What is bilinear pairing?

Bilinear pairings have been used to design ingenious protocols for such tasks as one-round three-party key agreement, identity-based encryption, and aggregate signatures. Suitable bilinear pairings can be constructed from the Tate pairing for specially chosen elliptic curves.

What is elliptic curve pairing?

An elliptic curve pairing is a function that takes a pair of points on an elliptic curve and returns an element of some other group, called the target group. Elliptic curve pairings have this nice essential property: For some g1 , g2 , and g3 on the curve and integers a and b .

What’s so special about elliptic curves?

The addition of points on elliptic curves has a different definition that is much more natural, can be defined for any curve, and makes it more obvious why it is interesting for elliptic curves specifically.

How do you show a map is bilinear?

Let V and W be vector spaces over the same base field F. If f is a member of V∗ and g a member of W∗, then b(v, w) = f(v)g(w) defines a bilinear map V × W → F. is a bilinear map. be a linear map, then (v, u) ↦ B(v, Lu) is a bilinear map on V × U.

What is bilinear map in cryptography?

A bilinear map is a map e : G × G → GT , where G is a Gap. Diffie-Hellman (GDH) group and GT is another multiplicative cyclic group of. prime order p with the following properties [16]: (i) Computable: there exists an. efficiently computable algorithm for computing e; (ii) Bilinear: for all h1, h2 ∈ G.

Is ECC a symmetric or asymmetric cipher?

asymmetric cryptography
ECC is an approach — a set of algorithms for key generation, encryption and decryption — to doing asymmetric cryptography. Asymmetric cryptographic algorithms have the property that you do not use a single key — as in symmetric cryptographic algorithms such as AES — but a key pair.

What is the order of elliptic curve?

The order of a point on an elliptic curve is the order of that point as an element of the group defined on the curve. = O, and m P = O for all integers 1 ≤ m < m. If such m exists, P is said to have finite order, otherwise it has infinite order.

What is zero point of an elliptic curve?

Zero point on elliptic curve, the elliptic curve is having single element that element is represented by O. Zero point is also called as point at infinity.