Bilinear definition

Bilinear given Q, R  G and a, bZ* , we have ê(aQ, bR) = ê(Q, R)ab • Non-degenerate : ê(P, P)1GT • Computable : ê is efficiently computable G is a subgroup of the group of points on an elliptic curve over a finite field. GT is a subgroup of a multiplicative group of a related finite field. Typically, the map ê can be derived from either the Weil pairing or ▇▇▇▇ pairing on an elliptic curve over a finite field. The computational effort of the ▇▇▇▇ pairing is less than the Weil pairing. A more comprehensive description of how these groups, pairings, and other parameters should be selected in practice for efficiency and security can be found in [17]. Throughout this paper, we will simply use the term “bilinear map” to refer to the admissible bilinear map.
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Examples of Bilinear in a sentence

  • Then, the bilinear pairing e : G1 × G1 → G2 should satisfy the followings: • Bilinear: Given P1, P2, Q, Q2 ∈ G1, then e(P1 + P2, Q1) = e(P1, Q1)e(P2, Q1), e(P1, Q1 + Q2) = e(P1, Q1)e(P1, Q2) and e(aP1, bQ1) = e(abP1, Q1) = e(P1, abQ1) = e(bP1, aQ1) = e(P1, Q1)ab for any a, b ∈ Zq∗.

  • Bilinear interpolation applies for performance between the threshold and maximum levels (in either direction).

  • When group size is 3, there exists one round group key agreement based on Bilinear map using Weil paring [17].

  • An ID-based Authenticated Key Exchange Protocol Based on Bilinear ▇▇▇▇▇▇-▇▇▇▇▇▇▇ Problem.

  • Bilinear: ∀(P1, P2) ∈ G1 × G2 and ∀(a, b) ∈ Zq × Zq, we have eˆ(aP1, bP2) = eˆ(P1, P2)ab.

  • Our proofs show that three of the TAK protocols are secure provided that the Bi-linear ▇▇▇▇▇▇-▇▇▇▇▇▇▇ Problem (BDHP) is hard.

  • Dividends payable on the Series D Preferred Shares for any period greater or less than a full Dividend Period will be computed on the basis of a 360-day year consisting of twelve 30-day months.

  • The Bilinear ▇▇▇▇▇▇-▇▇▇▇▇▇▇ (BDH) Problem for a bilinear pairing e : G1 G1 G2 is defined as follows: given P, aP, bP, cP G1, compute e(P, P )abc, where a, b, c are randomly chosen from Zq∗.

  • Security Analysis Bilinear graph plays an important role in significant cryptography problems like in Bilinear ▇▇▇▇▇▇- ▇▇▇▇▇▇▇ (BDH) problem which was presented by ▇▇▇▇▇ and ▇▇▇▇▇▇▇▇ and explained in [13].

  • We have defined a one round identity based authenticated asymmetric group key agreement protocol from Bilinear maps.