Elliptic divisibility sequences and their applications in cryptography

Rachel E. Shipsey

Elliptic Divisibility Sequences (EDS) are integer sequences defined by a recurrence formula with the property that if m divides n then the mth term of the sequence divides the nth term. Fascinating in their own right, EDS are also closely related to elliptic curves. Computations within the sequences can provide a new way of computing with elliptic curves. The main application of this is in cryptography. The EDS lead to a set of algorithms which can be used to solve the elliptic curve discrete log problem in certain special cases.