|
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] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elliptic Curve
In mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point . An elliptic curve is defined over a field and describes points in , the Cartesian product of with itself. If the field's characteristic is different from 2 and 3, then the curve can be described as a plane algebraic curve which consists of solutions for: :y^2 = x^3 + ax + b for some coefficients and in . The curve is required to be non-singular, which means that the curve has no cusps or self-intersections. (This is equivalent to the condition , that is, being square-free in .) It is always understood that the curve is really sitting in the projective plane, with the point being the unique point at infinity. Many sources define an elliptic curve to be simply a curve given by an equation of this form. (When the coefficient field has characteristic 2 or 3, the above equation is not quite general enough to include all non-singular cubic cu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
