Algebraic and topological structures on the discrete sets,
the extreme tasks of combinatorial analysis and theory of graphs,
final substitution groups,
theoretical cryptography.
Main publications:
F. M. Malyshev, “Simplexial systems of linear equations”, Algebra, MSU Press, Moscow, 1980, 53–56
F. M. Malyshev, “On the nilpotency class of Lie algebras satisfying the Engel condition”, Bulletin of MSU, mech.-math., 2 (1980), 55–58
F. M. Malyshev, “Methods of linear and differential relations in cryptography”, Diskr. Mat., 34:1 (2022), 36–63
F. M. Malyshev, “Proof of the Brunn–Minkowski Theorem by Brunn Cuts”, Math. Notes, 111:1 (2022), 82–92
F. M. Malyshev, “Embedding of provably unsolvable problems into stream ciphers”, Mat. Vopr. Kriptogr., 14:1 (2023), 65–83
5.
F. M. Malyshev, “Invariant sums of products of differentials”, Moscow University Mathematics Bulletin, 78:4 (2023), 198–202
6.
F. M. Malyshev, Chebyshevskii Sb., 24:4 (2023), 212–238
7.
F. M. Malyshev, “Realizatsiya podstanovok chetnoi stepeni proizvedeniyami trekh involyutsii bez nepodvizhnykh tochek”, Diskretnye modeli v teorii upravlyayuschikh sistem (Trudy XI Mezhdunarodnoi konferentsii), M., 2023, 74–77http://agora.guru.ru/dm11
2022
8.
F. M. Malyshev, “Proof of the Brunn–Minkowski Theorem by Brunn Cuts”, Math. Notes, 111:1 (2022), 82–92
9.
F. M. Malyshev, “$k$-Configurations”, Proc. Steklov Inst. Math., 316 (2022), 233–253
10.
F. M. Malyshev, “Proof of the Bruns theorem for schoolchildren”, Geometric aspects of teaching mathematics in higher and secondary school, Proceedings of the International Conference “Classical and Modern Geometry” in honor of Levon S. Atanasyan on his 100th birthday, MPGU, M., 2022, 130–138
2024
11.
F. M. Malyshev, “Methods of linear and differential relations in cryptography”, Discrete Math. Appl., 34:3 (2024), 145–166
2022
12.
M. M. Komyagin, F. M. Malyshev, “Izomorfizmy izvestnykh 5-konfiguratsii”, Algebra, teoriya chisel, diskretnaya geometriya i mnogomasshtabnoe modelirovanie: sovremennye problemy, prilozheniya i problemy istorii (Materialy XXI Mezhdunarodnoi konferentsii, posvyaschennoi 85-letiyu so dnya rozhdeniya A. A. Karatsuby. Tula), 2022, 106–110
13.
M. M. Komyagin, F. M. Malyshev, “Sposoby postroeniya i razlicheniya 5- konfiguratsii”, Diskretnaya matematika i ee prilozheniya (Materialy XIV Mezhdunarodnogo seminara im. O. B. Lupanova.), M., 2022, 159–162
2021
14.
F. M. Malyshev, “$k$-configuration”, Algebra, number theory, discrete geometry and multiscale modeling: modern problems, applications and problems of history, Proceedings of the XIX International Conference, 2021, 106–110
15.
F. M. Malyshev, “Completion of the proof of Brunn’s theorem by elementary means”, Chebyshevskii Sb., 22:2 (2021), 160–182
16.
F. M. Malyshev, “On the Brunn and Brunn–Minkowski theorems”, International Conference on Algebra, Analysis and Geometry, Proceedings of the International Conference. Kazan, 2021, 391–393
17.
F. M. Malyshev, “Prof of the Bruns theorem for schoolchildren”, Classical and Modern Geometry, Proceedings of the International Conference in honor of Levon S. Atanasyan on his 100th birthday, MPGU, Moscow, 2021, 391–393
18.
F. M. Malyshev, “Ciphers with provable durability”, Algebra, number theory, discrete geometry and multiscale modeling: modern problems, applications and problems of history, Proceedings of the XX International Conference, 2021, 12–16
19.
F. M. Malyshev, “Probabilistic relations for transformations of finite vector spaces”, Mat. Vopr. Kriptogr., 12:4 (2021), 43–58
20.
F. M. Malyshev, “Boolean analogues of Pascal triangle with the maximum possible number of ones”, Discrete Math. Appl., 31:5 (2021), 319–325
2020
21.
