  Digital signatures are widely used in modern communication to guarantee
authenticity and transferability of messages, The security of currently used
classical schemes relies on computational assumptions. We present a quantum
signature scheme that does not require trusted quantum channels. We prove that
it is unconditionally secure against the most general coherent attacks, and
show that it requires the transmission of significantly fewer quantum states
than previous schemes. We also show that the quantum channel noise threshold
for our scheme is less strict than for distilling a secure key using quantum
key distribution. This shows that direct quantum signature schemes can be
preferable to signature schemes relying on secret shared keys generated using
quantum key distribution.
