Zobrazeno 1 - 10
of 76
pro vyhledávání: '"Kudo, Momonari"'
Autor:
Kudo, Momonari, Yokoyama, Kazuhiro
In this paper, we study generalized cryptographic semi-regular sequences, which are expected to generic in the space of homogeneous polynomial sequences on which the coordinate rings have Krull dimension one. We provide an upper-bound on the complexi
Externí odkaz:
http://arxiv.org/abs/2410.23211
Autor:
Kudo, Momonari, Yokoyama, Kazuhiro
In this paper, we study the solving degrees for affine semi-regular sequences and their homogenized sequences. Some of our results are considered to give mathematically rigorous proofs of the correctness of methods for computing Gr\"{o}bner bases of
Externí odkaz:
http://arxiv.org/abs/2404.03530
In algebraic geometry, superspecial curves are important research objects. While the number of superspecial genus-3 curves in characteristic $p$ is known, the number of hyperelliptic ones among them has not been determined even for small $p$. In this
Externí odkaz:
http://arxiv.org/abs/2401.10500
Autor:
Kudo, Momonari, Yokoyama, Kazuhiro
Publikováno v:
Mathematical Foundations for Post-Quantum Cryptography (T. Takagi et al. eds), Mathematics for Industry, Springer, 2024
Gr\"{o}bner bases are nowadays central tools for solving various problems in commutative algebra and algebraic geometry. A typical use of Gr\"{o}bner bases is the multivariate polynomial system solving, which enables us to construct algebraic attacks
Externí odkaz:
http://arxiv.org/abs/2401.07768
Autor:
Kudo, Momonari
A Howe curve is defined as the normalization of the fiber product over a projective line of two hyperelliptic curves. Howe curves are very useful to produce important classes of curves over fields of positive characteristic, e.g., maximal, superspeci
Externí odkaz:
http://arxiv.org/abs/2401.00760
Autor:
Ohashi, Ryo, Kudo, Momonari
In algebraic geometry, enumerating or finding superspecial curves in positive characteristic $p$ is important both in theory and in computation. In this paper, we propose feasible algorithms to enumerate or find superspecial hyperelliptic curves of g
Externí odkaz:
http://arxiv.org/abs/2312.16858
Autor:
Moriya, Tomoki, Kudo, Momonari
In the past several years, Howe curves have been studied actively in the field of algebraic curves over fields of positive characteristic. Here, a Howe curve is defined as the desingularization of the fiber product over a projective line of two hyper
Externí odkaz:
http://arxiv.org/abs/2310.15993
In arithmetic and algebraic geometry, superspecial (s.sp.\ for short) curves are one of the most important objects to be studied, with applications to cryptography and coding theory. If $g \geq 4$, it is not even known whether there exists such a cur
Externí odkaz:
http://arxiv.org/abs/2210.14822
Autor:
Moriya, Tomoki, Kudo, Momonari
A Richelot isogeny between Jacobian varieties is an isogeny whose kernel is included in the $2$-torsion subgroup of the domain. A Richelot isogeny whose codomain is the product of two or more principally polarized abelian varieties is called a decomp
Externí odkaz:
http://arxiv.org/abs/2209.02926
Autor:
Kudo, Momonari, Harashita, Shushi
The number $N_9(5)$, the maximal number of $\mathbb{F}_9$-rational points on curves over $\mathbb{F}_9$ of genus $5$ is unknown, but it is known that $32 \le N_9(5)\le 35$. In this paper, we enumerate hyperelliptic curves and trigonal curves over $\m
Externí odkaz:
http://arxiv.org/abs/2204.06805