  Quantum key distribution (QKD) is known to be unconditionally secure in
principle, but quantifying the security of QKD protocols from a practical
standpoint continues to remain an important challenge. Here, we focus on
phase-based QKD protocols and characterize the security of the 3 and n-pulse
Differential Phase Shift Quantum Key Distribution (DPS QKD) protocols against
individual attacks. In particular, we focus on the minimum error discrimination
(MED) and cloning attacks and obtain the corresponding shrinking factor by
which the sifted key needs to be shrunk in order to get a secure key. We
compare the secure key rates thus obtained with the known lower bounds under a
general individual attack. In a departure from the theoretical lower bounds,
which have no explicit attack strategies, our work provides a practical
assessment of the security of phase-based protocols based on attacks with known
implementations.
