Research
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On the Discrete Logarithm Problem in the Ideal Class Group of Multiquadratic Fields.
In LatinCrypt 2023.
Slides. Code: Github -
On ideal class group computation of imaginary multiquadratic fields.
Prikl. Diskr. Mat., 2022, no. 58, 22–30.
Math-Net. Code: Github -
On the number of points on the curve \(y^2 = x^{7} + a x^4 + b x\) over a finite field (with Y. F. Boltnev).
In Journal of Applied and Industrial Mathematics, 2022, vol. 16, 302–312
SageMath: [code]. Examples: [2716 bit Jacobian] [3392 bit Jacobian] -
An algorithm for computing the Stickelberger ideal of multiquadratic number fields (with E. A. Kirshanova, E. S. Malygina, D. O. Olefirenko).
In Prikl. Diskr. Mat., 2021, no. 51, 9–30 [in Russian].
Math-Net. -
Counting points on hyperelliptic curves of type \(y^2=x^{2g+1}+ax^{g+1}+bx\).
In Finite Fields and Their Applications, 2020, vol. 68.
Preprint: arXiv. SageMath Notebooks: [genus 3 algorithm]. [genus 4 algorithm]. -
On the distribution of orders of Frobenius action on \(\ell\)-torsion of abelian surfaces (with N. S. Kolesnikov).
In Prikl. Diskr. Mat., 2020, no. 48, 22–33. Math-Net. [SageMath Notebook for §7]. -
Characteristic polynomials of the curve \(y^2=x^7+ax^4+bx\) over finite fields (with Y. F. Boltnev).
In SibeCrypt'19. Math-Net. SageMath: [genus 3 p.c. algorithm]. -
Hyperelliptic curves, Cartier–Manin matrices and Legendre polynomials.
In Prikl. Diskr. Mat., 2017, no. 37, 20–31.
PDF. -
On bounds for balanced embedding degree.
In Prikl. Diskr. Mat., 2016, no. 2(32), 63–86 [in Russian].
PDF. -
Thesis: Counting points on hyperelliptic curves with geometrically split Jacobians, 2022 [in Russian].
PDF.
Advisor: Ekaterina Malygina
Talks
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Approx-SVP in multiquadratic ideal lattices [slides].
Séminaire de Théorie Algorithmique des Nombres, Université de Bordeaux, Febrary 13, 2024. -
Elliptic curve cryptography (in Russian) [slides] [video].
at Mathematical school, MEPhI University, December 4, 2023. -
Counting points on hyperelliptic curves with geometrically split Jacobians [poster].
at Fourteenth Algorithmic Number Theory Symposium, ANTS-XIV,
University of Auckland, New Zealand June 30 - July 4, 2020. -
Isogeny-based cryptography (in Russian) [slides]
at Mathematical school, MEPhI University, December 6, 2024.
Teaching
2024 Autumn term
2023 Autumn term
2022 Autumn term
2022 Spring term
2021 Autumn term
2021 Spring term
2020 Autumn term