  We prove the unconditional security of quantum key distribution protocols
using attenuated laser pulses with M different linear polarizations. When M=4,
the proof covers the so-called SARG04 protocol [V.~Scarani et al., Phys. Rev.\
Lett. {\bf 92}, 057901 (2004)], which uses exactly the same quantum
communication as the Bennett-Brassard 1984 protocol. For a channel with
transmission $\eta$, we show that the key rate in SARG04 scales as
$O(\eta^{3/2})$. When we increase the number of states to M=2k-1 or 2k, the key
rate scaling improves as $O(\eta^{(k+1)/k})$.
