Geodesic
Spectral criterion for testing hypotheses on random permutations
Matematičeskie voprosy kriptografii, Tome 7 (2016) no. 3, pp. 19-28 
O. V. Denisov. Spectral criterion for testing hypotheses on random permutations. Matematičeskie voprosy kriptografii, Tome 7 (2016) no. 3, pp. 19-28. http://geodesic.mathdoc.fr/item/MVK_2016_7_3_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Suppose that for each of $N$ independent identically distributed random permutations we observe a pair consisting of a random uniformly distributed argument and a corresponding value of permutation. We consider the problem of testing the hypothesis that the distribution of permutations is uniform against the hypothesis that permutations are the products of r independent permutations with known distribution. A test constructed by eigenvectors of matrices of transition probabilities (arguments to values) is proposed and investigated.

[1] Borovkov A. A., Teoriya veroyatnostei, Editorial URSS, M., 1999, 472 pp. | MR

[2] Glukhov M. M., “O rasseivayuschikh lineinykh preobrazovaniyakh dlya blochnykh shifrsistem”, Matem. vopr. kriptogr., 2:2 (2011), 5–39

[3] Glukhov M. M., Elizarov V. P., Nechaev A. A., Algebra, v. 2, Gelios ARV, M., 2003, 416 pp.

[4] Lankaster P., Teoriya matrits, Nauka, M., 1978, 280 pp. | MR

[5] Mink Kh., Permanenty, Mir, M., 1982, 211 pp. | MR

[6] Lai X., Massey J., Murphy S., “Markov ciphers and differential cryptanalysis”, EUROCRYPT'91, Lect. Notes Comput. Sci., 547, 1991, 17–38 | DOI | MR | Zbl