F. M. Malyshev, “Proof of the Brunn–Minkowski theorem by elementary methods”, Proceedings of the International Conference “Classical and Modern Geometry” Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 4, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 182, VINITI, Moscow, 2020, 70–94
22.
F. M. Malyshev, “Obobschennye grafy de Breina”, Algebra, teoriya chisel i diskretnaya geometriya: sovremennye problemy, prilozheniya i problemy istorii, Materialy XVIII Mezhdunarodnoi konferentsii, posvyaschennoi stoletiyu so dnya rozhdeniya professorov B. M. Bredikhina, V. I. Nechaeva i S. B. Stechkina. Tula, 2020, 180–184
2022
23.
F. M. Malyshev, “Generalized de Bruijn graphs”, Discrete Math. Appl., 32:1 (2022), 11–38
2020
24.
F. M. Malyshev, A. E. Trishin, “Linear and differential cryptanalysis: Another viewpoint”, Matem. vopr. kriptogr., 11:2 (2020), 83–98;
F. M. Malyshev, Mat. Vopr. Kriptogr., 11:4 (2020), 97–105
2019
26.
F. M. Malyshev, “Novoe dokazatelstvo neravenstva Brunna-Minkovskogo”, Klassicheskaya i sovremennaya geometriya (Materialy Mezhdunarodnoi konferentsii, posvyaschennoi 100-letiyu so dnya rozhdeniya V. T. Bazyleva), MPGU, Moskva, 2019, 111–113
27.
F. M. Malyshev, “Probabilistic characteristics of differential and linear relations for nonhomogeneous linear medium”, Mat. Vopr. Kriptogr., 10:1 (2019), 41–72
28.
F. M. Malyshev, “Raznostnye kharakteristiki slozhenii elementov $GF(2)^n$ po ${\rm mod}\,2$ i po ${\rm mod}\,2^n$"”, Algebra, teoriya chisel i diskretnaya geometriya: sovremennye problemy, prilozheniya i problemy istorii., Materialy XVI Mezhdunarodnoi konferentsii, posvyaschennoi 80-letiyu so dnya rozhdeniya professora Mishelya Deza. TGPU im. L. N. Tolstogo, Tula, 2019, 175–179
29.
F. M. Malyshev, “Elementarnoe dokazatelstvo teoremy Brunna–Minkovskogo”, Algebra, teoriya chisel i diskretnaya geometriya: sovremennye problemy, prilozheniya i problemy istorii, Materialy XVII Mezhdunarodnoi konferentsii, posvyaschennoi stoletiyu so dnya rozhdeniya professora N. I. Feldmana i devyanostoletiyu so dnya rozhdeniya professorov A. I. Vinogradova, A. V. Malysheva i B. F. Skubenko, TGPU im. L. N. Tolstogo, Tula, 2019, 168–172
30.
F. M. Malyshev, “Functional circuits defining families of permutations of the space $GF(2)^N$”, Mat. Vopr. Kriptogr., 10:3 (2019), 81–87
31.
F. M. Malyshev, “Generation of the alternating group by modular additions”, Discrete Math. Appl., 29:5 (2019), 303–309
2018
32.
F. M. Malyshev, “Gruppy podstanovok, porozhdënnye modulnymi slozheniyami”, Materialy mezhdunarodnoi algebraicheskoi konferentsii, posvyaschënnoi 110-letiyu so dnya rozhdeniya A.G. Kurosha ((Moskva, 2018) mekh-mat MGU, Moskva), 2018, 132–135
33.
F. M. Malyshev, “Usloviya slaboi obratimosti dlya $n$-kvazigrupp”, Materialy mezhdunarodnoi algebraicheskoi konferentsii, posvyaschënnoi 110-letiyu so dnya rozhdeniya A.G. Kurosha ((Moskva, 2018) mekh-mat MGU, Moskva), 2018, 135–138
34.
F. M. Malyshev, A. E. Trishin, “Lineinyi i raznostnyi metody v kriptografii (drugoi vzglyad)”, Algebra, teoriya chisel i diskretnaya geometriya: sovremennye problemy i prilozheniya., Materialy XV mezhdunarodnoi konferentsii, posvyaschënnoi stoletiyu so dnya rozhdeniya Nikolaya Mikhailovicha Korobova. TGPU im. L.N. Tolstogo, Tula, 2018, 42–45
35.
