  Practical implementations of quantum cryptography use attenuated laser pulses
as the signal source rather than single photons. The channels used to transmit
are also lossy. Here we give a simple derivation of two beam-splitting attacks
on quantum cryptographic systems using laser pulses, either coherent or mixed
states with any mean photon number. We also give a simple derivation of a
photon-number splitting attack, the most advanced, both in terms of performance
and technology required. We find bounds on the maximum disturbance for a given
mean photon number and observed channel transmission efficiency for which a
secret key can be distilled. We start by reviewing two incoherent attacks that
can be used on single photon quantum cryptographic systems. These results are
then adapted to systems that use laser pulses and lossy channels.
