Efficient Computation of Eta Pairing over Binary Field with Vandermonde Matrix

This paper provides an efficient algorithm for computing the η_T pairing on supersingular elliptic curves over fields of characteristic two. In the proposed algorithm, we deploy a modified multiplication in using the Vandermonde matrix. For , the proposed multiplication method computes β · F · G instead of F · G with some because β is eliminated by the final exponentiation of the η_T pairing computation. The proposed multiplication method asymptotically requires only 7 multiplications in as n → ∞, while the cost of the previously fastest Karatsuba method is 9 multiplications in . Consequently, the cost of the η_T pairing computation is reduced by 14.3%.