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In algebraic geometry, the Twisted Edwards curves are plane models of elliptic curves, a generalisation of Edwards curves introduced by Bernstein et al. (2007) and named after Harold M. Edwards. Elliptic curves are important in public key cryptography and Twisted Edwards curves are at the heart of an electronic signature scheme called EdDSA that offers high performance while avoiding security problems that have surfaced in other digital signature schemes. Each twisted Edwards curve (as the name suggests) is a twist of an Edwards curve. A twisted Edwards curve E E,a,d over a field ''K'' which does not have 2=0 is an affine plane curve defined by the equation: :E E,a,d: where ''a'', ''d'' are distinct non-zero elements of ''K''. An Edwards curve is a twisted Edwards curve with ''a'' = 1. Every twisted Edward curve is birationally equivalent to an elliptic curve in Montgomery form and vice versa. ==Group law== As for all elliptic curves, also for the Twisted Edwards curve, it is possible to do some operations between its points, such as adding two of them or doubling (or tripling) one. The results of these operations are always points that belong to the curve itself. In the following sections some formulas are given to obtain the coordinates of a point resulted from an addition between two other points (addition), or the coordinates of point resulted from a doubling of a single point on a curve. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Twisted Edwards curve」の詳細全文を読む スポンサード リンク
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