Authentication of Quantum Messages

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). Authenticating quantum states is possible but signing quantum states is impossible, as concluded in (1). Also, unlike classical message authentication, quantum messages authentication requires encryption. However, classical messages can be publicly readable (not encrypted) and yet authenticated.

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

Use Case

• No classical analogue

Protocols

• Non-interactive Protocols
• Interactive Protocols

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 ${\mathcal {S}}$ (suppliant) 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 \mathcal{A}} (authenticator) together with a set of classical keys $K$ 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 $m$-qubit message system $M$ and a 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 a 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} of $m+t$ qubits.
2. ${\mathcal {A}}$ 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 $k\epsilon K$ and outputs two systems: a $m$-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 $k$, we denote the corresponding super-operators 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 S_k} and $A_{k}$.

• For non-interactive protocols, a QAS is secure with error $\epsilon$ 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 $k\epsilon K:A_{k}(S_{k}(|\psi \rangle \langle \psi |)=|\psi \rangle \langle \psi |\otimes |ACC\rangle \langle ACC|$
2. Soundness: : For all super-operators ${\mathcal {O}}$, let $\rho _{auth}$ be the state output be ${\mathcal {A}}$ when the adversary’s intervention

is characterized by ${\mathcal {O}}$, 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