# 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 (suppliant) over a communication line is received by a party on the other end (authenticator) 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

• ${\displaystyle s}$: security parameter
• ${\displaystyle m}$: number of qubits in the message.

## Properties

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