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We show that to solve the discrete log problem in a subgroup of order p of an elliptic curve over the nite eld of characteristic p one needs O(lnp) operations in this eld. Let Fq be the nite eld of q = pl elements. We dene an elliptic curve E over Fq to be an equation of the form

Evaluation of discrete logarithms in a group of 𝑝-torsion points of an elliptic curve in characteristic 𝑝