Аннотация:
В статье проводится анализ алгоритмов открытого построения ключа на некоммутативной группе. Рассмотрены алгоритмы факторизации и разложения ассоциативных алгебр (малой размерности). Дан обзор приложений (в том числе в криптографии) так называемых “спрятанных матриц”.
Образец цитирования:
А. С. Кузьмин, В. Т. Марков, А. А. Михалёв, А. В. Михалёв, А. А. Нечаев, “Криптографические алгоритмы на группах и алгебрах”, Фундамент. и прикл. матем., 20:1 (2015), 205–222; J. Math. Sci., 223:5 (2017), 629–641
Vitaly Roman'kov, Alexander Ushakov, Vladimir Shpilrain, “Algebraic and quantum attacks on two digital signature schemes”, Journal of Mathematical Cryptology, 17:1 (2023)
Alexandr A. Moldovyan, Dmitriy N. Moldovyan, “A new method for developing signature algorithms on finite non-commutative algebras”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2022, no. 1, 56–65
M. H. Nguyen, D. N. Moldovyan, N. A. Moldovyan, M. Q. Le, G. L. Nguyen, “Blind Signature Protocol Based on Hidden Discrete Logarithm Problem Set in a Commutative Algebra”, Iran J Sci Technol Trans Sci, 46:1 (2022), 323
С. С. Манаенко, С. В. Дворников, А. В. Пшеничников, “Теоретические аспекты формирования сигнальных конструкций сложной структуры”, Информатика и автоматизация, 21:1 (2022), 68–94 [S. Manaenko, S. Dvornikov, A. Pshenichnikov, “Theoretical aspects in forming complex structure signal”, Informatics and Automation, 21:1 (2022), 68–94]
N. M. Adrianov, V. A. Artamonov, I. N. Balaba, Yu. A. Bahturin, L. A. Bokut, V. V. Borisenko, E. I. Bunina, I. A. Chubarov, S. A. Gaifullin, S. T. Glavatskii, I. Z. Golubchik, S. González, A. V. Grishin, A. E. Guterman, N. I. Dubrovin, N. K. Ilyina, A. Ya. Kanel-Belov, A. L. Kanunnikov, E. S. Kislitsyn, V. K. Kharchenko, A. A. Klyachko, I. B. Kozhukhov, E. M. Kreines, O. V. Kulikova, T. P. Lukashenko, O. V. Markova, C. Martínez, A. A. Mikhalev, A. V. Mikhalev, A. Yu. Olshanskii, S. V. Pchelintsev, A. E. Pentus, A. V. Petrov, Yu. G. Prokhorov, A. A. Shafarevich, A. I. Shafarevich, I. P. Shestakov, E. E. Shirshova, V. E. Shpilrain, V. V. Tenzina, D. A. Timashev, A. A. Tuganbaev, I. N. Tumaykin, M. V. Zaicev, E. I. Zelmanov, “Victor Timofeevich Markov (21.06.1948–15.07.2019)”, J Math Sci, 262:5 (2022), 592
Minh Hieu Nguyen, Canh Ngoc Hoang, A.A. Moldovyan, N.A. Moldovyan, Huy Quang Vu, Danh Kim Le Tran, “A novel version of the hidden logarithm problem for post-quantum signature algorithms”, Theoretical Computer Science, 921 (2022), 36
N. A. Moldovyan, A. A. Moldovyan, “Digital signature scheme on the 2×2 matrix algebra”, Вестн. С.-Петербург. ун-та. Сер. 10. Прикл. матем. Информ. Проц. упр., 17:3 (2021), 254–261
Nikolay Andreevich Moldovyan, Dmitriy Nikolaevich Moldovyan, “A novel method for developing post-quantum cryptoschemes and a practical signature algorithm”, ACI, 2021
Dmitriy N. Moldovyan, Alexandr A. Moldovyan, Nikolay A. Moldovyan, “Post-quantum signature schemes for efficient hardware implementation”, Microprocessors and Microsystems, 80 (2021), 103487
А. А. Костина, А. Ю. Мирин, Д. Н. Молдовян, Р. Ш. Фахрутдинов, “Метод задания конечных некоммутативных ассоциативных алгебр произвольной четной размерности для построения постквантовых криптосхем”, Информ. и её примен., 14:1 (2020), 94–100
D. N. Moldovyan, “New form of the hidden logarithm problem and its algebraic support”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2020, no. 2, 3–10
N. A. Moldovyan, “Signature schemes on algebras, satisfying enhanced criterion of post-quantum security”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2020, no. 2, 62–67
D. N. Moldovyan, N. A. Moldovyan, A. A. Moldovyan, “Commutative encryption method based on hidden logarithm problem”, Вестн. ЮУрГУ. Сер. Матем. моделирование и программирование, 13:2 (2020), 54–68
Alexandr Andreevich Moldovyan, Nikolay Andreevich Moldovyan, Ngoc Han Phieu, Cong Manh Tran, Hieu Minh Nguyen, Advances in Intelligent Systems and Computing, 1014, Frontiers in Intelligent Computing: Theory and Applications, 2020, 1
Nguyen Hieu Minh, Dmitriy Nikolaevich Moldovyan, Nikolay Andreevich Moldovyan, Quang Minh Le, Sy Tan Ho, Long Giang Nguyen, Hai Vinh Nguyen, Cong Manh Tran, Advances in Intelligent Systems and Computing, 1125, Intelligent Computing in Engineering, 2020, 993
Nikolay A. Moldovyan, Dmitriy N. Moldovyan, Alexander A. Moldovyan, Hieu Minh Nguyen, Le Hoang Tuan Trinh, Lecture Notes in Computer Science, 12466, Future Data and Security Engineering, 2020, 325
D.Yu. Guryanov, D.N. Moldovyan, A. A. Moldovyan, “Post-quantum digital signature schemes: setting a hidden group with two-dimensional cyclicity”, I&C, 4 (2020), 75
N. A. Moldovyan, A. A. Moldovyan, “Finite non-commutative associative algebras as carriers of hidden discrete logarithm problem”, Вестн. ЮУрГУ. Сер. Матем. моделирование и программирование, 12:1 (2019), 66–81
N. A. Moldovyan, “Finite non-commutative associative algebras for setting the hidden discrete logarithm problem and post-quantum cryptoschemes on its base”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2019, no. 1, 71–78
Dmitriy N. Moldovyan, Alexandr A. Moldovyan, Han Ngoc Phieu, Minh Hieu Nguyen, Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, 298, Context-Aware Systems and Applications, and Nature of Computation and Communication, 2019, 205