Polynomial Code based Quantum Authentication

The example protocol provides a non-interactive scheme for the sender to encrypt as well as authenticate quantum messages. It was the first protocol designed to achieve the task of authentication for quantum states, i.e. it gives the guarantee that the message sent by a party (sender) over a communication line is received by a party on the other end (receiver) as it is and, has not been tampered with or modified by the dishonest party (eavesdropper).

Assumptions

• The sender and the receiver share a private (known to only the two of them), classical random key drawn from a probability distribution.

Notations

• 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} : security parameter
• $m$: number of qubits in the message.

Properties

• For an $m$ qubit message, the protocol requires $m+s$ qubits encoded state, and a private key 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 2m+O(s)} .

References

contributed by Shraddha Singh