Toric forms of elliptic curves and their arithmetic

DOI10.1016/j.jsc.2011.02.003zbMath1228.14024OpenAlexW2078045580MaRDI QIDQ548601

Frederik Vercauteren, Wouter Castryck

Publication date: 29 June 2011

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jsc.2011.02.003

zbMATH Keywords

Newton polytopecryptographyelliptic curvetoric geometry

Mathematics Subject Classification ID

Elliptic curves (14H52) Curves over finite and local fields (11G20) Computational aspects of algebraic curves (14Q05) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items (3)

On isogeny classes of Edwards curves over finite fields ⋮ Addition law structure of elliptic curves ⋮ Compression on the Twisted Jacobi Intersection

Uses Software

• Magma
• EFD
• Curve25519

Cites Work

• A generalization of Baker's theorem
• On the number of distinct elliptic curves in some families
• The arithmetic of characteristic 2 Kummer surfaces and of elliptic Kummer lines
• Factoring integers with elliptic curves
• Variations of the mixed Hodge structure of affine hypersurfaces in algebraic tori
• A criterion for the ideal of a projectively embedded toric surface to be generated by quadrics
• The Magma algebra system. I: The user language
• Sequences of numbers generated by addition in formal groups and new primality and factorization tests
• The resultant of an unmixed bivariate system
• The distribution of the number of points modulo an integer on elliptic curves over finite fields
• Lattice Polygons and the Number 12
• Rational simplification modulo a polynomial ideal
• Computing zeta functions of nondegenerate curves
• Twisted Edwards Curves
• Twisted Edwards Curves Revisited
• A Shortened Classical Proof of the Quadratic Reciprocity Law
• Speeding the Pollard and Elliptic Curve Methods of Factorization
• Elliptic Curve Cryptosystems
• Handbook of Elliptic and Hyperelliptic Curve Cryptography
• Faster Addition and Doubling on Elliptic Curves
• New Formulae for Efficient Elliptic Curve Arithmetic
• Public Key Cryptography - PKC 2006
• Public Key Cryptography - PKC 2006
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