Improved asymptotic estimates for the numbers of correlation-immune and k-resilient vectorial Boolean functions

References

[1] Denisov O. V. “An asymptotic formula for the number of correlation-immune of order k Boolean functions” Discrete Math. Appl. 2:4 (1992), 407–426.10.1515/dma.1992.2.4.407Search in Google Scholar

[2] Denisov O. V., “A local limit theorem for the distribution of a part of the spectrum of a random binary function”, Discrete Math. Appl., 10:1 (2000), 87–101.10.1515/dma.2000.10.1.87Search in Google Scholar

[3] Elizarov V. P., Finite rings, Gelios ARV, Moscow, 2006 (in Russian), 304 pp.Search in Google Scholar

[4] Lavrent’yev M. A., Shabat B. V., Methods of the complex variable function theory, Fizmatlit, Moscow, 1958 (in Russian), 680 pp.Search in Google Scholar

[5] Logachev O. A., Sal’nikov A. A., Smyshlyaev S. V., Yashchenko V. V., Boolean functions int coding theory and cryptology, URSS, Moscow, 2015 (in Russian), 576 pp.Search in Google Scholar

[6] Pankov K. N., “Asymptotic estimates for the numbers of binary mappings with given cryptographic properties”, Matematicheskie voprosy kriptografii, 5:4 (2014), 73–97 (in Russian).10.4213/mvk136Search in Google Scholar

[7] Pankov K. N., “Local limit theorem for the distribution of a part of vectorweight subfunctions of the components of a random binary mapping”, Matematicheskie voprosy kriptografii, 5:3 (2014), 49–80 (in Russian).10.4213/mvk129Search in Google Scholar

[8] Pankov K.N., “Estimates of the convergence rate in limit theorems for joint distributions of a part of characteristics of random binary mappings”, Prikladnaya diskretnaya matematika, 5:4 (2012), 14–30 (in Russian).10.17223/20710410/18/2Search in Google Scholar

[9] Prokhorov Yu. V., “Limit theorem for sums of random vectors, whose dimension tends to infinity”, Theory Probab. Appl., 35:4 (1990), 755–757.10.1137/1135106Search in Google Scholar

[10] Development of the distributed registry technology, Report for public consultation, Central Bank of the Russian Federation, Moscow, 2017 (in Russian), 16 pp., http://www.cbr.ru/analytics/ppc/Consultation_Paper_1712129(2).pdfSearch in Google Scholar

[11] Ryazanov B. V., “On the distribution of the spectral complexity of Boolean functions”, DiscreteMath. Appl., 4:3 (1994), 279–288.10.1515/dma.1994.4.3.279Search in Google Scholar

[12] Sachkov V. N., Introduction to the combinatorial methods of discrete mathematics, MCCME, Moscow, 2004 (in Russian), 424 pp.Search in Google Scholar

[13] Sachkov V. N., Course of combinatorial analysis, NITs “Regulyarnaya i khaoticheskaya dinamika”, Moscow, Izhevsk, 2013 (in Russian), 336 pp.Search in Google Scholar

[14] Sevast’yanov B. A., Course of probability theory and mathematical statistics, Nauka, Moscow, 1982 (in Russian), 256 pp.Search in Google Scholar

[15] Dictionary of cryptographic terms, eds. B. A. Pogorelov, V. N. Sachkov, MCCME, Moscow, 2006 (in Russian), 94 pp.Search in Google Scholar

[16] Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables, eds. Abramowitz M., Stegun I. A., 1965, 1046 pp.Search in Google Scholar

[17] Tarannikov Yu. V., “On the correlation-immune and stable Boolean functions”, Matematicheskie voprosy kibernetiki, 11 (2002), 91–149 (in Russian).Search in Google Scholar

[18] Feller W., An Introduction to Probability Theory and Its Applications. V. 1, 3rd ed., Wiley, 1968, 528 pp.Search in Google Scholar

[19] Yashchenko V. V., “Properties of Boolean mappings, reducible to the properties of their coordinate functions”, Vestnik MGU. Ser. Matem., 33:1 (1997), 11–13 (in Russian).Search in Google Scholar

[20] Bach E., “Improved asymptotic formulas for counting correlation immune Boolean functions”, SIAM J. Discrete Math., 23:3 (2009), 1525–1538.10.1137/070705520Search in Google Scholar

[21] Canfield E. R., Gao Z., Greenhill C., McKay B.D., Robinson R.W., “Asymptotic enumeration of correlation-immune Boolean functions”, Cryptography and Communications, 2:1 (2010), 111–126.10.1007/s12095-010-0019-xSearch in Google Scholar

[22] Carlet C., “Vectorial Boolean functions for cryptography”, chapter 9 in book, Boolean Models and Methods in Mathematics, Computer Science, and Engineering. Encyclopedia of Mathematics and its Applications. Vol. 134, Cambridge University Press, Cambridge, 2010, 398–472.10.1017/CBO9780511780448.012Search in Google Scholar

[23] Xiao G.- Z., Massey J. L., “A spectral characterization of correlation-immune combining functions”, IEEE Trans. Inf. Theory, 34:3 (1988), 569–571.10.1109/18.6037Search in Google Scholar