EDS Over Finite Fields
An EDS over a finite field Fq, or more generally over any field, is a sequence of elements of that field satisfying the EDS recursion. An EDS over a finite field is always periodic, and thus has a rank of apparition r. The period of an EDS over Fq then has the form rt, where r and t satisfy
More precisely, there are elements A and B in Fq* such that
The values of A and B are related to the Tate pairing of the point on the associated elliptic curve.
Read more about this topic: Elliptic Divisibility Sequence
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