Zobrazeno 1 - 10
of 94
pro vyhledávání: '"Deng Yingpu"'
Publikováno v:
Journal of Mathematical Cryptology, Vol 15, Iss 1, Pp 454-464 (2021)
Loops and cycles play an important role in computing endomorphism rings of supersingular elliptic curves and related cryptosystems. For a supersingular elliptic curve E defined over 𝔽p2, if an imaginary quadratic order O can be embedded in End(E)
Externí odkaz:
https://doaj.org/article/901b77dc661f431985bdcc1c58edd201
Autor:
Zhang, Chi, Deng, Yingpu
In 2021, the $p$-adic signature scheme and public-key encryption cryptosystem were introduced. These schemes have good efficiency but are shown to be not secure. The attack succeeds because the extension fields used in these schemes are totally ramif
Externí odkaz:
http://arxiv.org/abs/2410.17982
Autor:
Deng, Yingpu
Dual lattice is an important concept of Euclidean lattices. In this paper, we first give the right definition of the concept of the dual lattice of a $p$-adic lattice from the duality theory of locally compact abelian groups. The concrete constructio
Externí odkaz:
http://arxiv.org/abs/2401.14023
In 2018, the longest vector problem (LVP) and the closest vector problem (CVP) in $p$-adic lattices were introduced. These problems are closely linked to the orthogonalization process. In this paper, we first prove that every $p$-adic lattice has an
Externí odkaz:
http://arxiv.org/abs/2311.17415
Autor:
Wang, Zhaonan, Deng, Yingpu
$p$-adic continued fractions, as an extension of the classical concept of classical continued fractions to the realm of $p$-adic numbers, offering a novel perspective on number representation and approximation. While numerous $p$-adic continued fract
Externí odkaz:
http://arxiv.org/abs/2309.05601
Autor:
Deng, Yingpu
In his famous book ``Basic Number Theory", Weil proved several theorems about the existence of norm-orthogonal bases in finite-dimensional vector spaces and lattices over local fields. In this paper, we transform Weil's proofs into algorithms for fin
Externí odkaz:
http://arxiv.org/abs/2305.07886
Autor:
Wang, Zhaonan, Deng, Yingpu
The properties of continued fractions whose partial quotients belong to a quadratic number field K are distinct from those of classical continued fractions. Unlike classical continued fractions, it is currently impossible to identify elements with pe
Externí odkaz:
http://arxiv.org/abs/2304.11803
Autor:
Wang, Zhaonan, Deng, Yingpu
The problem of representing a given positive integer as a sum of four squares of integers has been widely concerned for a long time, and for a given positive odd $n$ one can find a representation by doing arithmetic in a maximal order of quaternion a
Externí odkaz:
http://arxiv.org/abs/2205.00642
It is well known that there is a one-to-one correspondence between supersingular $j$-invariants up to the action of $\text{Gal}(\mathbb{F}_{p^2}/\mathbb{F}_p)$ and type classes of maximal orders in $B_{p,\infty}$ by Deuring's theorem. Interestingly,
Externí odkaz:
http://arxiv.org/abs/2203.02097
For a prime $p>3$, let $D$ be the discriminant of an imaginary quadratic order with $|D|< \frac{4}{\sqrt{3}}\sqrt{p}$. We research the solutions of the class polynomial $H_D(X)$ mod $p$ in $\mathbb{F}_p$ if $D$ is not a quadratic residue in $\mathbb{
Externí odkaz:
http://arxiv.org/abs/2101.04937