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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
<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>
Authentication, quantum information
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.2002.1181969
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