Quantum cryptography is best known for key distribution. However, previous proposed proofs of security of Quantum Key Distribution (QKD) contain various technical subtleties. In this paper, a conceptually simpler proof of security of QKD is proposed. Also, the error rate of a teleportation channel has no concern with the signal being transmitted. This is because the non-trivial error patterns are permuted under teleportation. This inherent fact is combined with the recently proposed quantum to classical reduction theorem. In the argument, supposed Alice and Bob to have fault-tolerant quantum computer, the result shows that QKD can be made unconditionally secure over arbitrarily long distances even against the most general type of eavesdropping attacks and in the presence of all types of noises.