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Orienteering with One Endomorphism. [PDF]
Mathematica (N Y), 2023 In supersingular isogeny-based cryptography, the path-finding problem reduces to the endomorphism ring problem. Can path-finding be reduced to knowing just one endomorphism?
Arpin S +5 more
europepmc +6 more sources
Endomorphism algebras of 2-term silting complexes [PDF]
, 2016 We study possible values of the global dimension of endomorphism algebras of 2-term silting complexes. We show that for any algebra A whose global dimension gl.dim A ≤ 2 and any 2-term silting complex P in the bounded derived category Db(A) of A, the ...
Aslak Bakke Buan, Yu Zhou
openalex +2 more sources
The supersingular Endomorphism Ring and One Endomorphism problems are equivalent [PDF]
IACR Cryptology ePrint Archive, 2023 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.
Aurel Page, Benjamin Wesolowski
semanticscholar +1 more source
The supersingular endomorphism ring problem given one endomorphism [PDF]
IACR Cryptology ePrint Archive, 2023 Given a supersingular elliptic curve E and a non-scalar endomorphism α of E, we prove that the endomorphism ring of E can be computed in classical time about disc(Z[α])^1/4, and in quantum subexponential time, assuming the generalised Riemann hypothesis.
Arthur Herlédan Le Merdy +1 more
semanticscholar +1 more source
The supersingular isogeny path and endomorphism ring problems are equivalent [PDF]
IEEE Annual Symposium on Foundations of Computer Science, 2021 We prove that the path-finding problem in isogeny graphs and the endomorphism ring problem for supersingular elliptic curves are equivalent under reductions of polynomial expected time, assuming the generalised Riemann hypothesis.
B. Wesolowski
semanticscholar +1 more source
Endomorphism kernel property for finite groups [PDF]
Mathematica Bohemica, 2022 A group $G$ has the endomorphism kernel property (EKP) if every congruence relation $\theta$ on $G$ is the kernel of an endomorphism on $G$. In this note we show that all finite abelian groups have EKP and we show infinite series of finite non-abelian ...
Heghine Ghumashyan, Jaroslav Guričan
doaj +1 more source
Computing endomorphism rings of supersingular elliptic curves and connections to path-finding in isogeny graphs [PDF]
The Open Book Series, 2020 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.
Kirsten Eisentraeger +4 more
semanticscholar +1 more source
Endomorphism Spectra of Double-Edge Fan Graphs
Mathematics, 2023 There are six classes of endomorphisms for a graph. The sets of these endomorphisms form a chain under the inclusion of sets. In order to systematically study these endomorphisms, Böttcher and Knauer defined the concepts of the endomorphism spectrum and ...
Kaidi Xu, Hailong Hou, Yu Li
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Descending endomorphism graphs of groups
AKCE International Journal of Graphs and Combinatorics, 2023 We define a new type of graph of a group with reference to the descending endomorphisms of the group. A descending endomorphism of a group is an endomorphism that induces a corresponding endomorphism in every homomorphic image of the group. We define the
Vinay Madhusudanan +2 more
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On the endomorphism semigroups of extra-special $p$-groups and automorphism orbits [PDF]
International Journal of Group Theory, 2022 For an odd prime $p$ and a positive integer $n$, it is well known that there are two types of extra-special $p$-groups of order $p^{2n+1}$, first one is the Heisenberg group which has exponent $p$ and the second one is of exponent $p^2$.
Chudamani Pranesachar Anil Kumar +1 more
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