Výsledky vyhledávání - "Endomorphism ring"

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The torsion ideal lattice of the endomorphism ring of an abelian p-group

Autor: Schultz, Phill

The lattice of ideals of the torsion ideal of the endomorphism ring of an abelian p-group is classified by a system of cardinal invariants.
Comment: 12 pages

Externí odkaz: http://arxiv.org/abs/2405.16010

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The supersingular Endomorphism Ring and One Endomorphism problems are equivalent

Autor: Page, Aurel, Wesolowski, Benjamin

The supersingular Endomorphism Ring problem is the following: given a supersingular elliptic curve, compute all of its endomorphisms. The presumed hardness of this problem is foundational for isogeny-based cryptography. The One Endomorphism problem o

Externí odkaz: http://arxiv.org/abs/2309.10432

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The supersingular endomorphism ring problem given one endomorphism

Autor: Merdy, Arthur Herlédan Le, Wesolowski, Benjamin

Given a supersingular elliptic curve E and a non-scalar endomorphism $\alpha$ of E, we prove that the endomorphism ring of E can be computed in classical time about disc(Z[$\alpha$])^1/4 , and in quantum subexponential time, assuming the generalised

Externí odkaz: http://arxiv.org/abs/2309.11912

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Hidden Stabilizers, the Isogeny To Endomorphism Ring Problem and the Cryptanalysis of pSIDH

Autor: Chen, Mingjie, Imran, Muhammad, Ivanyos, Gábor, Kutas, Péter, Leroux, Antonin, Petit, Christophe

The Isogeny to Endomorphism Ring Problem (IsERP) asks to compute the endomorphism ring of the codomain of an isogeny between supersingular curves in characteristic $p$ given only a representation for this isogeny, i.e. some data and an algorithm to e

Externí odkaz: http://arxiv.org/abs/2305.19897

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Computing the endomorphism ring of an elliptic curve over a number field

Autor: Cremona, John E., Sutherland, Andrew V.

We describe deterministic and probabilistic algorithms to determine whether or not a given monic irreducible polynomial H in Z[X] is a Hilbert class polynomial, and if so, which one. These algorithms can be used to determine whether a given algebraic

Externí odkaz: http://arxiv.org/abs/2301.11169

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The endomorphism ring of the trivial module in a localized category

Autor: Carlson, Jon F.

Suppose that $G$ is a finite group and $k$ is a field of characteristic $p >0$. Let $\mathcal{M}$ be the thick tensor ideal of finitely generated modules whose support variety is in a fixed subvariety $V$ of the projectivized prime ideal spectrum $\o

Externí odkaz: http://arxiv.org/abs/2210.01424

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