algebraic geometry, number theory, finite fields, hyperelliptic curves
Main publications:
E. A. Kirshanova, E. S. Malygina, S. A. Novoselov, D. O. Olefirenko, “An algorithm for computing the Stickelberger ideal for multiquadratic number fields”, Prikl. Diskr. Mat., 2021, no. 51, 9–30
S. A. Novoselov, “Counting points on hyperelliptic curves of type $y^2=x^{2g+1}+ax^{g+1}+bx$”, Finite Fields and Their Applications, 68 (2020) , 27 pp., 101757
S. A. Novoselov, “Hyperelliptic curves, Cartier–Manin matrices and Legendre polynomials”, PDM, 2017, no. 37, 20–31
E. S. Malygina, A. V. Kutsenko, S. A. Novoselov, N. S. Kolesnikov, A. O. Bakharev, I. S. Khilchuk, A. S. Shaporenko, N. N. Tokareva, “Post-quantum cryptosystems: open problems and solutions. Lattice-based cryptosystems”, J. Appl. Industr. Math., 17:4 (2023), 767–790
4.
S. A. Novoselov, “Counting points on hyperelliptic curves of type $y^2=x^{2g+1}+ax^{g+1}+bx$”, Finite Fields and Their Applications, 68 (2020) , 27 pp., 101757
S. A. Novoselov, Yu. F. Boltnev, “On the number of points on the curve $y^2 = x^{7} + ax^4 + bx$ over a finite field”, Diskretn. Anal. Issled. Oper., 29:2 (2022), 62–79
6.
S. A. Novoselov, “On ideal class group computation of imaginary multiquadratic fields”, PDM, 2022, no. 58, 22–30;
E. A. Kirshanova, N. S. Kolesnikov, E. S. Malygina, S. A. Novoselov, “Post-quantum signature proposal for standardisation”, Prikl. Diskr. Mat. Suppl., 2020, no. 13, 44–51
8.
D. O. Olefirenko, E. A. Kirshanova, E. S. Malygina, S. A. Novoselov, “An algorithm for computing the Stickelberger elements for imaginary multiquadratic fields”, Prikl. Diskr. Mat. Suppl., 2020, no. 13, 12–17
9.
N. S. Kolesnikov, S. A. Novoselov, “On the order of the Frobenius endomorphism action on $l$-torsion subgroup of abelian surfaces”, Prikl. Diskr. Mat. Suppl., 2019, no. 12, 11–12
10.
S. A. Novoselov, “Hyperelliptic curves, Cartier–Manin matrices and Legendre polynomials”, PDM. Prilozhenie, 2017, no. 10, 29–32
E. A. Kirshanova, E. S. Malygina, S. A. Novoselov, D. O. Olefirenko, “An algorithm for computing the Stickelberger ideal for multiquadratic number fields”, Prikl. Diskr. Mat., 2021, no. 51, 9–30
12.
N. S. Kolesnikov, S. A. Novoselov, “On the distribution of orders of Frobenius action on $\ell$-torsion of abelian surfaces”, PDM, 2020, no. 48, 22–33;
13.
E. S. Malygina, S. A. Novoselov, “Division polynomials for hyperelliptic curves defined by Dickson polynomials”, Matem. vopr. kriptogr., 11:2 (2020), 69–81;
14.
E. M. Melnichuk, S. A. Novoselov, “On characteristic polynomials for some genus $2$ and $3$ curves with $p$-rank $1$”, Prikl. Diskr. Mat. Suppl., 2019, no. 12, 21–24
15.
S. A. Novoselov, “Counting points on hyperelliptic curves of type $y^2=x^{2g+1}+ax^{g+1}+bx$”, PDM. Prilozhenie, 2018, no. 11, 30–33
16.
S. A. Novoselov, “On bounds for balanced embedding degree”, Prikl. Diskr. Mat., 2016, no. 2(32), 63–86
17.
E. S. Malygina, A. V. Kutsenko, S. A. Novoselov, N. S. Kolesnikov, A. O. Bakharev, I. S. Khilchuk, A. S. Shaporenko, N. N. Tokareva, “Post-quantum cryptosystems: open problems and current solutions. Isogeny-based and code-based cryptosystems”, J. Appl. Industr. Math., 18:1 (2024), 103–121
18.
S. A. Novoselov, “The characteristic polynomials of geometrically split ordinary abelian varieties of dimension 3”, Prikl. Diskr. Mat. Suppl., 2024, no. 17, 12–16
19.
E. S. Malygina, A. V. Kutsenko, S. A. Novoselov, N. S. Kolesnikov, A. O. Bakharev, I. S. Khilchuk, A. S. Shaporenko, N. N. Tokareva, “Main approaches in post-quantum cryptography: description, a comparative study”, Prikl. Diskr. Mat. Suppl., 2023, no. 16, 58–65
20.
Yu. F. Boltnev, S. A. Novoselov, V. A. Osipov, “On construction of maximal genus 3 hyperelliptic curves”, Prikl. Diskr. Mat. Suppl., 2021, no. 14, 24–30
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