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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
Brandt--Sohn correspondence shows a connection between maximal orders in quaternion algebra $B_{p,\infty}$ and ternary quadratic forms with discriminant $p$. In this paper, we use this correspondence to compute endomorphism rings of supersingular ell
Externí odkaz:
http://arxiv.org/abs/2409.11025
Let $p>3$ be a prime and $E$ be a supersingular elliptic curve defined over $\mathbb{F}_{p^2}$. Let $c$ be a prime with $c < 3p/16$ and $G$ be a subgroup of $E[c]$ of order $c$. The pair $(E,G)$ is called a supersingular elliptic curve with level-$c$
Externí odkaz:
http://arxiv.org/abs/2312.08844
Publikováno v:
In Finite Fields and Their Applications December 2024 100
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
Isogenies occur throughout the theory of elliptic curves. Recently, the cryptographic protocols based on isogenies are considered as candidates of quantum-resistant cryptographic protocols. Given two elliptic curves $E_1, E_2$ defined over a finite f
Externí odkaz:
http://arxiv.org/abs/2001.00126
Publikováno v:
Journal of Mathematical Cryptology, vol. 15, no. 1, 2021, pp. 454-464
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 $\mathbb{F}_{p^2}$, if an imaginary quadratic order $O$ can be emb
Externí odkaz:
http://arxiv.org/abs/1912.03073
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Publikováno v:
P-Adic Numbers, Ultrametric Analysis & Applications; Mar2024, Vol. 16 Issue 1, p23-42, 20p