Genus 2 curves
Constructing Pairing-Friendly Genus 2 Curves with Split Jacobian
... Abstract. Genus 2 curves with simple but not absolutely simple jacobians can be used to construct pairing-based cryptosystems more efficient than for a generic genus 2 ...elliptic ...
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Jacobian Coordinates on Genus 2 Curves
... imaginary genus 2 curves, Gaudry showed in [20] that one can perform cryptographic scalar multiplications much more efficiently in the special case that the Jacobian of the curve C/K has K-rational ...
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Admissible constants for genus 2 curves
... Let X be a smooth projective geometrically connected curve of genus g ≥ 2 over a field k which is either a number field or the function field of a curve over a field. Assume that X has semistable reduction ...
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Genus 2 curves with given split Jacobian
... The N´ eron-Severi group N S(X) of a surface X is the group of divisors modulo algebraic equivalence. This group is finitely generated, and there is a pairing on the group, the intersection pairing. For an elliptic ...
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The supersingular isogeny problem in genus 2 and beyond
... dual of the previous, which is a prohibited backtracking step). The message m is therefore coded in base 14. While traversing the graph, the vertices are handled as concrete genus-2 curves ...
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Fast Cryptography in Genus 2
... elliptic curves, or genus 1 curves, has been well studied and consequently all of the speed records for fast curve-based cryptography are for elliptic curves ...hyperelliptic curves of ...
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Pairing-based methods for genus 2 jacobians with maximal endomorphism ring
... > 2 and is independent of the value of the discriminant of Z [π, ...of genus 2 curves over finite fields, which are the framework for this ...
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Improved CRT Algorithm for Class Polynomials in Genus 2
... “Going up” is the process of finding genus-2 curves with maximal endomorphism ring by moving from any curve in the isogeny class to a maximal one via isogenies. This is not always possible and we ...
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Fast, uniform, and compact scalar multiplication for elliptic curves and genus 2 Jacobians with applications to signature schemes
... elliptic curves and Jacobians of genus 2 curves appear to be roughly ...Full genus 2 Ja- cobian arithmetic is relatively slow compared with elliptic curves, and hard to ...
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Parity of ranks of Jacobians of hyperelliptic curves of genus 2
... particular 2-isogeny ...dimension 2, there are roughly 150 cases to consider, excluding infinite places, which complicate the ...of genus 2 curves and examining infinite places and ...
191
Reaction curves
... Before that, Cournot model was mostly considered as a dynamic analysis involving a sequential adjustment process undertaken by two firms who ignored that their own choices could influence the rival’s behavior. The ...
8
Elliptic Curves
... We will let the point at infinity be the identity element O of our group, hence O is considered rational. So the points on our elliptic curve come from A 2 ∪ {O}. Now every line will meet the given elliptic curve ...
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Studies in the Marchantiales (Hepaticae) from southern Africa. 2. The genus Athalamia and A. spathysü ; the genus Oxymitra and O. cristata
... Thallus medium-sized, medianly concave, bright green, in crowded patches; on soil in rocky clefts or under over hangs. Branches simple or once pseudodichotomously fur cate; thickened over midrib, thinning toward ...
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The genus Stipa L in Tasmania Part 2 Distribution of the species
... Areas of overlap between open woodland and scrub lidry sclerophyll", Map i coastal heath, and cleared land which lie below 300 m with a mean annual rainfall of less than 1020 mm.. Survey[r] ...
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Minimal Generators for the Rees Algebra of Rational Space Curves of Type (1,1,d-2)
... In this paper, we specialize the setting in Kustin, Polini and Ulrich [18] to rational space curves of type (1, 1, d − 2) in projective 3-space. We do not prove any new theorems about the structure of Rees ...
31
Dickson curves
... Javier Gomez-Calderon: Department of Mathematics, The Pennsylvania State University, New Kensington Campus, New Kensington, PA 15068, USA E-mail address: [email protected].[r] ...
6
Gradients of curves
... 6 A motorcycle police officer pursues a car exceeding the speed limit. After travelling at 30 m/s for 6 s, the officer catches the car and slows down to 20 m/s to signal the other driver to pull over. It takes 5 s for ...
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Contractive curves
... Remark 5.1 . It is important that U be connected: let f (x) = x 2 (x −2) 2 = g(x)/2, and A = { 0,1,2 } . We have f (A) ∪ g(A) = A, f |A = 0 = g |A , and f (U ) ∪ g(U ) ⊂ U, where U is the ...
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Special Bertrand Curves in semi-Euclidean space E4^2 and their Characterizations
... 4-dimensional Euclidean space. In this paper , by using the similar methods of Matsuda and Yorozu , we define a quaternionic Bertrand curve in semi-Euclidean space E 2 4 and investigate its properties. Then we ...
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sketching of curves
... symmetrical with respect to Polar axis (Initial line), if the equation of curve remains unchanged when we replace θ by–θ in the equation of curve.. Symmetry[r] ...
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