Inverted Edwards Coordinates

DOI10.1007/978-3-540-77224-8_4zbMath1195.14047OpenAlexW1481078266MaRDI QIDQ5386074

Tanja Lange, Daniel J. Bernstein

Publication date: 17 April 2008

Published in: Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (Search for Journal in Brave)

Full work available at URL: https://research.tue.nl/nl/publications/b0d9add6-9830-4d0c-9984-c5144ea3e59a

zbMATH Keywords

elliptic curvesadditionexplicit formulasEdwards coordinatesdoublingside-channel countermeasuresinverted Edwards coordinatesstrongly unified addition formulasunified addition formulas

Mathematics Subject Classification ID

Cryptography (94A60) Elliptic curves over global fields (11G05) Elliptic curves (14H52) Curves over finite and local fields (11G20)

Related Items (20)

On Various Families of Twisted Jacobi Quartics ⋮ Further refinements of Miller's algorithm on Edwards curves ⋮ On the number of distinct elliptic curves in some families ⋮ Isomorphism classes of Edwards curves over finite fields ⋮ A note on inverted twisted Edwards curve ⋮ A formula for disaster: a unified approach to elliptic curve special-point-based attacks ⋮ A Tree-Based Approach for Computing Double-Base Chains ⋮ Using \(5\)-isogenies to quintuple points on elliptic curves ⋮ On Edwards curves and ZVP-attacks ⋮ Endomorphisms for faster elliptic curve cryptography on a large class of curves ⋮ Practical-Sized Instances of Multivariate PKCs: Rainbow, TTS, and ℓIC-Derivatives ⋮ ECM using Edwards curves ⋮ Huff’s Model for Elliptic Curves ⋮ Twisted Edwards Curves Revisited ⋮ Pairing Computation on Twisted Edwards Form Elliptic Curves ⋮ Exponentiation in Pairing-Friendly Groups Using Homomorphisms ⋮ Cryptography on twisted Edwards curves over local fields ⋮ О вычислении кратных точек на эллиптических кривых над конечными полями с использованием нескольких оснований систем счисления и новых видов координат ⋮ Endomorphisms for Faster Elliptic Curve Cryptography on a Large Class of Curves ⋮ Deterministic Encoding into Twisted Edwards Curves

Cites Work

• Complete systems of two addition laws for elliptic curves
• Improving the arithmetic of elliptic curves in the Jacobi model
• Progress in cryptology -- INDOCRYPT 2006. 7th international conference on cryptology in India, Kolkata, India, December 11-13, 2006. Proceedings
• Faster Addition and Doubling on Elliptic Curves
• A normal form for elliptic curves
• Optimizing Double-Base Elliptic-Curve Single-Scalar Multiplication
• Extended Double-Base Number System with Applications to Elliptic Curve Cryptography

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