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In algebraic geometry, a hyperelliptic curve is an algebraic curve of genus g > 1, given by an equation of the form y 2 + h ( x ) y = f ( x ) {\displaystyle...

Hyperelliptic curve cryptography is similar to elliptic curve cryptography (ECC) insofar as the Jacobian of a hyperelliptic curve is an abelian group...

there are two types of hyperelliptic curves, a class of algebraic curves: real hyperelliptic curves and imaginary hyperelliptic curves which differ by the...

using hyperelliptic curves to factor integers. Cosset shows in his article (of 2010) that one can build a hyperelliptic curve with genus two (so a curve y...

A hyperelliptic curve is a particular kind of algebraic curve. There exist hyperelliptic curves of every genus g ≥ 1 {\displaystyle g\geq 1} . If the...

genus 2 curve C / F 41 : y 2 + y = x 5 , {\displaystyle C/{\bf {F}}_{41}:y^{2}+y=x^{5},} which was introduced in the section on hyperelliptic curves. The...

curves) Crunode Curve Curve sketching Jacobian variety Klein quartic List of curves Hilbert's sixteenth problem Cubic plane curve Hyperelliptic curve...

curve point multiplication Homomorphic signatures for network coding Hyperelliptic curve cryptography Pairing-based cryptography Public-key cryptography Quantum...

g − 1. When C is a hyperelliptic curve, the canonical curve is a rational normal curve, and C a double cover of its canonical curve. For example if P is...

The hyperelliptic curves are prototypic examples. An unramified covering then is the occurrence of an empty ramification locus. Morphisms of curves provide...

Bicuspid curve Cassini oval Cubic curve Elliptic curve Watt's curve Butterfly curve (algebraic) Elkies trinomial curves Hyperelliptic curve Klein quartic...

of Waterloo. He is the creator of hyperelliptic curve cryptography and the independent co-creator of elliptic curve cryptography. Koblitz received his...

surface Elkies trinomial curves Hyperelliptic curve Classical modular curve Cassini oval Bowditch curve Brachistochrone Butterfly curve (transcendental) Catenary...

Great-circle distance Harmonograph Hedgehog (curve) [1] Hilbert's sixteenth problem Hyperelliptic curve cryptography Inflection point Inscribed square...

generalise the elliptic integrals to all curves over the complex numbers. They include for example the hyperelliptic integrals of type ∫ x k d x Q ( x ) {\displaystyle...

over that field. One of the most important examples of such curves is hyperelliptic curves in characteristic 2, whose Jacobian varieties have been suggested...

curve Rose curve Bicuspid curve Cassini oval Cassinoide Cubic curve Elliptic curve Watt's curve Butterfly curve Elkies trinomial curves Hyperelliptic...

linear systems is used in the classification of algebraic curves. A hyperelliptic curve is a curve C {\displaystyle C} with a degre 2 {\displaystyle 2} morphism...

Christiane Peters, ECM using Edwards curves (PDF) http://hyperelliptic.org/EFD/g1p/index.html http://hyperelliptic.org/EFD/g1p/auto-twisted.html The Ed25519...

Thomae (1870) relating theta constants to the branch points of a hyperelliptic curve (Mumford 1984, section 8). In 1824 the Abel–Ruffini theorem established...