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Authentication of Quantum Messages: Difference between revisions
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*'''Definition 1:''' A quantum authentication scheme (QAS) is a pair of polynomial time quantum algorithms <math>\mathcal{S}</math> (suppliant) and <math>\mathcal{A}</math> (authenticator) together with a set of classical keys <math>K</math> such that: | *'''Definition 1:''' A quantum authentication scheme (QAS) is a pair of polynomial time quantum algorithms <math>\mathcal{S}</math> (suppliant) and <math>\mathcal{A}</math> (authenticator) together with a set of classical keys <math>K</math> such that: | ||
# <math>\mathcal{S}</math> takes as input an <math>m</math>-qubit message system <math>M</math> and a key <math>k\epsilon K</math> and outputs a transmitted system <math>T</math> of <math>m + t</math> qubits. | # <math>\mathcal{S}</math> takes as input an <math>m</math>-qubit message system <math>M</math> and a key <math>k\epsilon K</math> and outputs a transmitted system <math>T</math> of <math>m + t</math> qubits. | ||
# <math>\mathcal{A}</math> takes as input the (possibly altered) transmitted system <math>T</math>' and a classical key <math>k\epsilon K</math> and outputs two systems: a <math>m</math>-qubit message state <math>M</math>, and a single qubit <math>V</math> which indicates acceptance or rejection. The classical basis states of <math>V</math> are called <math>|ACC\rangle, |REJ\rangle</math> by convention. For any fixed key <math>k</math>, we denote the corresponding super-operators by <math>S_k</math> and <math>A_k</math>. | |||
*For non-interactive protocols, a QAS is secure with error <math>\epsilon</math> for a state <math>|\psi\rangle</math> if it satisfies: | |||
#Completeness: For all keys <math>k\epsilon K: A_k(S_k(|\psi\rangle \langle\psi|)=|\psi\rangle \langle\psi| \otimes |ACC\rangle \langle ACC|</math> | |||
#Soundness: : For all super-operators <math>\mathcal{O}</math>, let <math>\rho_{auth}</math> be the state output be <math>\mathcal{A}</math> when the adversary’s intervention | |||
is characterized by <math>\mathcal{O}</math>, that is: | |||
==Further Information== | ==Further Information== | ||
#[https://arxiv.org/pdf/quant-ph/0205128.pdf Barnum et al (2002)] First protocol on authentication of quantum messages. It is also used later for verification of quantum computation in [[Interactive Proofs for Quantum Computation]]. Protocol file for this article is given as the [[Polynomial Code based Quantum Authentication]] | #[https://arxiv.org/pdf/quant-ph/0205128.pdf Barnum et al (2002)] First protocol on authentication of quantum messages. It is also used later for verification of quantum computation in [[Interactive Proofs for Quantum Computation]]. Protocol file for this article is given as the [[Polynomial Code based Quantum Authentication]] | ||
<div style='text-align: right;'>''contributed by Shraddha Singh''</div> | <div style='text-align: right;'>''contributed by Shraddha Singh''</div> | ||