In mathematics, Tate pairing is any of several closely related
bilinear pairings involving
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 ...
s or
abelian varieties
In mathematics, particularly in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular func ...
, usually over
local or
finite field
In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subt ...
s, based on the
Tate duality pairings introduced by and extended by . applied the Tate pairing over finite fields to cryptography.
See also
*
Weil pairing
Weil may refer to:
Places in Germany
*Weil, Bavaria
*Weil am Rhein, Baden-Württemberg
* Weil der Stadt, Baden-Württemberg
*Weil im Schönbuch, Baden-Württemberg
Other uses
* Weil (river), Hesse, Germany
* Weil (surname), including people with ...
References
*
*
*
*
Pairing-based cryptography
Elliptic curve cryptography
Elliptic curves
{{Crypto-stub