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**2008/061**

**Title:**

Abelian varieties with prescribed embedding degree

**Authors:**
David Freeman, Peter Stevenhagen, Marco Streng

**Abstract:**

We present an algorithm that, on input of a CM-field K, an integer k \ge 1, and a prime r \equiv 1 \bmod k, constructs a q-Weil number \pi \in \O_K corresponding to an ordinary, simple abelian variety A over the field \F of q elements that has an \F-rational point of order r and embedding degree k with respect to r. We then discuss how CM-methods over K can be used to explicitly construct A.

**ePrint:**
https://eprint.iacr.org/2008/061

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