Results 11 to 20 of about 16,878 (163)
Orienteering with One Endomorphism [PDF]
La Matematica, 2022 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?
Sarah Arpin +5 more
semanticscholar +8 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 +9 more sources
The supersingular endomorphism ring problem given one endomorphism [PDF]
IACR Communications in Cryptology, 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 +10 more sources
Computing supersingular endomorphism rings using inseparable endomorphisms [PDF]
Journal of Algebra, 2023 We give an algorithm for computing an inseparable endomorphism of a supersingular elliptic curve $E$ defined over $\mathbb F_{p^2}$, which, conditional on GRH, runs in expected $O(p^{1/2}(\log p)^2(\log\log p)^3)$ bit operations and requires $O((\log p ...
Jenny G. Fuselier +4 more
semanticscholar +7 more sources
Endomorphism Breaking in Graphs [PDF]
The Electronic Journal of Combinatorics, 2013 We introduce the endomorphism distinguishing number $D_e(G)$ of a graph $G$ as the least cardinal $d$ such that $G$ has a vertex coloring with $d$ colors that is only preserved by the trivial endomorphism.
W. Imrich +3 more
semanticscholar +5 more sources
Nilpotency in endomorphism rings [PDF]
Proceedings of the American Mathematical Society, 1974 Nil subrings of the endomorphism ring of a module with finite Krull dimension sequence are nilpotent. This includes the case of a module with finite Krull dimension as well as noetherian modules. The method used is to embed the endomorphism ring, modulo a nilpotent ideal, in the endomorphism ring of an artinian object of a Grothendieck category.
Robert Gordon
openaire +3 more sources
Endomorphism spectra of graphs [PDF]
Discrete Mathematics, 1992 Consider graphs \(G,H\) and a mapping \(f:V(G) \to V(H)\). Suppose that \(f\) is a homomorphism of \(G\) to \(H\), i.e., that any two vertices \(u,v\) in \(f(V(G))\), for which the sets \(f^{-1} (u)\) and \(f^{-1}(v)\) are joined in \(G\) by at least one edge, are adjacent in \(H\). If also conversely, for any two vertices \(u,v \in f(V(G))\) which are
Michael Böttcher, Ulrich Knauer
openaire +2 more sources
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
ON THE ZARISKI TOPOLOGY ON ENDOMORPHISM MONOIDS OF OMEGA-CATEGORICAL STRUCTURES [PDF]
Journal of Symbolic Logic (JSL), 2023 The endomorphism monoid of a model-theoretic structure carries two interesting topologies: on the one hand, the topology of pointwise convergence induced externally by the action of the endomorphisms on the domain via evaluation; on the other hand, the ...
M. Pinsker, C. Schindler
semanticscholar +1 more source
Endomorphism kernel property for finite groups [PDF]
, 2022 summary: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 ...
Ghumashyan, Heghine, Guričan, Jaroslav
core +4 more sources