Connecting Legendre with Kummer and Edwards

DOI10.3934/amc.2019003zbMath1409.14057OpenAlexW2794919770MaRDI QIDQ1726008

Sabyasachi Karati, Palash Sarkar

Publication date: 15 February 2019

Published in: Advances in Mathematics of Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/amc.2019003

zbMATH Keywords

elliptic curvesLegendre formKummer lineEdwards form

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Cryptography (94A60) Elliptic curves (14H52) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items (2)

Kummer versus Montgomery Face-off over Prime Order Fields ⋮ Connecting Legendre

Uses Software

• EFD
• GitHub
• Curve25519
• KummerLineV02

Cites Work

• The arithmetic of characteristic 2 Kummer surfaces and of elliptic Kummer lines
• The strong Lefschetz principle in algebraic geometry
• Kummer for genus one over prime order fields
• Tata lectures on theta. I: Introduction and motivation: Theta functions in one variable. Basic results on theta functions in several variables. With the assistance of C. Musili, M. Nori, E. Previato, and M. Stillman
• Jacobian coordinates on genus 2 curves
• Lefschetz's principle
• Twisted Edwards Curves
• Twisted Edwards Curves Revisited
• Pairing Computation on Twisted Edwards Form Elliptic Curves
• The Arithmetic of Elliptic Curves
• Speeding the Pollard and Elliptic Curve Methods of Factorization
• Elliptic Curve Cryptosystems
• Faster Addition and Doubling on Elliptic Curves
• A normal form for elliptic curves
• Fast genus 2 arithmetic based on Theta functions
• Public Key Cryptography - PKC 2006
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