2013 IEEE 54th Annual Symposium on Foundations of Computer Science (2002)

Vancouver, BC, Canada

Nov. 16, 2002 to Nov. 19, 2002

ISSN: 0272-5428

ISBN: 0-7695-1822-2

pp: 449

Daniel Gottesman , University of California at Berkeley

Adam Smith , Massachusetts Institute of Technology

Howard Barnum , Los Alamos National Laboratories

Claude Crépeau , McGill University

Alain Tapp , Université de Montréal

ABSTRACT

<p>Authentication is a well-studied area of classical cryptography: a sender A and a receiver B sharing a classical secret key want to exchange a classical message with the guarantee that the message has not been modified or replaced by a dishonest party with control of the communication line. In this paper we study the authentication of messages composed of quantum states.</p> <p>We give a formal definition of authentication in the quantum setting. Assuming A and B have access to an insecure quantum channel and share a secret, classical random key, we provide a non-interactive scheme that enables A to both encrypt and authenticate an m qubit message by encoding it into m + s qubits, where the error probability decreases exponentially in the security parameter s . The scheme requires a secret key of size 2m +O(s). To achieve this, we give a highly efficient protocol for testing the purity of shared EPR pairs.</p> <p>It has long been known that learning information about a general quantum state will necessarily disturb it. We refine this result to show that such a disturbance can be done with few side effects, allowing it to circumvent cryptographic protections. Consequently, any scheme to authenticate quantum messages must also encrypt them. In contrast, no such constraint exists classically.</p> <p>This reasoning has two important consequences: It allows us to give a lower bound of 2m key bits for authenticating m qubits, which makes our protocol asymptotically optimal. Moreover, we use it to show that digitally signing quantum states is impossible.</p>

INDEX TERMS

Authentication, quantum information

CITATION

Daniel Gottesman,
Adam Smith,
Howard Barnum,
Claude Crépeau,
Alain Tapp,
"Authentication of Quantum Messages",

*2013 IEEE 54th Annual Symposium on Foundations of Computer Science*, vol. 00, no. , pp. 449, 2002, doi:10.1109/SFCS.2002.1181969SEARCH