Hyperelliptic Curve Cryptography

Hyperelliptic curve cryptography is similar to elliptic curve cryptography (ECC) insofar as the Jacobian of a hyperelliptic curve is an Abelian group on which to do arithmetic, just as we use the group of points on an elliptic curve in ECC.

Read more about Hyperelliptic Curve CryptographyDefinition, Attacks Against The DLP, Order of The Jacobian

Other articles related to "curve, curve cryptography, hyperelliptic curve cryptography, hyperelliptic curve, hyperelliptic curves, curves":

Elliptic Curve Diffie–Hellman
... Elliptic curve Diffie–Hellman (ECDH) is an anonymous key agreement protocol that allows two parties, each having an elliptic curve public-private key pair, to ... of the Diffie–Hellman protocol using elliptic curve cryptography ...
Hyperelliptic Curve Cryptography - Order of The Jacobian
... Hence, in order to choose a good curve and a good underlying finite field, it is important to know the order of the Jacobian ... Consider a hyperelliptic curve of genus over the field where is the power of a prime number and define as but now over the field ... the order using the zeta-function on hyperelliptic curves ...
Envelope Theorem
... A curve in a two dimensional space is best represented by the parametric equations like x(c) and y(c) ... The family of curves can be represented in the form where c is the parameter ... The envelope of a family of curves g(x,y,c) = 0 is a curve such that at each point on the curve there is some member of the family that touches that particular point tangentially ...
Parallel Curve
... A parallel of a curve is the envelope of a family of congruent circles centered on the curve ... It can also be defined as a curve whose points are at a fixed normal distance of a given curve ... It is sometimes called the offset curve but the term "offset" often refers also to translation ...
Algebraic Curve
... Algebraic curves are the curves considered in algebraic geometry ... A plane algebraic curve is the locus of the points of coordinates x, y such that f(x, y) = 0, where f is a polynomial in two variables defined over some field F ... If C is a curve defined by a polynomial f with coefficients in F, the curve is said defined over F ...

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