The Tate Pairing and the Discrete LogarithmApplied to Elliptic Curve
نویسنده
چکیده
1 The Tate{Lichtenbaum pairing In the paper F-R] it is shown how the Tate pairing on Abelian varieties in Licht-enbaum`s version can be used to relate the discrete logarithm in the group J m (F q) of m{torsion points of the Mordell-Weil group of the Jacobian J of a curve over a nite eld F q to the discrete logarithm in F q if q ? 1 is divisible by m. 1 More precisely the main result of F-R] can be stated as follows: Theorem 1.1 Let m be a natural number prime to q, and let m (F q) be the group of roots of unity in F q whose order divides m. We assume that J(F q) contains a point of order m.
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