[PDF] Top 20 Requirements for Standard Elliptic Curves
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Requirements for Standard Elliptic Curves
... Brainpool Curves [3] have been generated this ...NUMS curves [5] have been ...selecting elliptic curves, see ...trustworthy curves, which are already rolled-out in large infrastructure ... See full document
5
New algorithm for the discrete logarithm problem on elliptic curves
... complexity of two stages. First collecting a system of ≤ 2 k , k = dn/me linear relations (7) and then solving them. The probability of producing one linear relation by solving at least one system of multivariate Boolean ... See full document
17
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
... Edwards curve has a = 1 and d 6 = f 0; 1 g . For such curve it is easy to see that point (0; 1) is the neutral element of addition law. Points (1; 0) and ( 1; 0) have order 4 and point (0; 1) has order 2. Point ( x; y) ... See full document
22
Explicit n descent on elliptic curves III Algorithms
... 6.1. Central simple algebras. We recall some standard theory. See for example [43, Part II]. Let K be a field. A central simple algebra A over K is a finite-dimensional algebra over K with centre K and no ... See full document
44
A note on high-security general-purpose elliptic curves
... high-efficiency elliptic curves tailored for security levels beyond 2 128 ...legacy-level curves at standard security levels. The choice of curves was made to facilitate ... See full document
14
Analogue of Vélu's Formulas for Computing Isogenies over Hessian Model of Elliptic Curves
... liptic curves isogenies (SIDH) ...These curves are almost all birationally equivalent to the Weierstrass model but depending on the properties of each curve such as arithmetic of points, a careful choice of ... See full document
23
On Isogeny Graphs of Supersingular Elliptic Curves over Finite Fields
... The remainder of the paper is organized as follows. In §2 we provide a concise sum- mary of the relevant background on elliptic curves and isogenies between them. Standard references for the material ... See full document
14
Complete addition formulas for prime order elliptic curves
... Weierstrass elliptic curve addition ...3 standard addition function “ec GFp simple add”, the initial three that check whether the input points are equal, op- posite, or at infinity can cause timing ... See full document
25
Summation polynomial algorithms for elliptic curves in characteristic two
... a standard idea [30, 31, 2] they call the “hybrid method”, which is to partially evaluate the system at some random points before applying Gr¨obner basis ... See full document
21
TNFS Resistant Families of Pairing-Friendly Elliptic Curves
... underlying elliptic curve groups and extension ...pairing-friendly elliptic curves considering these new TNFS attacks in finite extensions of composite embedding ... See full document
23
On the cost of computing isogenies between supersingular elliptic curves
... attack on CSSI has an expected running time of O(p 1/4 ), but also has O(p 1/4 ) storage requirements. In this paper, we demonstrate that the van Oorschot-Wiener golden colli- sion finding algorithm has a lower ... See full document
20
Binary quadratic forms, elliptic curves and Schoof's algorithm
... Unfortunately, also with this test we did not nd what we were looking for. The failure in the research of a counter-example despite the number of tested curves, suggest that a more organic investigature is needed. ... See full document
134
Elliptic GW invariants of blowups along curves and surfaces
... In [5, 6], we mainly concentrated on the changes of genus zero GW invariants under blowup along smooth curves and surfaces. In this paper, we mainly concentrate on the elliptic GW invariants. These ... See full document
10
Proxy Signcrypion Scheme Based on Hyper Elliptic Curves
... Delegation of rights is promising in Internet applications like distributed computing, e-cash systems, global distribution networks, grid computing, mobile agent applications, and mobile communications. This paper ... See full document
10
On Efficient Pairings on Elliptic Curves over Extension Fields
... suitable elliptic curves for pairings, namely pairing-friendly curves, which contain the large prime subgroup and the small embedding ...strong elliptic curves used in ECC can be ... See full document
17
Improved Arithmetic on Elliptic Curves over Prime Field
... refers to 5.1, * * refers to 5.2 and * * * refers to 5.3 Some special cases have been recommended, for example, assuming a = 3 in equation 5. Using the proposed coordinates system with these special cases will reduce ... See full document
10
Applications of S unit equations to the arithmetic of elliptic curves
... compute curves up to ...compute curves with only one non–trivial point of order 2. We split these curves in two categories; (i) those which are isogenous to a curve without full 2–torsion and (ii) ... See full document
113
2-Selmer groups and Heegner points on elliptic curves
... of elliptic curves, using a different strategy based on the p-adic Waldspurger formula of Bertolini–Darmon–Prasanna [BDP13] and Liu– Zhang–Zhang [LZZ14] for p = ... See full document
104
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 rational ... See full document
5
Efficient Pairings Computation on Jacobi Quartic Elliptic Curves
... The rest of this paper is organized as follows: Section 2 provides a background on the Jacobi elliptic curve, and notions on pairings that are useful in the paper. In Section 3, we present the computation of the ... See full document
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