  Franson interferometers are increasingly being proposed as a means of
securing high-dimensional energy-time entanglement-based quantum key
distribution (QKD) systems. Heuristic arguments have been proposed that purport
to demonstrate the security of these schemes. We show, however, that such
systems are vulnerable to attacks that localize the photons to several
temporally separate locations. This demonstrates that a single pair of Franson
interferometers is not a practical approach to securing high-dimensional
energy-time entanglement based QKD. This observations leads us to investigate
the security of modified Franson-based-protocols, where Alice and Bob have two
or more Franson interferometers. We show that such setups can improve the
sensitivity against attacks that localize the photons to multiple temporal
locations. While our results do not constituting a full security proof, they do
show that a single pair of Franson interferometers is not secure and that
multiple such interferometers could be a promising candidate for experimentally
realizable high-dimensional QKD.
