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We show in this paper that the Gentry-Szydlo algorithm for cyclotomic orders, previously revisited by Lenstra-Silverberg, can be extended to complex-multiplication (CM) orders, and even to a more ge...
Let E be an elliptic curve dened over a nite eld. Balasubramanian and Koblitz have proved that if the `th roots of unity ` is not contained in the ground eld, then a eld extension of the groun...
Consider the Jacobian of a genus two curve defined over a finite field and with complex multiplication. In this paper we show that if the e-Sylow subgroup of the Jacobian is not cyclic, then the emb...

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