Authentication of Quantum Messages: Difference between revisions
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# <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>. | # <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, | *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| | ||
==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 11:37, 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
- Clifford Based Quantum Authentication: requires authenticator to be able to prepare and measure quantum states.
- 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 such that:
- takes as input an -qubit message system and a key and outputs a transmitted system of qubits.
- takes as input the (possibly altered) transmitted system ' 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 -qubit message state , and a single qubit which indicates acceptance or rejection. The classical basis states of 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 , we denote the corresponding super-operators by and .
- For non-interactive protocols, a QAS is secure with error for a state 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|
Further Information
- 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