Exploiting the randomness of the measurement basis in quantum cryptography: Secure Quantum Key Growing without Privacy Amplification

We suggest that the randomness of the choices of measurement basis by Alice and Bob provides an additional important resource for quantum cryptography. As a specific application, we present a novel protocol for quantum key distribution (QKD) which enhances the BB84 scheme by encrypting the information sent over the classical channel during key sifting. We show that, in the limit of long keys, this process prevents an eavesdropper from reproducing the sifting process carried out by the legitimate users. The inability of the eavesdropper to sift the information gathered by tapping the quantum channel reduces the amount of information that an eavesdropper can gain on the sifted key. We further show that the protocol proposed is self sustaining, and thus allows the growing of a secret key.