F. M. Malyshev, “Beskonechnye serii prostykh obobschënnykh grafov de Breina”, Algebra, teoriya chisel i diskretnaya geometriya: sovremennye problemy i prilozheniya., Materialy XV mezhdunarodnoi konferentsii, posvyaschënnoi stoletiyu so dnya rozhdeniya Nikolaya Mikhailovicha Korobova. TGPU im. L.N. Tolstogo, Tula, 2018, 187–190
2019
36.
F. M. Malyshev, “On affine classification of permutations on the space $GF(2)^3$”, Discrete Math. Appl., 29:6 (2019), 363–371
2018
37.
F. M. Malyshev, “Weakly invertible $n$-quasigroups”, Chebyshevskii Sb., 19:2 (2018), 304–318
2017
38.
F. M. Malyshev, “Kriptograficheski slabye funktsii uslozhneniya dlya trekhchlennykh lineinykh rekurrentnykh posledovatelnostei”, Matem. vopr. kriptogr., 8:1 (2017), 69–80
39.
A. V. Erokhin, F. M. Malyshev, A. E. Trishin, “Multidimensional linear method and diffusion characteristics of linear medium of ciphering transform”, Mat. Vopr. Kriptogr., 8:4 (2017), 29–62
2016
40.
F. M. Malyshev, “The Post-Gluskin-Hosszú theorem for finite $n$-quasigroups and self-invariant families of permutations”, Sb. Math., 207:2 (2016), 226–237
2017
41.
F. M. Malyshev, “Distribution density of commutant of random rotations of three-dimensional Euclidean space”, Theory Probab. Appl., 61:2 (2017), 277–294
2016
42.
F. M. Malyshev, “The Post – Gluskin – Hosszu theorem for $n$-quasigroups”, Proceedings of the XIV international conference “Algebra and Number Theory: Contemporary Problems and Applications” (Saratov, 2016), SSU, Saratov, 2016, 59–62
2017
43.
F. M. Malyshev, “Distribution of the extreme values of the number of ones in Boolean analogues of the Pascal triangle”, Discrete Math. Appl., 27:3 (2017), 149–176
2016
44.
F. M. Malyshev, D. I. Trifonov, “Diffusion properties of XSLP-ciphers”, Mat. Vopr. Kriptogr., 7:3 (2016), 47–60
2015
45.
F. M. Malyshev, “Family of Equal-Sized $n$-Dimensional Polyhedra Satisfying Cavalieri's Principle”, Math. Notes, 97:2 (2015), 213–229
46.
F. M. Malyshev, “The complexity of initial state recovery for a class of filter generators”, Mat. Vopr. Kriptogr., 6:1 (2015), 109–116
47.
F. M. Malyshev, “Kombinatornye konfiguratsii i odnorodnye triangulyatsii torov”, Materialy XIII Mezhdunarodnoi konferentsii «Algebra, teoriya chisel i diskretnaya geometriya: sovremennye problemy i prilozheniya» (Tula, 2015), TGPU, Tula, 2015, 309–312
48.
F. M. Malyshev, “Bases of recurrent sequences”, Chebyshevskii Sb., 16:2 (2015), 155–185
2014
49.
F. M. Malyshev, “The duality of differential and linear methods in cryptography”, Mat. Vopr. Kriptogr., 5:3 (2014), 35–47
50.
F. M. Malyshev, “On the fraction of matrices with maximal additive complexity”, Discrete Math. Appl., 24:6 (2014), 359–361
2013
51.
F. M. Malyshev, “Three series of $5$-configurations”, Mat. Vopr. Kriptogr., 4:3 (2013), 83–97
52.
F. M. Malyshev, “Four infinite series of $k$-configurations”, Mat. Vopr. Kriptogr., 4:4 (2013), 65–75
2012
53.
F. M. Malyshev, A. A. Frolov, “Classification of $(v,3)$-Configurations”, Math. Notes, 91:5 (2012), 689–696
54.
F. M. Malyshev, “Metric properties of embeddings of the set of integers into the cylider”, Mat. Vopr. Kriptogr., 3:3 (2012), 57–79
2011
55.
F. M. Malyshev, “Basises of integers under the multiplace shift operations”, Mat. Vopr. Kriptogr., 2:1 (2011), 29–73
56.
F. M. Malyshev, A. A. Frolov, “Classification theorems for (v,k)–configurations”, Proceedings of MaBIT-2010, “Mathematical aspects of information security” (Moscow, 2010), MCCME, 2011, 61–65
2010
57.
F. M. Malyshev, “Doubly transitive XLS-families of permutations”, Mat. Vopr. Kriptogr., 1:2 (2010), 93–103
58.
