  We prove that the teleportation based quantum cryptography protocol presented
in [Opt. Commun. 283, 184 (2010)], which is built using only orthogonal states
encoding the classical bits that are teleported from Alice to Bob, is
asymptotically secure against all types of individual and collective attacks.
We then investigate modifications to that protocol leading to greater
secret-key rates and to security against coherent attacks. In other words, we
show an unconditional secure quantum key distribution protocol that does not
need non-orthogonal quantum states to encode the bits of the secret key sent
from Alice to Bob. We also revisit the security proof of the BB84 protocol by
exploring the non-uniqueness of the Schmidt decomposition of its
entanglement-based representation. This allows us to arrive at a secure
transmission of the key for a slightly greater quantum bit error rate (quantum
communication channel's noise) when compared to its standard security analysis.
