### Elliptic divisibility sequences and their applications in cryptography

Rachel E. Shipsey
*Goldsmiths*

Elliptic Divisibility Sequences (EDS) are integer sequences defined by
a recurrence formula with the property that if *m* divides *n* then the *m*th
term of the sequence divides the *n*th 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.