Vulnerability of quantum cryptography with phase–time coding under attenuation conditions

Abstract— The protocol of quantum cryptography with phase–time coding uses a configuration of states with the splitting into bases located in different time windows, as a result of which the eavesdropper information is estimated using two parameters. We show that some attacks using the attenuation in the communication links were not taken into account in analyzing the protocol security. We construct an attack that explicitly demonstrates the protocol vulnerability: the protocol loses its security completely even in the case of an arbitrarily short communication link, i.e., the entire cryptographic key becomes known to the eavesdropper.