Abelian Varieties with Prescribed Embedding Degree

We present an algorithm that, on input of a CM-field K, an integer k 1, and a prime r 1 mod k, constructs a q-Weil number OK 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.

• Type: Conference
• Year: 2008
• Where: ANTS
• Authors: David Freeman, Peter Stevenhagen, Marco Streng
• Keywords: Algorithms, ANTS 2008, Mod K, Number Ok Corresponding, Simple Abelian Variety