Editing Practical Quantum Electronic Voting (section)

==Properties==
<!-- important information on the protocol: parameters (threshold values), security claim, success probability... -->
* <math>(\sigma_H,\sigma_D,\gamma)</math>-''Correctness'': This notion of approximate correctness includes two properties:
** <math>\sigma_H</math>-''Completeness'': If all agents are honest, the election is accepted with probability more than <math>\sigma_H</math> - Pr[election accepted] <math> \geq \sigma_H</math>
** <math>(\sigma_D,\gamma)</math>-''Soundness'': the probability that the election result is accepted, given that the set of the votes '''E''' computed from the bulletin board '''B''' resulting from the election is more than <math>\gamma</math> away from the real votes '''V''', is smaller than <math>\sigma_D</math> - 
:: Pr[election accepted <math>| \frac{1}{N}||</math>'''V''' - '''E'''<math>||_1 \geq \gamma] \leq \sigma_D </math>
: This particular protocol is <math>([1-\epsilon(1-S)]^N, S^{N(1+\lambda)[\epsilon(1-\eta)+\eta]},(1+\lambda)[\epsilon(1-\eta)+\eta])</math>-correct, for a small constant <math>\lambda > 0</math>

* <math>\zeta</math>-''Privacy'': The privacy of the election scheme implies that for any voter <math>k</math>, the probability that any subset of malicious parties <math>D</math> that deviates from the honest protocol can guess the vote <math>v_k</math> of the voter is at most <math>\zeta</math> more than in the case they just have access to the bulletin board and to their own votes - 
: <math>\forall k, </math> Pr<math>[v_k|D] -</math> Pr<math>[v_k|B,v_j \in </math> '''V'''<math>_D] \leq \zeta</math>
: This particular protocol is <math>\zeta</math>-private with <math>\zeta = (1-\eta)^N\epsilon + (1 - (1-\eta)^N)</math>

* ''Authentication'': This e-voting protocol does not provide authentication, which should be taken care of by the physical implementation of the protocol.

* ''Double voting'': Each voter can vote at most once. Since the number of voters is known in advance for this protocol, double voting is easily taken care of.

* ''Verifiability'': Each voter can verify that their vote has been counted correctly. In this protocol, the tally is performed by the voters themselves. The bulletin board produced as an output of the protocol is public and can always be checked by everyone, while still appearing random.

* ''Receipt freeness'': In order to prevent vote-selling, voters should not be able to prove how they voted. As the unique indices stay secret, voters cannot produce a receipt of their vote.

* ''Additional candidates'': The protocol described here only allows an election consisting of 2 candidates. This can be extended to more candidates by repeating the protocol multiple times in sequence. In particular, if there are K candidates, we can express each of them using log<math>_2</math>K bits and repeat the election as many times so that each vote set corresponds to one bit. This however does affect the correctness and privacy.