[PDF] Top 20 A note on high-security general-purpose elliptic curves
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A note on high-security general-purpose elliptic curves
... this note we describe some general-purpose, high-efficiency elliptic curves tailored for security levels beyond 2 128 ...legacy-level curves at standard ... See full document
14
Fast, uniform, and compact scalar multiplication for elliptic curves and genus 2 Jacobians with applications to signature schemes
... In §7 we specialize to the Gaudry model for Kummer surfaces, which have the fastest known arithmetic. The result is exceptionally fast one- and two- dimensional scalar multiplication algorithms for the genus 2 Jacobians ... See full document
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Requirements for Standard Elliptic Curves
... and high-assurance software is leading to other needs, ...and security is most important and performance ranks ...elliptic curves. A potential compromise is the construction of new ... See full document
5
A New Family of Pairing-Friendly elliptic curves
... supersingular curves of small characteristic, and to the reconsid- eration of the field sizes required for implementation based on non- supersingular curves of large ...suitable curves, particularly ... See full document
16
Group law and the Security of elliptic curves on Fp [e1, … , en]
... The elliptic curves are a very fashionable subject in ...of security. In 2008, Virat introduced the elliptic curves over local ring F p [] = F p [X]/(X 2 )[2], and a proposed a new ... See full document
5
Heights on elliptic curves over number fields, period lattices, and complex elliptic logarithms
... and elliptic logarithms is an important computation in its own right, and also has a number of applications towards certain algorithms, in- cluding one for determining a lower bound for the canonical height on ... See full document
233
Efficient Elliptic Curve Diffie-Hellman Computation at the 256-bit Security Level
... of general purpose high security elliptic ...the curves M [1504058] or E[376015/376014] appear earlier in the ...proposing curves over the corresponding fields do not ... See full document
10
Elliptic and Hyperelliptic Curves: a Practical Security Analysis
... the curves with m > 2. Note that the number of computer cycles per step, when not using the group automorphism optimization, is lower for the BN254 curve compared to ...NIST curves, and the ... See full document
16
Point Decomposition Problem in Binary Elliptic Curves
... memory). Note that, PDP(15, 5, 3) is solved in about 175 seconds (with 2635 MB memory) in ...In general, our experimental findings with m = 3, 4, 5 extend and improve on the recently reported results in ... See full document
13
On Isogeny Graphs of Supersingular Elliptic Curves over Finite Fields
... supersingular elliptic curves having j-invariant equal to 0 and 1728. We note that the security of the aforementioned cryptographic schemes relies on the difficulty of constructing certain ... See full document
14
An Algebraic Proof of the Associative Law of Elliptic Curves
... Problem For given P and Q is it possible to find n in polynomial time? This is called the discrete logarithm problem and it is known as a very hard one to solve [9]. The security of the elliptic curve ... See full document
11
Fixed Argument Pairing Inversion on Elliptic Curves
... They mentioned that the above is generally hard. However the description is insufficient to give an explanation for the hardness of EI for relevant parings precisely. In fact one can find a d-th root y in polynomial time ... See full document
10
Hashing to elliptic curves of $j$-invariant $1728$
... ordinary elliptic curves of j (E) = 0, 1728 are only interesting [13, ...of high-degree twists for them, leading to faster pairing computation [13, § ... See full document
17
Analogue of Vélu's Formulas for Computing Isogenies over Hessian Model of Elliptic Curves
... To our knowledge, only formulas for degree-2 isogenies exist over this curve [6]. At the time we are submitting this work, we are aware of the latest preprint [7] just uploaded online and computing also isogenies over ... See full document
23
Trapdoor DDH groups from pairings and isogenies
... We note that a group of known order is among Seurin’s open problems, and in particular the Strong RSA assumption does not hold for our new construction in Section ... See full document
21
Symmetric Digit Sets for Elliptic Curve Scalar Multiplication without Precomputation
... In his seminal work [13, 14], Solinas developed a τ-and-add method where the integer n is expanded in basis τ. In this way, in the Horner scheme, point doubling is replaced by the (faster) Frobenius endomorphism. Solinas ... See full document
21
2-Selmer groups and Heegner points on elliptic curves
... Shimura curves with non-maximal level at a prime p ramified in the quaternion algebra (in the special case when p = ...These curves have a p-adic uniformization by a tame étale covering of Drinfeld’s p-adic ... See full document
104
On Abelian and Discrete Symmetries in F-Theory
... the general strategy to determine matter in an F-theory compactification on a Calabi-Yau manifold with a higher rank Mordell-Weil ...in general rational curves c mat obtained from resolving a ... See full document
292
GENERAL INSTRUCTIONS. Purpose
... Report the weighted average pricing for collateralized CP sponsored by the firm. 16.20 Unsecured Funding Pricing Report the weighted average pricing for wholesale unsecured funding. Wholesale unsecured funding is defined ... See full document
40
General Purpose Software
... 1. Imagine you are a NEW administrator in the sales office of a large company. Each month, a newsletter is distributed to all staff in the sales department. All previous newsletters produced before you arrived have been ... See full document
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