Efficient computation of eta pairing over binary field with vandermonde matrix

This paper provides an efficient algorithm for computing the η_Tpairing on supersingular elliptic curves over fields of characteristic two. In the proposed algorithm, we deploy ploy a modified multiplication in F₂ ⁴ⁿusing the Vandermonde matrix. For F, G;₂ ⁴ⁿthe proposed multiplication method computes B . F .G instead ofF G . with some β.F.G because β is eliminated by the final exponentiation of the pairing computation. The proposed multiplication method asymptotically requires only 7 multiplications in 2n F as n 8 , while the cost of the previously fastest Karatsuba method is 9 multiplications in 2n F . Consequently, the cost of the T pairing computation is reduced by 14.3%.