F. M. Malyshev, “On the asymptotic behavior of the probability distributions on the residue rings”, Proceedings of MaBIT-2009, “Mathematical aspects of information security” (Moscow, 2009), MCCME, 2010, 23–31
2009
59.
F. M. Malyshev, V. L. Migunov, “On the limit behavior of a probability distribution on the circle”, Chebyshevskii Sb., 10:1 (2009), 59–64
2008
60.
F. M. Malyshev, “Generating sets of elements of recurrent sequences”, Tr. Diskr. Mat., 11, no. 2, Fizmatlit, Moscow, 2008, 86–111
2007
61.
F. M. Malyshev, “On a generating system of alternating groups on finite vector spaces”, Tr. Diskr. Mat., 10, Fizmatlit, Moscow, 2007, 175–181
62.
F. M. Malyshev, “Bazisnye nabory v rekurrentnykh posledovatelnostyakh”, Materialy IX mezhdunar. sem. “Diskretnaya matematika i eë prilozheniya” (Moskva, 2007), mekhmat MGU, M., 2007, 442–444
63.
F. M. Malyshev, V. N. Romanov, “Strongly essential transforms of the Cartesian products of a set”, Bulletin of Tomsk state university, 23 (2007), 42–43
2006
64.
F. M. Malyshev, E. V. Kutyreva, “On the distribution of the number of ones in a Boolean Pascal's triangle”, Discrete Math. Appl., 16:3 (2006), 271–279
65.
F. M. Malyshev, “On a generating system of a symmetrical group”, Tr. Diskr. Mat., 9, Gelios APB, Moscow, 2006, 110–120
2005
66.
F. M. Malyshev, “Generation of uniform distribution robust to nonequiprobability of the initial digits”, Discrete Math. Appl., 15:6 (2005), 581–589
2004
67.
F. M. Malyshev, “Inheritance of some properties of generating families by a substitution group”, Tr. Diskr. Mat., 8, Fizmatlit, Moscow, 2004, 155–175
68.
F. M. Malyshev, E. V. Kutyreva, “On a property of the Boolean analogs of Pascal triangle”, Proceedings of the 4th All-Russian Symposium on Applied and Industrial Mathematics, 2004, 245–246
2003
69.
F. M. Malyshev, “Cryptography and mathematics”, Mathematics and practice, mathematics and culture, M., 2003, 30–33
70.
F. M. Malyshev, “Robust simulation of uniform distribution on the combinatorial objects”, Bulletin of ICSI, 2003
2001
71.
F. M. Malyshev, V. E. Tarakanov, “On $(v,k)$-configurations”, Sb. Math., 192:9 (2001), 1341–1364
1997
72.
F. M. Malyshev, V. E. Tarakanov, “Generalized de Bruijn graphs”, Math. Notes, 62:4 (1997), 449–456
73.
F. M. Malyshev, “An optimization problem for the Brunn–Minkowski inequality”, Proc. Steklov Inst. Math., 218 (1997), 257–260
1980
74.
F. M. Malyshev, “Decompositions of root systems”, Math. Notes, 27:6 (1980), 418–421
75.
F. M. Malyshev, “Simplexial systems of linear equations”, Algebra, MSU Press, Moscow, 1980, 53–56
76.
F. M. Malyshev, “On the nilpotency class of Lie algebras satisfying the Engel condition”, Bulletin of MSU, mech.-math., 2 (1980), 55–58
77.
F. M. Malyshev, “Complete complex structures on homogeneous spaces of semisimple Lie groups”, Math. USSR-Izv., 15:3 (1980), 501–522
1979
78.
F. M. Malyshev, “Compact complex uniform spaces with the finite fundamental group”, Proceedings of I.G. Petrovsky seminar, 7, MSU Press, Moscow, 1979, 228–231
1978
79.
F. M. Malyshev, “Decompositions of nilpotent Lie algebras”, Math. Notes, 23:1 (1978), 17–18
1977
80.
F. M. Malyshev, “Complex homogeneous spaces of semisimple Lie groups of type $D_n$”, Math. USSR-Izv., 11:4 (1977), 783–805
81.
F. M. Malyshev, “Decompositions of root systems”, Uspekhi Mat. Nauk, 32:4(196) (1977), 261–262
82.
F. M. Malyshev, “On closed subsets of roots and cohomology of regular subalgebras”, Math. USSR-Sb., 33:1 (1977), 125–135
83.
