MEMORY EFFICIENT HYPERELLIPTIC CURVE POINT COUNTING

DOI10.1142/S1793042111004034zbMath1222.11079arXivmath/0609032OpenAlexW2122931377MaRDI QIDQ3085111

Hendrik Hubrechts

Publication date: 28 March 2011

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0609032

zbMATH Keywords

hyperelliptic curvedeformationdifferential equationpoint counting

Mathematics Subject Classification ID

Curves over finite and local fields (11G20) Computational aspects of algebraic curves (14Q05) (p)-adic cohomology, crystalline cohomology (14F30) (p)-adic differential equations (12H25) Applications to coding theory and cryptography of arithmetic geometry (14G50) Computational number theory (11Y99)

Related Items

Computing Zeta Functions in Families of C a,b Curves Using Deformation ⋮ Point counting in families of hyperelliptic curves ⋮ Fast arithmetic in unramified \(p\)-adic fields ⋮ Computing zeta functions of generic projective hypersurfaces in larger characteristic

Cites Work

• Unnamed Item
• Matrix multiplication via arithmetic progressions
• Point counting in families of hyperelliptic curves
• Fast arithmetic in unramified \(p\)-adic fields
• On fast multiplication of polynomials over arbitrary algebras
• An extension of Kedlaya's algorithm to hyperelliptic curves in characteristic \(2\)
• Point Counting in Families of Hyperelliptic Curves in Characteristic 2
• An algorithm for polynomial multiplication that does not depend on the ring constants
• Deformation theory and the computation of zeta functions
• Computing Zeta Functions in Families of C a,b Curves Using Deformation

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