Anonymous Conference Key Agreement using GHZ states


This example protocol achieves the functionality of quantum conference key agreement. This protocol allows multiple parties in a quantum network to establish a shared secret key anonymously.

Tags: Multi Party Protocols, Quantum Enhanced Classical Functionality, Specific Task

RequirementsEdit

We require the following resources for this protocol:

  1. A source of n-party GHZ states
  2. Private randomness sources
  3. A randomness source that is not associated with any party
  4. A classical broadcasting channel
  5. Pairwise private communication channels

OutlineEdit

  • First, the sender notifies each receiver in the network anonymously
  • The entanglement source generates and distributes sufficient GHZ states to all nodes in the network
  • The GHZ states are distilled to establish multipartite entanglement shared only by the participating parties (the sender and receivers)
  • Each GHZ state is randomly chosen to be used for either Verification or Key Generation. For Key Generation rounds, a single bit of the key is established using one GHZ state by measuring in the Z-basis
  • If the sender is content with the Verification results, they can anonymously validate the protocol and conclude that the key has been established successfully.

NotationEdit

  •  : Total number of nodes in the network
  •  : Number of receiving nodes
  •  : Number of GHZ states used
  •  : Security parameter; expected number of GHZ states used to establish one bit of key
  •  -partite GHZ state:  

Protocol DescriptionEdit

Protocol 1: Anonymous Verifiable Conference Key AgreementEdit

Input: Parameters   and  

Requirements: A source of n-party GHZ states; private randomness sources; a randomness source that is not associated with any party; a classical broadcasting channel; pairwise private communication channels

Goal: Anonymoous generation of key between sender and   receivers

  1. The sender notifies the   receivers by running the Notification protocol
  2. The source generates and shares   GHZ states
  3. The parties run the Anonymous Multipartite Entanglement protocol on the GHZ states
  4. For each  -partite GHZ state, the parties do the following:
    • They ask a source of randomness to broadcast a bit   such that Pr 
    • Verification round: If b = 0, the sender runs Verification as verifier on the state corresponding to that round, while only considering the announcements of the   receivers. The remaining parties announce random values.
    • KeyGen round: If b = 1, the sender and receivers measure in the Z-basis.
  5. If the sender is content with the checks of the Verification protocol, they can anonymously validate the protocol

Protocol 2: NotificationEdit

Input: Sender's choice of   receivers

Goal: The   receivers get notified

Requirements: Private pairwise classical communication channels and randomness sources

For agent  :

  1. All agents   do the following:
    • When agent   is the sender: If   is not a receiver, the sender chooses   random bits   such that  . Otherwise, if   is a receiver, the sender chooses   random bits such that  . The sender sends bit   to agent  
    • When agent   is not the sender: The agent chooses   random bits   such that   and sends bit   to agent  
  2. All agents   receive  , and compute   and send it to agent  
  3. Agent   takes the received   to compute  . If  , they are thereby notified to be a designated receiver.

Protocol 3: Anonymous Multiparty EntanglementEdit

Input:  -partite GHZ state  

Output:  -partite GHZ state   shared between the sender and receivers

Requirements: A broadcast channel; private randomness sources

  1. Sender and receivers draw a random bit each. Everyone else measures their qubits in the X-basis, yielding a measurement outcome bit  
  2. All parties broadcast their bits in a random order, or if possible, simultaneously.
  3. The sender applies a Z gate to their qubit if the parity of the non-participating parties' bits is odd.

Protocol 4: VerificationEdit

Input: A verifier V; a shared state between   parties

Goal: Verification or rejection of the shared state as the GHZ  state by V

Requirements: Private randomness sources; a classical broadcasting channel

  1. Everyone but V draws a random bit   and measures in the X or Y basis if their bit equals 0 or 1 respectively, obtaining a measurement outcome  . V chooses both bits at random
  2. Everyone (including V) broadcasts  
  3. V resets her bit such that  mod  . She measures in the X or Y basis if her bit equals 0 or 1 respectively, thereby also resetting her  
  4. V accepts the state if and only if  mod  

PropertiesEdit

  • Protocol 1 has an asymptotic key rate of  
  • This protocol satisfies the following notions of anonymity:
    • Sender Anonymity: A protocol allows a sender to remain anonymous sending a message to   receivers, if an adversary who corrupts   players, cannot guess the identity of the sender with probability higher than  
    • Receiver Anonymity: A protocol allows a receiver to remain anonymous receiving a message, if an adversary who corrupts   players, cannot guess the identity of the receiver with probability higher than  
  • Error correction and privacy amplification must be carried out anonymously and are not considered in the analysis of this protocol.

ReferencesEdit

  • The protocols and their security analysis, along with an experimental implementation for   can be found in Hahn et al.(2020)
*contributed by Chirag Wadhwa