Authentication of quantum messages

Howard Barnum, Claude Crépeau, Daniel Gottesman, Adam Smith, Alain Tapp

Research output: Contribution to journalConference articlepeer-review

163 Scopus citations

Abstract

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. 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. 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. 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.

Original languageEnglish (US)
Pages (from-to)449-458
Number of pages10
JournalAnnual Symposium on Foundations of Computer Science - Proceedings
StatePublished - Dec 1 2002
EventThe 34rd Annual IEEE Symposium on Foundations of Computer Science - Vancouver, BC, Canada
Duration: Nov 16 2002Nov 19 2002

All Science Journal Classification (ASJC) codes

  • Hardware and Architecture

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