Zobrazeno 1 - 10
of 42
pro vyhledávání: '"Eisentraeger, Kirsten"'
We give a deterministic polynomial time algorithm to compute the endomorphism ring of a supersingular elliptic curve in characteristic p, provided that we are given two noncommuting endomorphisms and the factorization of the discriminant of the ring
Externí odkaz:
http://arxiv.org/abs/2402.05059
Publikováno v:
The Bulletin of Symbolic Logic, 2023 Dec 01. 29(4), 626-655.
Externí odkaz:
https://www.jstor.org/stable/27285435
For any subset $Z \subseteq \mathbb{Q}$, consider the set $S_Z$ of subfields $L\subseteq \overline{\mathbb{Q}}$ which contain a co-infinite subset $C \subseteq L$ that is universally definable in $L$ such that $C \cap \mathbb{Q}=Z$. Placing a natural
Externí odkaz:
http://arxiv.org/abs/2010.09551
Computing endomorphism rings of supersingular elliptic curves is an important problem in computational number theory, and it is also closely connected to the security of some of the recently proposed isogeny-based cryptosystems. In this paper we give
Externí odkaz:
http://arxiv.org/abs/2004.11495
Autor:
Bank, Efrat, Camacho-Navarro, Catalina, Eisentraeger, Kirsten, Morrison, Travis, Park, Jennifer
We study the problem of generating the endomorphism ring of a supersingular elliptic curve by two cycles in $\ell$-isogeny graphs. We prove a necessary and sufficient condition for the two endomorphisms corresponding to two cycles to be linearly inde
Externí odkaz:
http://arxiv.org/abs/1804.04063
Autor:
Arora, Sonny, Eisentraeger, Kirsten
Publikováno v:
Open Book Series 2 (2019) 21-36
We give a new algorithm for constructing Picard curves over a finite field with a given endomorphism ring. This has important applications in cryptography since curves of genus 3 allow for smaller key sizes than elliptic curves. For a sextic CM-field
Externí odkaz:
http://arxiv.org/abs/1803.00514
We show that rings of $S$-integers of a global function field $K$ of odd characteristic are first-order universally definable in $K$. This extends work of Koenigsmann and Park who showed the same for $\mathbb{Z}$ in $\mathbb{Q}$ and the ring of integ
Externí odkaz:
http://arxiv.org/abs/1609.09787
Publikováno v:
Transactions of the American Mathematical Society 369 (2017) 11, 8291-8315
Hilbert's Tenth Problem over the field $\mathbb Q$ of rational numbers is one of the biggest open problems in the area of undecidability in number theory. In this paper we construct new, computably presentable subrings $R$ of $\mathbb Q$ having the p
Externí odkaz:
http://arxiv.org/abs/1601.07158
We prove that the existential theory of any function field $K$ of characteristic $p> 0$ is undecidable in the language of rings provided that the constant field does not contain the algebraic closure of a finite field. We also extend the undecidabili
Externí odkaz:
http://arxiv.org/abs/1306.2669
We show that Hilbert's Tenth Problem is undecidable for complementary subrings of number fields and that the p-adic and archimedean ring versions of Mazur's conjectures do not hold in these rings. More specifically, given a number field K, a positive
Externí odkaz:
http://arxiv.org/abs/1012.4878