Authentication of Quantum Messages: Difference between revisions

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# <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>.
# <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:
*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: B_k(A_k(|\psi\rangle \langle\psi|)=|\psi\rangle \langle\psi| \otimes |\ACC\rangle \langle\ACC|</math>
#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:
#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>

Revision as of 12:44, 18 June 2019

Functionality

If a person sends some information over an insecure channel (a dishonest/malicious party has access to the channel), what is the guarantee that the receiver on the other end will receive the same information as sent and not something which is modified or replaced by the dishonest party? Authentication of quantum channels/quantum states/quantum messages provides this guarantee to the users of a quantum communication line/ channel. The sender is called the suppliant (prover) and the receiver is called the authenticator. Note that, it is different from the functionality of digital signatures, a multi-party (more than two) protocol, which comes with additional properties (non-repudiation, unforgeability and transferability). Also, authenticating quantum states is possible but signing quantum states is impossible, as concluded in (1).

Tags: Two Party Protocol, Quantum Digital Signature, Quantum Functionality, Specific Task, Building Block

Protocols

  • Non-interactive Protocols
  1. Clifford Based Quantum Authentication: requires authenticator to be able to prepare and measure quantum states.
  2. Polynomial Code based Quantum Authentication: requires authenticator to only prepare and send quantum states

Properties

  • Any scheme which authenticates quantum messages must also encrypt them. (1)
  • Definition 1: A quantum authentication scheme (QAS) is a pair of polynomial time quantum algorithms (suppliant) and (authenticator) together with a set of classical keys Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle K} such that:
  1. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathcal{S}} takes as input an Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle m} -qubit message system Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M} and a key and outputs a transmitted system of qubits.
  2. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathcal{A}} takes as input the (possibly altered) transmitted system Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T} ' and a classical key Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k\epsilon K} and outputs two systems: a Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle m} -qubit message state Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M} , and a single qubit Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V} which indicates acceptance or rejection. The classical basis states of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V} are called Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle |ACC\rangle, |REJ\rangle} by convention. For any fixed key Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k} , we denote the corresponding super-operators by and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A_k} .
  • For non-interactive protocols, a QAS is secure with error Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \epsilon} for a state Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle |\psi\rangle} if it satisfies:
  1. Completeness: For all keys Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k\epsilon K: A_k(S_k(|\psi\rangle \langle\psi|)=|\psi\rangle \langle\psi| \otimes |ACC\rangle \langle ACC|}
  2. Soundness: : For all super-operators Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathcal{O}} , let Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho_{auth}} be the state output be Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathcal{A}} when the adversary’s intervention is characterized by Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathcal{O}} , that is:

Further Information

  1. 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
contributed by Shraddha Singh
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