Supersingular isogeny graphs and endomorphism rings: reductions and solutions
K Eisenträger, S Hallgren, K Lauter, T Morrison… - Advances in Cryptology …, 2018 - Springer
In this paper, we study several related computational problems for supersingular elliptic
curves, their isogeny graphs, and their endomorphism rings. We prove reductions between …
curves, their isogeny graphs, and their endomorphism rings. We prove reductions between …
Computing endomorphism rings of supersingular elliptic curves and connections to path-finding in isogeny graphs
K Eisenträger, S Hallgren, C Leonardi, T Morrison… - Open Book Series, 2020 - msp.org
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 …
computational number theory, and it is also closely connected to the security of some of the …
Hard and easy problems for supersingular isogeny graphs
We consider the endomorphism ring computation problem for supersingular elliptic curves,
constructive versions of Deuring's correspondence, and the security of Charles-Goren …
constructive versions of Deuring's correspondence, and the security of Charles-Goren …
The supersingular isogeny path and endomorphism ring problems are equivalent
B Wesolowski - 2021 IEEE 62nd Annual Symposium on …, 2022 - ieeexplore.ieee.org
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 …
problem for supersingular elliptic curves are equivalent under reductions of polynomial …
Failing to hash into supersingular isogeny graphs
J Booher, R Bowden, J Doliskani… - The Computer …, 2024 - academic.oup.com
An important open problem in supersingular isogeny-based cryptography is to produce,
without a trusted authority, concrete examples of 'hard supersingular curves' that is …
without a trusted authority, concrete examples of 'hard supersingular curves' that is …
The supersingular endomorphism ring and one endomorphism problems are equivalent
A Page, B Wesolowski - Annual International Conference on the Theory …, 2024 - Springer
Abstract The supersingular Endomorphism Ring problem is the following: given a
supersingular elliptic curve, compute all of its endomorphisms. The presumed hardness of …
supersingular elliptic curve, compute all of its endomorphisms. The presumed hardness of …
Orientations and the supersingular endomorphism ring problem
B Wesolowski - Annual International Conference on the Theory and …, 2022 - Springer
We study two important families of problems in isogeny-based cryptography and how they
relate to each other: computing the endomorphism ring of supersingular elliptic curves, and …
relate to each other: computing the endomorphism ring of supersingular elliptic curves, and …
Rational isogenies from irrational endomorphisms
In this paper, we introduce a polynomial-time algorithm to compute a connecting O O-ideal
between two supersingular elliptic curves over F _p F p with common F _p F p …
between two supersingular elliptic curves over F _p F p with common F _p F p …
Computing isogenies between supersingular elliptic curves over
C Delfs, SD Galbraith - Designs, Codes and Cryptography, 2016 - Springer
Abstract Let p> 3 p> 3 be a prime and let EE, E'E′ be supersingular elliptic curves over F _p
F p. We want to construct an isogeny ϕ: E → E'ϕ: E→ E′. The currently fastest algorithm for …
F p. We want to construct an isogeny ϕ: E → E'ϕ: E→ E′. The currently fastest algorithm for …
Hash functions from superspecial genus-2 curves using Richelot isogenies
In 2018 Takashima proposed a version of Charles, Goren and Lauter's hash function using
Richelot isogenies, starting from a genus-2 curve that allows for all subsequent arithmetic to …
Richelot isogenies, starting from a genus-2 curve that allows for all subsequent arithmetic to …