Computing the number of points on an elliptic curve over a finite field: algorithmic aspects

DOI10.5802/jtnb.143zbMath0843.11030OpenAlexW2067361453MaRDI QIDQ1909876

François Morain

Publication date: 24 March 1996

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=JTNB_1995__7_1_255_0

zbMATH Keywords

modular curveselliptic curveprime fieldnumber of rational pointsfactors of division polynomialsSchoof's algorithm

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Curves over finite and local fields (11G20) Holomorphic modular forms of integral weight (11F11) Computational aspects of algebraic curves (14Q05)

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Quantum lattice enumeration and tweaking discrete pruning ⋮ Modular equations for hyperelliptic curves ⋮ Schwarzian conditions for linear differential operators with selected differential Galois groups ⋮ Efficient computation of Cantor's division polynomials of hyperelliptic curves over finite fields ⋮ ``Chinese & Match, an alternative to Atkin's ``Match and Sort method used in the SEA algorithm ⋮ Towards practical key exchange from ordinary isogeny graphs ⋮ Modular polynomials via isogeny volcanoes ⋮ Computing the cardinality of CM elliptic curves using torsion points ⋮ Fast algorithms for computing isogenies between elliptic curves ⋮ Remarks on the Schoof-Elkies-Atkin algorithm ⋮ Computing the $\ell $-power torsion of an elliptic curve over a finite field ⋮ Computing modular polynomials in quasi-linear time ⋮ Construction of elliptic curves with cyclic groups over prime fields ⋮ Papers from the conference 21st Journées Arithmétiques held at the Università Lateranense, Rome, July 12--16, 2001 ⋮ Modular polynomials on Hilbert surfaces ⋮ Modular forms, Schwarzian conditions, and symmetries of differential equations in physics

Cites Work

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• Modular functions of one variable. IV. Proceedings of the international summer school, University of Antwerp, RUCA, July 17 -- August 3, 1972
• Modular curves and the Eisenstein ideal
• Counting points on elliptic curves over finite fields
• Elliptic Curves Over Finite Fields and the Computation of Square Roots mod p
• Formes modulaires de poids $1$
• Les Schémas de Modules de Courbes Elliptiques

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