Arithmetic on superelliptic curves
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Publication:2759108
DOI10.1090/S0025-5718-00-01297-7zbMath1013.11026WikidataQ61914071 ScholiaQ61914071MaRDI QIDQ2759108
Sachar Paulus, Steven D. Galbraith, Nigel P. Smart
Publication date: 10 December 2001
Published in: Mathematics of Computation (Search for Journal in Brave)
Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Number-theoretic algorithms; complexity (11Y16) Jacobians, Prym varieties (14H40) Curves over finite and local fields (11G20) Computational aspects of algebraic curves (14Q05)
Related Items (21)
Multiradical isogenies ⋮ On the Mordell-Weil lattice of \(y^2=x^3+bx+t^{3^n+1}\) in characteristic 3 ⋮ A review on the isomorphism classes of hyperelliptic curves of genus 2 over finite fields admitting a Weierstrass point ⋮ Explicit bounds of polynomial coefficients and counting points on Picard curves over finite fields ⋮ The arithmetic of Jacobian groups of superelliptic cubics ⋮ Construction of CM Picard curves ⋮ Index calculus algorithm for non-planar curves ⋮ The number of rational points of a class of superelliptic curves ⋮ Constructing Picard curves with complex multiplication using the Chinese remainder theorem ⋮ An addition algorithm in Jacobian of \(C_{ab}\) curves. ⋮ Picard curves over with good reduction away from 3 ⋮ Group arithmetic in \(C_{3,5}\) curves ⋮ Klein's fundamental 2-form of second kind for the \(C_{ab}\) curves ⋮ Algebraic curves and cryptography ⋮ Efficient computation of roots in finite fields ⋮ Linear algebra algorithms for divisors on an algebraic curve ⋮ The arithmetic of certain cubic function fields ⋮ Factoring polynomials over finite fields ⋮ The infrastructure of a global field of arbitrary unit rank ⋮ Computing Riemann-Roch spaces in algebraic function fields and related topics. ⋮ Isomorphism classes of Picard curves over finite fields
Cites Work
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- Algebraic function fields and codes
- Factoring multivariate polynomials over finite fields
- Ideal arithmetic and infrastructure in purely cubic function fields
- Efficient algorithms for the Riemann-Roch problem and for addition in the Jacobian of a curve
- Key-exchange in real quadratic congruence function fields
- Computing in the Jacobian of a Hyperelliptic Curve
- Computing discrete logarithms in real quadratic congruence function fields of large genus
- Real and imaginary quadratic representations of hyperelliptic function fields
- Sieving in Function Fields
- Voronoi's algorithm in purely cubic congruence function fields of unit rank 1
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