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Doubling-oriented Doche–Icart–Kohel Curve
In mathematics, the doubling-oriented Doche–Icart–Kohel curve is a form in which an elliptic curve can be written. It is a special case of the Weierstrass form and it is also important in elliptic-curve cryptography because the doubling speeds up considerably (computing as composition of 2- isogeny and its dual). It was introduced by Christophe Doche, Thomas Icart, and David R. Kohel in ''Efficient Scalar Multiplication by Isogeny Decompositions.''Christophe Doche, Thomas Icart, and David R. Kohel, ''Efficient Scalar Multiplication by Isogeny Decompositions'' Definition Let K be a field and let a\in K. Then, the doubling-oriented Doche–Icart–Kohel curve with parameter ''a'' in affine coordinates is represented by: y^2=x^3+ax^2+16ax. Equivalently, in projective coordinates: ZY^2=X^3+aZX^2+16aXZ^2, with x=\frac and y=\frac . Since this curve is a special case of the Weierstrass form, transformations to the most common form of elliptic curve (Weierstrass for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doubling Oriented
Doubling may refer to: Mathematics * Arithmetical doubling of a count or a measure, expressed as: ** Multiplication by 2 ** Increase by 100%, i.e. one-hundred percent ** Doubling the cube (i. e., hypothetical geometric construction of a cube with twice the volume of a given cube) * Doubling time, the length of time required for a quantity to double in size or value * Doubling map, a particular infinite two-dimensional geometrical construction Music * The composition or performance of a melody with itself or itself transposed at a constant interval such as the octave, third, or sixth, Voicing (music)#Doubling * The assignment of a melody to two instruments in an arrangement * The playing of two (or more) instruments alternately by a single player, e.g. ''Flute, doubling piccolo'' ** Musicians who play more than one woodwind instrument are called woodwind doublers or reed players * Double tracking, a recording technique in which a musical part (or vocal) is recorded twice ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |