proposed. They are used to calculate the characteristics of differential distinguishing attacks on random permutations generated by ciphers of SmallPresent family with block lengths $n\in\{8,12,16\}$ and $4\le R\le 9$ rounds.
Key words:
random permutations, transition probabilities matrix, eigenvectors, cipher SmallPresent, differential distinguishing attack.
Received 12.V.2022
Citation:
O. V. Denisov, “Multidimensional spectral criterion for testing hypotheses on random permutations”, Mat. Vopr. Kriptogr., 14:3 (2023), 85–106
Linking options:
https://www.mathnet.ru/eng/mvk448https://doi.org/10.4213/mvk448 https://www.mathnet.ru/eng/mvk/v14/i3/p85
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