Elliptic Divisibility Sequence - Applications of EDS

Applications of EDS

Bjorn Poonen has applied EDS to logic. He uses the existence of primitive divisors in EDS on elliptic curves of rank one to prove the undecidability of Hilbert's tenth problem over certain rings of integers.

Katherine Stange has applied EDS and their higher rank generalizations called elliptic nets to cryptography. She shows how EDS can be used to compute the value of the Weil and Tate pairings on elliptic curves over finite fields. These pairings have numerous applications in pairing-based cryptography.