F. M. Malyshev, On the classification of the complex uniform spaces of the semisimple Lie groups, Candidate thesis, MIAN, M., 1977
1976
84.
F. M. Malyshev, “Complex homogeneous spaces of the Lie group $SO(2k+1,2l+1)$”, Math. USSR-Izv., 10:4 (1976), 763–782
85.
F. M. Malyshev, “Classification of two-dimensional algebras”, Geometry, v. 5, Gertsen LGPI, 1976, 87–93
1975
86.
F. M. Malyshev, “Complex homogeneous spaces of semisimple Lie groups of the first category”, Math. USSR-Izv., 9:5 (1975), 939–949
87.
F. M. Malyshev, “The decomposition of almost compact Lie algebras”, Bulletin of MSU, mech.-math., 2 (1975), 87–90
1974
88.
F. M. Malyshev, “Local decompositions of pseudo-orthogonal groups”, Math. Notes, 16:4 (1974), 969–974
Инвариантные дифференциальные полиномы F. M. Malyshev All-russian scientific and practical conference "Scientist, teacher, mentor", dedicated to the 85th anniversary of the birth of professor A. R. Esayan. Tula April 20, 2023 12:40
9.
Способы построения и различения 5-конфигураций M. M. Komiagin, F. M. Malyshev Fourteenth international seminar "Discrete mathematics and its applications" named after academician O.B. Lupanov June 22, 2022 14:30
10.
Изоморфизмы извеcтных 5-конфигураций M. M. Komyagin, F. M. Malyshev XXI International Conference «Algebra, Number Theory, Discrete Geometry and Multiscale Modeling: Modern Problems, Applications and Problems of History», Dedicated to the 85th Anniversaryof the Birth of A. A. Karatsuba May 19, 2022 12:10
$k$-configuration F. M. Malyshev Research Seminar of the Department of Higher Algebra MSU November 15, 2021 16:45
13.
Proof of the Bruns theorem for schoolchildren F. M. Malyshev The International Conference "Classical and Modern Geometry" in honor of Levon S. Atanasyan on his 100th birthday November 1, 2021 13:05
14.
$k$-configurations F. M. Malyshev Seminar by Department of Discrete Mathematic, Steklov Mathematical Institute of RAS September 28, 2021 16:00
15.
Шифры с доказуемой стойкостью F. M. Malyshev XX International Conference "Algebra, Number Theory, Discrete Geometry and Multiscale Modeling: Modern Problems, Applications and Problems of History", Dedicated to 130 Anniversary of Academician I. M. Vinogradov September 22, 2021 10:50
$k$-configuration F. M. Malyshev XIX International Conference "Algebra, number theory, discrete geometry and multiscale modeling: modern problems, applications and problems of history". Tula. 18–22 May 2021 May 20, 2021 15:40
18.
Обобщённые графы де Брейна F. M. Malyshev XVIII Международная конференция «Алгебра, теория чисел и дискретная геометрия: современные проблемы, приложения и проблемы истории». Тула. 23–26 сентября 2020 г. September 23, 2020 15:00
Элементарное доказательство теоремы Брунна–Минковского F. M. Malyshev XVII International Conference «Algebra, Number Theory and Discrete Geometry: modern problems, applications and problems of history» September 25, 2019 11:40
Новое доказательство неравенства Брунна-Минковского F. M. Malyshev Международная конференция "Классическая и современная геометрия", посвящённая 100-летию со дня рождения Вячеслава Тимофеевича Базылева April 23, 2019 16:40
Infinite series of simple generalized de Brein graphs F. M. Malyshev XV International Conference «Algebra, Number Theory and Discrete Geometry: modern problems and applications», dedicated to the centenary of the birth of the Doctor of Physical and Mathematical Sciences, Professor of the Moscow State University Korobov Nikolai Mikhailovich May 30, 2018 15:00
29.
Проблемы обоснования
линейного и разностного методов в криптографии F. M. Malyshev, A. E. Trishin XV International Conference «Algebra, Number Theory and Discrete Geometry: modern problems and applications», dedicated to the centenary of the birth of the Doctor of Physical and Mathematical Sciences, Professor of the Moscow State University Korobov Nikolai Mikhailovich May 30, 2018 13:15
30.
Условия слабой обратимости для $n$-квазигрупп F. M. Malyshev Международная алгебраическая конференция, посвящённая 110-летию со дня рождения А.Г. Куроша (Москва, 2018) May 24, 2018 16:05
2023
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