Results 11 to 20 of about 5,894 (213)
Orienteering with One Endomorphism. [PDF]
Mathematica (N Y), 2023 AbstractIn supersingular isogeny-based cryptography, the path-finding problem reduces to the endomorphism ring problem. Can path-finding be reduced to knowing just one endomorphism? It is known that a small degree endomorphism enables polynomial-time path-finding and endomorphism ring computation (in: Love and Boneh, ANTS XIV-Proceedings of the ...
Arpin S +5 more
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The Supersingular Endomorphism Ring and One Endomorphism Problems are Equivalent [PDF]
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 only asks to find a single non-scalar endomorphism.
Page, Aurel, Wesolowski, Benjamin
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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
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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
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Cogenerator endomorphism rings [PDF]
Proceedings of the American Mathematical Society, 1971 If R R is a ring and P P is a finitely generated projective right R R -module, what properties of R R does the R R -endomorphism ring of P P inherit? Rosenberg and Zelinsky have shown that if R R is quasi-Frobenius, and P
Ronald L. Wagoner
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The supersingular endomorphism ring problem given one endomorphism [PDF]
IACR Communications in CryptologyGiven 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. Previous results either had higher complexities, or relied on heuristic assumptions.
Herlédan Le Merdy, Arthur +1 more
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The endomorphism semiring of a semilattice [PDF]
Semigroup Forum, 2008 The authors prove that the endomorphism semiring of a nontrivial semilattice is subdirectly irreducible and describe its monolith. They characterize the case when the endomorphism semiring is congruence simple.
Jezek, J., Kepka, T., Maróti, Miklós
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Canadian Mathematical Bulletin, 1993 AbstractA characterization is given of when all kernels (respectively images) of endomorphisms of a module are direct summands, a necessary condition being that the endomorphism ring itself is a left (respectively right) PP-ring. This result generalizes theorems of Small, Lenzing and Colby-Rutter and shows that R is left hereditary if and only if the ...
W. K. Nicholson
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Analysis of endomorphisms [PDF]
Journal of Physics: Conference Series, 2012 In this expository article, we discuss the recent progress in the study of endomorphisms and automorphisms of the Cuntz algebras and, more generally graph C* -algebras (or Cuntz-Krieger algebras). In particular, we discuss the definition and properties of both the full and the restricted Weyl group of such an algebra.
CONTI, ROBERTO +2 more
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The supersingular Endomorphism Ring and One Endomorphism problems are equivalent [PDF]
, 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.
Page, Aurel, Wesolowski, Benjamin
core +2 more sources