Editing Practical Quantum Electronic Voting (section)

===Protocol 1 : Quantum e-voting===
''Inputs'': <math>V = \{v_k\}_{k \in [N]} </math> - Set of votes; <math>S</math> - Security parameter; <math>\epsilon</math> - Distance from the perfect GHZ state; <math>\delta</math> - Threshold for verification; <math>\eta</math> Probability of failure of verification

''Output'': The candidate with majority votes or ''Abort''
 
''Resources'': Classical communication, random numbers, N-qubit GHZ source, quantum channels
* Phase 1 [getting unique secret indices]
** Agents perform '''UniqueIndex''' until each agent has a secret unique random index  <math>\omega_k</math>
* Phase 2 [casting votes]
** For <math>l = 1</math> to <math>N</math>
*** The voting agent is the agent <math>k</math> with <math>\omega_k = l</math>
*** Repeat until '''Voting''' is announced
**** The source distributes to each of the N agents one qubit of the GHZ source
**** All agents <math> j \in [N] </math> set rejections<math>_j = </math> trials<math>_j = 0</math>
**** The voting agent tosses log<math>_2[\frac{16N\epsilon^2}{(\epsilon^2-4\delta)^2}</math>ln<math>(\frac{1}{\eta})]</math> <!--NEEDS FORMATTING CHANGES-->
**** The agents perform '''LogicalOR''', where output 1 indicates '''Verification''' and output 0 indicates '''Voting'''. Everyone except the voting agent inputs 0; if the coin toss is 'all heads' the voting agent also inputs 0, otherwise the voting agent inputs 1
**** If '''Verification''' is chosen, the agents perform '''RandomAgent''' and the voting agent anonymously picks an agent <math>j \in [N]</math> to be the verifier. Agent <math>j</math> updates trials<math>_j+ = 1</math> and if '''Verification''' outputs reject: rejections<math>_j+ = 1</math>
*** If for any <math>j \in [N], \delta_j = \frac{rejections_j}{trials_j} > \delta </math>, the protocol ''Aborts''
*** Perform '''Voting'''. The outcome is one row of the Bulletin Board '''B'''. The parity of the row gives one entry in the vote vector '''E'''.
** Given the votes '''E''', the tally '''T''' can be computed.
*Phase 3 [Verification of results]:
** All agents perform '''LogicalOR''' with security parameter <math>S</math>, and input 1 if their vote is not the same as the entry in '''E''' for the round in which they voted, and 0 otherwise.
** If '''LogicalOR''' outputs 1, ''Abort'' the protocol. Else output the candidate with the most votes according to the tally '''T'''.