Zobrazeno 1 - 10
of 220
pro vyhledávání: '"Yokoyama Kazuhiro"'
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:
Ishihara, Yuki, Yokoyama, Kazuhiro
We present an effective method for computing parametric primary decomposition via comprehensive Gr\"obner systems. In general, it is very difficult to compute a parametric primary decomposition of a given ideal in the polynomial ring with rational co
Externí odkaz:
http://arxiv.org/abs/2408.15917
Autor:
Takahashi Yasushi, Kudo Momonari, Fukasaku Ryoya, Ikematsu Yasuhiko, Yasuda Masaya, Yokoyama Kazuhiro
Publikováno v:
Journal of Mathematical Cryptology, Vol 15, Iss 1, Pp 31-44 (2020)
Recently, supersingular isogeny cryptosystems have received attention as a candidate of post-quantum cryptography (PQC). Their security relies on the hardness of solving isogeny problems over supersingular elliptic curves. The meet-in-the-middle appr
Externí odkaz:
https://doaj.org/article/3ba2f1827cf246d99016113ef3aee61b
Publikováno v:
Journal of Mathematical Cryptology, Vol 14, Iss 1, Pp 460-485 (2020)
Since Semaev introduced summation polynomials in 2004, a number of studies have been devoted to improving the index calculus method for solving the elliptic curve discrete logarithm problem (ECDLP) with better complexity than generic methods such as
Externí odkaz:
https://doaj.org/article/bb64b7a98fd2462c84a20ffe0d32dd6b
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
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
Publikováno v:
Journal of Mathematical Cryptology, Vol 11, Iss 1, Pp 1-24 (2017)
In 2015, Fukase and Kashiwabara proposed an efficient method to find a very short lattice vector. Their method has been applied to solve Darmstadt shortest vector problems of dimensions 134 to 150. Their method is based on Schnorr’s random sampling
Externí odkaz:
https://doaj.org/article/8cb832d029e54d99b78edce1c77dbd08
Solving a polynomial system, or computing an associated Gr\"obner basis, has been a fundamental task in computational algebra. However, it is also known for its notorious doubly exponential time complexity in the number of variables in the worst case
Externí odkaz:
http://arxiv.org/abs/2311.12904
Publikováno v:
Journal of Mathematical Cryptology, Vol 8, Iss 3, Pp 305-329 (2014)
In this paper, we revisit the fully homomorphic encryption (FHE) scheme implemented by Gentry and Halevi, which is just an instantiation of Gentry's original scheme based on ideal lattices. Their FHE scheme starts from a somewhat homomorphic encrypti
Externí odkaz:
https://doaj.org/article/0f52c51c11e44e7f9605e409875bd5d5
Publikováno v:
ISSAC '20: International Symposium on Symbolic and Algebraic Computation, Jul 2020, Kalamata Greece, France. pp.257-264
Let K be a field equipped with a valuation. Tropical varieties over K can be defined with a theory of Gr{\"o}bner bases taking into account the valuation of K. Because of the use of the valuation, the theory of tropical Gr{\"o}bner bases has proved t
Externí odkaz:
http://arxiv.org/abs/2009.02067