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Quantum Protocol Zoo β

Distributed Ballot Based Protocol

This example protocol implements the task of Quantum E-voting. In this protocol, the election authority prepares and distributes to each voter a blank ballot, and gathers it back after all voters have cast their vote in order to compute the final outcome.

Contents

AssumptionsEdit

  • The tallier is assumed to be trusted to correctly prepare specific states.


OutlineEdit

In the beginning, the election authority prepares an N-qudit ballot state where the kth qudit of the state corresponds to  ’s blank ballot and sends the corresponding blank ballot to   together with two option qudits, one for the “yes” and one for the “no” vote. then each voter decides on “yes” or “no” by appending the corresponding option qudit to the blank ballot and performing a 2-qudit measurement, then based on its result she performs a unitary correction and sends the 2-qudits ballot along with the measurement result back to the election authority. At the end of the election, the election authority applies a unitary operation on one of the qudits in the global state and another unitary operation on one of the qudits to find the number of yes votes.

NotationsEdit

  •   voter
  • c: number of possible candidates
  • N: number of voters
  •  : vote of   voter
  • T: election authority
  • m: number of yes votes

RequirementsEdit

  • Quantum channel capable of sending qubits -> (qudit) between the election authority and voters
  • Qudit Measurement Device for election authority and voters

PropertiesEdit

This protocol is vulnerable to double voting. Specifically, an adversary can mount a “d-transfer attack”, and transfer d votes for one option of the referendum election to the other.


Knowledge GraphEdit

Protocol DescriptionEdit

  • Setup phase:
  1. T prepares an N-qudit ballot state  .

    The states   form an orthonormal basis for the D-dimensional Hilbert space, and D > N. The k-th qudit of   is  's blank ballot.

  2. T sends to   the corresponding blank ballot and two option qudits,for the "yes" and "no" option:

     

    ,

    no: .

    For   we have  , where   and  . Values   and   are chosen uniformly at random from their domain and   is chosen such that   < D.
  • Casting phase:
  1. Each   appends the corresponding option qudit to the blank ballot and performs a 2-qudit measurement   where  

    According to the result   performs a unitary correction   and sends the 2-qudits ballot and   back to T

  • Tally phase:
  1. The global state of the system is:   where ,
     

    For every k, T applies   on one of the qudits in the global state.

  2. By applying the unitary operator  on one of the qudits we have   where  . with the corresponding measurement, T retrieves q and uses values   to compute m.

Further InformationEdit

*contributed by Sara Sarfaraz