Results 11 to 20 of about 55,047 (231)
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
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
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
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
openaire +3 more sources
Rigorous computation of the endomorphism ring of a Jacobian [PDF]
Mathematics of Computation, 2017 We describe several improvements to algorithms for the rigorous computation of the endomorphism ring of the Jacobian of a curve defined over a number field.
Edgar Costa +3 more
semanticscholar +1 more source
On the finiteness of the derived equivalence classes of some stable endomorphism rings [PDF]
Mathematische Zeitschrift, 2018 We prove that the stable endomorphism rings of rigid objects in a suitable Frobenius category have only finitely many basic algebras in their derived equivalence class and that these are precisely the stable endomorphism rings of objects obtained by ...
Jenny August
semanticscholar +1 more source
On determinability of idempotent medial commutative quasigroups by their endomorphism semigroups; pp. 81–87 [PDF]
Proceedings of the Estonian Academy of Sciences, 2011 We extend the result of P. Puusemp (Idempotents of the endomorphism semigroups of groups. Acta Comment. Univ. Tartuensis, 1975, 366, 76â104) about determinability of finite Abelian groups by their endomorphism semigroups to finite idempotent medial ...
Alar Leibak, Peeter Puusemp
doaj +1 more source
Irreducibility of a free group endomorphism is a mapping torus invariant [PDF]
Commentarii Mathematici Helvetici, 2019 We prove that the property of a free group endomorphism being irreducible is a group invariant of the ascending HNN extension it defines. This answers a question posed by Dowdall-Kapovich-Leininger.
Jean Pierre Mutanguha
semanticscholar +1 more source