[PDF] Top 20 Edwards model of elliptic curves defined over any fields
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Edwards model of elliptic curves defined over any fields
... an Edwards model of elliptic curves dened over elds of all char- ...a model of elliptic curve called level 4 theta model, comming from theta functions of level 4 ... See full document
18
A criterion to rule out torsion groups for elliptic curves over number fields
... of any elliptic curve over suitable (families of) number ...of elliptic curves over cubic and quartic ...of elliptic curves occurring over a specific cubic ... See full document
13
Darmon points on elliptic curves over number fields of arbitrary signature
... points defined over ring class fields of ...to curves defined over imaginary quadratic base ...for curves E/F where either F is totally real or imaginary ... See full document
36
CRYPTOGRAPHIC PROTOCOLS USING ELLIPTIC CURVE OVER FINITE FIELDS
... also defined over any extension field of ...the elliptic curve is ...of elliptic curve of third degree over the field of integers K having the form y 2 x 3 ax b ... See full document
6
Faster point scalar multiplication on NIST elliptic curves over GF(p) using (twisted) Edwards curves over GF(p)
... of elliptic curves, for example Edwards and twisted Edwards ...NIST curves over GF (p), because they are not NIST curves isomorphic to any special kind of ... See full document
26
Modular elliptic curves over real abelian fields and the generalized Fermat equation $x^{2\ell}+y^{2m}=z^p$
... Frey curves (Sections 6 and 7) attached to (2) that are defined over the real cyclotomic field K = Q (ζ + ζ −1 ) where ζ is a p-th root of unity, or, for p ≡ 1 ( mod 4 ) , defined over ... See full document
30
Faster arithmetic on elliptic curves using Fp2. Application to GLV-GLS and NIST elliptic curves over Fp isomorphic to twisted Hessian curves over fields extension
... Using Edwards addition law (especially using inverted coordinates) requires much less multiplications than standard coordinates systems on short Weierstrass curve (like projective ... See full document
22
Fast Scalar Multiplication for Elliptic Curves over Prime Fields by Efficiently Computable Formulas
... for elliptic curves over finite ...basic elliptic curves arithmetic in the family of twisted Edwards curves over prime ... See full document
26
On Serre's uniformity conjecture for semistable elliptic curves over totally real fields
... is irreducible for any prime p > 163 and elliptic curve E over Q. Recently, Bilu, Parent and Rebolledo [3] proved, for p ≥ 11, p 6= 13, and E/Q without complex multiplication, that the image of ... See full document
8
Effective bounds for Brauer groups of Kummer surfaces over number fields
... Our effective bound explicitly depends on the Faltings height of the Jacobian of C, so it does not provide any uniform bound as conjectured in [TVA15], [AVA16], and [VA16]. However, it is an open question whether ... See full document
38
Universal adelic groups for imaginary quadratic number fields and elliptic curves
... an elliptic curve E/Q which gives rise to a different topo- logical group is a non-trivial problem that one can solve in a simple way using the extensive database [RZB14] that was compiled by Rouse and ... See full document
114
Algebraic divisibility sequences over function fields
... of elliptic divisibility sequences over Q depends on writing a fraction in lowest ...EDS over function fields that does not depend on a choice of model, but only depends on E/K and P ∈ ... See full document
28
On elliptic curves of prime power conductor over imaginary quadratic fields with class number one
... studies curves of odd conductor over K with a rational 2-torsion ...such curves (up to twist) is ...all curves of prime power conductor p r with a rational 2-torsion point, according to the ... See full document
34
Heights on elliptic curves over number fields, period lattices, and complex elliptic logarithms
... In this thesis, we will develop an alternative method for determining a larger positive lower bound for the canonical height on elliptic curves over number fields. The underlying methodology ... See full document
233
On Isogeny Graphs of Supersingular Elliptic Curves over Finite Fields
... a non-constant rational map defined over k with φ(∞) = ∞. An endomorphism on E is an isogeny from E to itself; the zero map P 7→ ∞ is also considered to be an endomorphism on E. If the field of definition ... See full document
14
On Efficient Pairings on Elliptic Curves over Extension Fields
... use curves de- fined over certain extension fields, such as the extension fields with small charac- teristics, and the optimal extension fields which possess the fast field multiplica- ... See full document
17
Analogue of Vélu's Formulas for Computing Isogenies over Hessian Model of Elliptic Curves
... isogenies over Weierstrass model of elliptic curves has been extended to other models of elliptic curves such as the Huff model, the Edwards model and the ... See full document
23
On the Torsion Subgroups of Certain Elliptic Curves over Q
... is nonzero, is a nonsingular curve. By Mordell’s theorem, is a finitely generated abelian group and its torsion subgroup is a finite abelian group. Mazur proved that of an elliptic curve over the ... See full document
5
A note on the cost of computing odd degree isogenies
... not taken into account here. Also for the Edwards curves, the computation of the constant e = a − d used in [3] to attain faster curve arithmetic is disregarded. Table 3 summarizes the operation counts of ... See full document
16
JD Edwards World CASE Guide. Release A9.2
... Source of Data Indicates what information is to be loaded into the “Write To” field on the screen. This field is loaded automatically by CAP during the data field generation process initiated by adding files to the file ... See full document
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