Complete group law for genus 2 Jacobians on Jacobian coordinates
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Date
2024
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Publisher
Springer Science and Business Media Deutschland GmbH
Open Access Color
HYBRID
Green Open Access
No
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Abstract
This manuscript provides complete inversion-free and explicit group law formulas in Jacobian coordinates for the genus 2 hyperelliptic curves of the form y2=x5+a<inf>3</inf>x3+a<inf>2</inf>x2+a<inf>1</inf>x+a<inf>0</inf> over a field K with char(K)≠2. The formulas do not require the use of polynomial arithmetic operations such as resultant mod or gcd computations but only operations in K. © 2024 Elsevier B.V. All rights reserved.
Description
Keywords
Explicit Formulas, Genus 2, Group Law, Hyperelliptic Curves, Jacobian Coordinates, Arithmetic Operations, Explicit Formula, Genus 2, Group Law, Hyper-elliptic Curves, Jacobian Coordinate, Jacobians, Polynomial Arithmetic, Geometry, Arithmetic operations, Explicit formula, Genus 2, Group law, Hyper-elliptic curves, Jacobian coordinate, Jacobians, Polynomial arithmetic, Geometry, Genus 2, Group Law, Explicit Formulas, Hyperelliptic Curves, Jacobian Coordinates, Group law, Jacobian coordinates, Explicit formulas, Hyperelliptic curves, Genus 2
Fields of Science
0101 mathematics, 01 natural sciences
Citation
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OpenCitations Citation Count
N/A
Source
Journal of Cryptographic Engineering
Volume
14
Issue
1
Start Page
87
End Page
101
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