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Перспективные подходы к реализации методов генерации криптографически стойких эллиптических кривых
Т. 1: Перспективные технологии в средствах передачи информации.
-, 2019.
Смирнов И. А., Разумов П. В., Черкесова Л. В., Сафарьян О. А., Бачило А. О.
Popov V., Труды Математического института им. В.А. Стеклова РАН 2025 Т. 329 С. 209–226
Let X be the variety of flexes of plane cubics. The following statements are proved in this paper: (1) X is an irreducible rational algebraic variety equipped with an effective algebraic action of the group PSL(3); (2) X is PSL(3)-equivariantly birationally isomorphic to a homogeneous fiber bundle over PSL(3)/K with fiber being a projective line, ...
Added: December 16, 2025
Kuninets A., Malygina E., Раточка В. Л. et al., Прикладная дискретная математика 2023 № 62 С. 83–105
Рассматриваются теоретические основы алгебраических кривых и их функциональных полей, необходимые для построения алгеброгеометрических (АГ) кодов, а также пар, исправляющих ошибки, с целью их дальнейшего применения для декодирования кодов. Приведены теория, необходимая для обоснования корректности работы алгоритма декодирования АГ-кодов на основе пар, исправляющих ошибки, и сам алгоритм декодирования. Рассмотрены примеры построения АГ-кодов, ассоциированных с эллиптической кривой, ...
Added: December 12, 2025
Popov V., Успехи математических наук 2024 Т. 79 № 6 С. 169–170
Let X be the variety of flexes of plane cubics. The following properties of the algebraic variety X are proven: (1) X is irreducible and endowed with a faithful algebraic action of the group G=PSL(3). (2) X is rational. (3) There is a subgroup K of G isomorphic to the binary tetrahedral group such that ...
Added: December 2, 2024
Malygina E., Кунинец А. А., Раточка В. Л. et al., Прикладная дискретная математика 2023 № 62 С. 83–105
We consider the basic theory of algebraic curves and their function fields necessary for constructing algebraic geometry codes and a pair of codes constituting error-correction pair which is used in a precomputation step of the decoding algorithm for the algebraic geometry codes. Also, we consider the decoding algorithm and give the necessary theory to prove ...
Added: March 19, 2024
Buryak A., Moscow Mathematical Journal 2023 Vol. 23 No. 3 P. 309–317
An algorithm to determine all the Gromov–Witten invariants of any smooth projective curve was obtained by Okounkov and Pandharipande in 2006. They identified stationary invariants with certain Hurwitz numbers and then presented Virasoro type constraints that allow to determine all the other Gromov–Witten invariants in terms of the stationary ones. In the case of an ...
Added: November 20, 2023
Разумов П. В., Черкесова Л. В., Пилипенко И. А. et al., Вестник Донского государственного технического университета 2019 Т. 19 № 2 С. 185–194
The NTRUEncrypt cryptographic system, the
calculation of the algorithmic complexity of the development
of the NTRUEncrypt cryptosystem and its modifications are
considered. The study objectives are to develop NTRUEncrypt,
an efficient post-quantum cryptographic algorithm,
which has high cryptographic resistance to quantum computer
attacks, to work out a modification of the proposed algorithm,
to analyze and experimentally validate its advantages. ...
Added: May 9, 2023
Черкесова Л. В., Разумов П. В., Смирнов И. А., Молодой исследователь Дона 2022 № 3 (18) С. 78–83
The article is devoted to the comparative analysis of the lightweight Nash block encryption algorithm and the algorithm presented by the us national security Agency in 2013 - Speck. Their detailed description is given, the analysis is made. The task of the study is to investigate and analyze cryptographic encryption algorithms used in devices with ...
Added: May 9, 2023
Radomskii A., Известия РАН. Серия математическая 2023 Т. 87 № 1 С. 119–160
We obtain some results related to Romanoff’s theorem. ...
Added: February 15, 2023
Malakhov S., В кн.: Межвузовская научно-техническая конференция студентов, аспирантов и молодых специалистов им. Е.В. Арменского.: М.: МИЭМ НИУ ВШЭ, 2019. С. 208–209.
Работа отражает исследование некоторых эллиптических кривых из зарубежных стандартов на соответствие требованиям ГОСТ Р 34.10-2012. При этом для рассмотрения были выбраны эллиптические кривые над полем простого порядка, поддерживаемые криптографической библиотекой OpenSSL 1.0.2. ...
Added: September 26, 2019
Serge Lvovski, Moscow Mathematical Journal 2019 Vol. 19 No. 3 P. 597–613
We show that if we are given a smooth non-isotrivial family of curves of genus 1 over C with a smooth base B for which the general fiber of the mapping J : B → A 1 (assigning j-invariant of the fiber to a point) is connected, then the monodromy group of the family (acting ...
Added: August 30, 2019
Nesterenko A., Математические вопросы криптографии 2019 Vol. 10 No. 2 P. 135–144
An algorithm for the construction of elliptic curves satisfying special requirements is presented. The choice of requirements aims to prevent known attacks on the elliptic curve discrete logarithm problem in special cases. The results of practical experiments are discussed, some parameters of concrete elliptic curves are given. ...
Added: August 26, 2019
Poberezhny V. A., Matveeva A., Journal of Geometry and Physics 2017 Vol. 114 P. 384–393
We consider a generalization of Riemann–Hilbert problem on elliptic curves. For a given elliptic curve and irreducible representation of free group with two generators we construct explicitly a semistable vector bundle of degree zero obeying a logarithmic connection such that its monodromy over fundamental parallelogram is equivalent to given free group representation, monodromy along a−cycle is ...
Added: October 26, 2016
Matveeva A., Poberezhny V. A., Математические заметки 2017 Т. 101 № 1 С. 91–100
A one-dimensional generalization of the Riemann–Hilbert problem from the Riemann sphere to an elliptic curve is considered. A criterion for its positive solvability is obtained and an explicit form of all possible solutions is found. As in the spherical case, the solutions turn out to be isomonodromic. ...
Added: October 18, 2016
Takebe T., Kuroki G., Journal of Physics A: Mathematical and Theoretical 2001 Vol. 34 No. 11 P. 2403–2413
We construct a Gaudin type lattice model as the Wess-Zumino-Witten model on elliptic curves at the critical level. Bethe eigenvectors are obtained by the bosonisation technique. ...
Added: August 14, 2014
Takebe T., International Journal of Modern Physics A 2004 Vol. 19, May suppl. P. 418–435
Trigonometric degeneration of the Baxter-Belavin elliptic r matrix is described by the degeneration of the twisted WZW model on elliptic curves. The spaces of conformal blocks and conformal coinvariants of the degenerate model are factorised into those of the orbifold WZW model. ...
Added: August 14, 2014