Secure communication requires message authentication. In this paper we address the problem of how to authenticate quantum information sent through a quantum channel between two communicating parties with the minimum amount of resources. Specifically, our objective is to determine whether one elementary quantum message (a qubit) can be authenticated with a key of minimum length. We show that, unlike the case of classical-message quantum authentication, this is not possible.

A general class of authentication schemes for arbitrary quantum messages is proposed. The class is based on the use of sets of unitary quantum operations in both transmission and reception, and on appending a quantum tag to the quantum message used in transmission. The previous secret between partners required for any authentication is a classical key. We obtain the minimal requirements on the unitary operations that lead to a probability of failure of the scheme less than one. This failure may be caused by someone performing a unitary operation on the message in the channel between the communicating partners, or by a potential forger impersonating the transmitter.

Galileo, the European Global Navigation Satellite System, will provide to its users highly accurate global positioning services and their associated integrity information. The element in charge of the computation of integrity messages within the Galileo Ground Mission Segment is the integrity processing facility (IPF), which is developed by GMV Aerospace and Defence. The main objective of this paper is twofold: to present the integrity algorithms implemented in the IPF and to show the achieved performance with the IPF software prototype, including aspects such as: implementation of the Galileo overbounding concept, impact of safety requirements on the algorithm design including the threat models for the so-called feared events, and finally the achieved performance with real GPS and simulated Galileo scenarios.

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We study the potential of general quantum operations, Trace-Preserving Completely-Positive Maps (TPCPs), as encoding and decoding mechanisms in quantum authentication protocols. The study shows that these general operations do not offer significant advantage over unitary encodings. We also propose a practical authentication protocol based on the use of two successive unitary encodings.