Collisions and incidence of vertices and components in the graph of k-fold iteration of the uniform random mapping

References

[1] Zubkov A. M., “Computation of distributions of the numbers of components and cyclic points for randommappings”,Matematicheskie voprosy kriptografii, 1:2 (2010), 5–18 (in Russian).10.4213/mvk7Search in Google Scholar

[2] Zubkov A. M., Serov A. A., “Limit theorem for the size of an image of subset under compositions of random mappings”, Discrete Math. Appl., 28:2 (2018), 131–138.10.1515/dma-2018-0013Search in Google Scholar

[3] Zubkov A. M., Serov A. A., “Estimates of the mean size of the subset image under composition of randommappings”, Discrete Math. Appl., 28:5 (2018), 331–338.10.1515/dma-2018-0029Search in Google Scholar

[4] Mikhailov V. G., “Repetition of states of a random-number generator under multiple access”, Theory Probab. Appl., 40:4 (1995), 679–689.10.1137/1140077Search in Google Scholar

[5] Mikhailov V. G., “A study of combinatorial probabilistic model of automata formed by registers with nonregular steps”, Trudy po diskretnoy matematike, 6 (2003), 139–149 (in Russian).Search in Google Scholar

[6] Mikhailov V. G., “A study of the number of cyclic points of automata formed by registers with nonregular steps”, Trudy po diskretnoy matematike, 5 (2002), 167–172 (in Russian).Search in Google Scholar

[7] A Dictionary of Cryptographic Terms, eds. Pogorelov B. A., Sachkov V.N., M. : MCCME, 2006 (in Russian), 94 pp.Search in Google Scholar

[8] VasilenkoO.N., Number-theoretic Algorithms in Cryptography, M. : MCCME, 2003 (in Russian), 328 pp.Search in Google Scholar

[9] Hellman M. E., “A cryptanalytic time-memory trade-off”, IEEE Trans. Inf. Theory, IT-26 (1980), 401–406.10.1109/TIT.1980.1056220Search in Google Scholar

[10] PilshchikovD. V., “Estimation of the characteristics of time-memory-data tradeoff methods via generating functions of the number of particles and the total number of particles in the Galton-Watson process”, Matematicheskie voprosy kriptografii, 5:2 (2014), 103–108 (in Russian).Search in Google Scholar

[11] PilshchikovD. V., “On the limiting mean values in probabilistic models of time-memory-data tradeoff methods”, Matematicheskie voprosy kriptografii, 6:2 (2015), 59–65 (in Russian).10.4213/mvk145Search in Google Scholar

[12] PilshchikovD. V., “Complexity analysis of the method of rainbow tables with fingerprints”, Matematicheskie voprosy kriptografii, 8:4 (2017), 99–116 (in Russian).10.4213/mvk241Search in Google Scholar

[13] Avoine G., Junod P., Oechslin P., “Characterization and improvement of time-memory trade-off based on perfect tables”, Trans. Inf. Syst. Secur., 11:17 (2008), 1-17.10.1145/1380564.1380565Search in Google Scholar

[14] Oechslin P., “Making a faster cryptanalytic time-memory trade-off”, Lect. Notes Comput. Sci., 2729 (2003), 617–630.10.1007/978-3-540-45146-4_36Search in Google Scholar

[15] Zubkov A. M., Mironkin V.O., “Distribution of the length of aperiodicity segment in the graph of 𝑘-fold iteration of uniform random mapping”, Matematicheskie voprosy kriptografii, 8:4 (2017), 63–74 (in Russian).10.4213/mvk239Search in Google Scholar

[16] Zubkov A. M., Serov A. A., “Images of subset of finite set under iterations of random mappings”, Discrete Math. Appl., 25:3 (2015), 179–185.10.1515/dma-2015-0017Search in Google Scholar

[17] Mironkin V.O., Mikhailov V. G., “On the sets of images of 𝑘-fold iteration of uniform random mapping”, Matematicheskie voprosy kriptografii, 9:3 (2018), 99–108 (in Russian).10.4213/mvk264Search in Google Scholar

[18] Mironkin V.O., “On estimates of the distribution of the length of aperiodicity segment in the graph of 𝑘-fold iteration of uniform random mapping”, Prikladnaya diskretnaya matematika, 42 (2018), 6–17 (in Russian).10.17223/20710410/42/1Search in Google Scholar

[19] PilshchikovD. V., “Asymptotic behaviour of the complete preimage cardinality for the image of a random set under repeated applications of mappings of a finite set into itself”, Matematicheskie voprosy kriptografii, 8:1 (2017), 95–106 (in Russian).10.4213/mvk217Search in Google Scholar

[20] Rubin H., Sitgreaves R., “Probability distributions related to random transformations of a finite set”, Tech. Rept.№19A, Appl. Math. and Statist. Lab., Stanford Univ., 1954, 50 pp.Search in Google Scholar

[21] Mironkin V.O., “Layers of the graph of 𝑘-fold iteration of the uniform random mapping”, Matematicheskie voprosy kriptografii, 10:1 (2019), 73–82 (in Russian).10.4213/mvk277Search in Google Scholar

[22] Mironkin V.O., “On some probabilistic characteristics of the key derivation algorithm «CRYPTOPRO KEY MESHING»”, Information Security Problems. Computer Systems, 2015,№4, 140–146 (in Russian).Search in Google Scholar

[23] Chistyakov V. P., Probability theory course (7th ed. ), M.: Drofa, 2007 (in Russian), 253 pp.Search in Google Scholar

[24] Khalipov P. V., Probability of covering the finite set by the component of random mapping, Thesis, mech-mat, Lomonosov Moscow State University, 2008 (in Russian).Search in Google Scholar

[25] Harris B., “Probability distributions related to random mapping”, Ann. Math. Statist., 31:4 (1960), 1045–1062.10.1214/aoms/1177705677Search in Google Scholar

[26] TokarevaN.N., Symmetric Cryptography. A Short Course: Textbook,Novosib. gos. un-t.Novosibirsk, 2012 (in Russian), 234 pp.Search in Google Scholar