  Quispel-Roberts-Thompson (QRT) maps are a family of birational maps of the
plane which provide the simplest discrete analogue of an integrable Hamiltonian
system, and are associated with elliptic fibrations in terms of biquadratic
curves. Each generic orbit of a QRT map corresponds to a sequence of points on
an elliptic curve. In this preliminary study, we explore versions of the
elliptic curve method (ECM) for integer factorization based on iterating three
different QRT maps with particular initial data. Pseudorandom number generation
and other possible applications are briefly discussed.
