Computing the Tate Pairing using Generalized Jacobians

چکیده مقاله

Let E be an elliptic curve over the finite field F_q, and E[m] be the group m-torsion points of E. In [3] Frey and Rouck showed that the Tate pairing can be used to solve the discrete logarithm problem on E[m], if q-1 is divisible by m. In this paper we use the generalized jacobian of elliptic curves to computing the Tate pairing.