Results 61 to 70 of about 10,181 (241)

Isogenies of Elliptic Curves: A Computational Approach [PDF]

, 2009
Isogenies, the mappings of elliptic curves, have become a useful tool in cryptology. These mathematical objects have been proposed for use in computing pairings, constructing hash functions and random number generators, and analyzing the reducibility of ...
Shumow, Daniel
core   +2 more sources

Relations among modular points on elliptic curves

, 2007
Given a correspondence between a modular curve and an elliptic curve A we study the group of relations among the CM points of A. In particular we prove that the intersection of any finite rank subgroup of A with the set of CM points of A is finite.
Buium, Alexandru, Poonen, Bjorn
core   +2 more sources

Hasse principle for Kummer varieties in the case of generic 2‐torsion

Proceedings of the London Mathematical Society, Volume 131, Issue 1, July 2025.
Abstract Conditional on finiteness of relevant Shafarevich–Tate groups, Harpaz and Skorobogatov used Swinnerton‐Dyer's descent‐fibration method to establish the Hasse principle for Kummer varieties associated to a 2‐covering of a principally polarised abelian variety under certain largeness assumptions on its mod 2 Galois image.
Adam Morgan
wiley   +1 more source

SIDH on ARM: Faster Modular Multiplications for Faster Post-Quantum Supersingular Isogeny Key Exchange

Transactions on Cryptographic Hardware and Embedded Systems, 2018
We present high-speed implementations of the post-quantum supersingular isogeny Diffie-Hellman key exchange (SIDH) and the supersingular isogeny key encapsulation (SIKE) protocols for 32-bit ARMv7-A processors with NEON support.
Hwajeong Seo, Zhe Liu, Patrick Longa, Zhi Hu   +3 more
doaj   +1 more source

Parabolic subgroups in characteristics 2 and 3

Journal of the London Mathematical Society, Volume 111, Issue 6, June 2025.
Abstract This text brings to an end the classification of non‐reduced parabolic subgroups in positive characteristic, especially 2 and 3: they are all obtained as intersections of parabolics having maximal reduced part. We prove this result and deduce a few geometric consequences on rational projective homogeneous varieties.
Matilde Maccan
wiley   +1 more source

Constructing elliptic curve isogenies in quantum subexponential time

Journal of Mathematical Cryptology, 2014
Given two ordinary elliptic curves over a finite field having the same cardinality and endomorphism ring, it is known that the curves admit a nonzero isogeny between them, but finding such an isogeny is believed to be computationally difficult.
Childs Andrew, Jao David, Soukharev Vladimir   +2 more
doaj   +1 more source

Fine Selmer Groups and Isogeny Invariance

, 2017
We investigate fine Selmer groups for elliptic curves and for Galois representations over a number field. More specifically, we discuss Conjecture A, which states that the fine Selmer group of an elliptic curve over the cyclotomic extension is a finitely
A Chandrakant, C Wuthrich, J Coates, J. Neukirch, Algebraic number theory, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 322, Springer-Verlag, Berlin, JL Parish, Joseph H. Silverman, JS Milne, M Witte, M Witte, P Billot, P Schneider, R. Sujatha, S Jha, Somnath Jha   +13 more
core   +1 more source

Elliptic curves in isogeny classes [PDF]

Journal of Number Theory, 2018
We show that the distribution of elliptic curves in isogeny classes of curves with a given value of the Frobenius trace $t$ becomes close to uniform even when $t$ is averaged over very short intervals inside the Hasse-Weil interval.
Igor E. Shparlinski, Liangyi Zhao
openaire   +3 more sources

Strong subgroup recurrence and the Nevo–Stuck–Zimmer theorem

Proceedings of the London Mathematical Society, Volume 130, Issue 6, June 2025.
Abstract Let Γ$\Gamma$ be a countable group and Sub(Γ)$\mathrm{Sub}(\Gamma)$ its Chabauty space, namely, the compact Γ$\Gamma$‐space consisting of all subgroups of Γ$\Gamma$. We call a subgroup Δ∈Sub(Γ)$\Delta \in \mathrm{Sub}(\Gamma)$ a boomerang subgroup if for every γ∈Γ$\gamma \in \Gamma$, γniΔγ−ni→Δ$\gamma ^{n_i} \Delta \gamma ^{-n_i} \rightarrow ...
Yair Glasner, Waltraud Lederle
wiley   +1 more source

Efficient Commutative PQC Algorithms on Isogenies of Edwards Curves

Cryptography
The article presents the author’s works in the field of modifications and modeling of the Post-Quantum Cryptography (PQC) Commutative Supersingular Isogeny Diffie-Hellman (CSIDH) algorithm on non-cyclic supersingular Edwards curves and its predecessor ...
Anatoly Bessalov, Volodymyr Sokolov, Serhii Abramov   +2 more
doaj   +1 more source