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Practical Quantum Electronic Voting: Difference between revisions
Practical Quantum Electronic Voting (edit)
Revision as of 23:30, 16 December 2021
, 16 December 2021Add assumptions and further information
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<!--Tags: related pages or category --> | <!--Tags: related pages or category --> | ||
'''Tags:''' [[:Category: Multi Party Protocols|Multi Party Protocols]], [[:Category: Quantum Enhanced Classical Functionality| Quantum Enhanced Classical Functionality]], [[:Category:Specific Task | Specific Task]] | |||
==Assumptions== | ==Assumptions== | ||
<!-- It describes the setting in which the protocol will be successful. --> | <!-- It describes the setting in which the protocol will be successful. --> | ||
* Voting agents can communicate classically. | |||
* Voting agents can generate random numbers. | |||
* There is a multipartite entanglement source connected to each agent by a quantum channel. The source need not be trusted. | |||
==Outline== | ==Outline== | ||
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# The verifier generates random angles <math>\theta_j \in [0, \pi)</math> for all agents including themselves, such that the sum is a multiple of <math>\pi</math>. The angles are then sent out to all the agents. | # The verifier generates random angles <math>\theta_j \in [0, \pi)</math> for all agents including themselves, such that the sum is a multiple of <math>\pi</math>. The angles are then sent out to all the agents. | ||
# Agent <math>j</math> measures in the basis <math>[|+_\theta\rangle,|-_\theta\rangle] = [\frac{1}{\sqrt{2}}(|0\rangle + e^{i\theta_j}|1\rangle), \frac{1}{\sqrt{2}}(|0\rangle - e^{i\theta_j}|1\rangle)]</math> and publicly announces the result <math>Y_j = \{0,1\}</math> | # Agent <math>j</math> measures in the basis <math>[|+_\theta\rangle,|-_\theta\rangle] = [\frac{1}{\sqrt{2}}(|0\rangle + e^{i\theta_j}|1\rangle), \frac{1}{\sqrt{2}}(|0\rangle - e^{i\theta_j}|1\rangle)]</math> and publicly announces the result <math>Y_j = \{0,1\}</math> | ||
# The state passes the verification test when the following condition is satisfied: if the sum of the randomly chosen angles is an even multiple of <math>\pi</math>, there must be an even number of 1 outcomes for <math>Y_j</math> , and if the sum is an odd multiple of <math>\pi</math>, there must be an odd number of 1 outcomes for <math>Y_j : \bigoplus_j Y_j = \frac{1}{\pi}\sum_i\theta_i</math> | # The state passes the verification test when the following condition is satisfied: if the sum of the randomly chosen angles is an even multiple of <math>\pi</math>, there must be an even number of 1 outcomes for <math>Y_j</math> , and if the sum is an odd multiple of <math>\pi</math>, there must be an odd number of 1 outcomes for <math>Y_j : \bigoplus_j Y_j = \frac{1}{\pi}\sum_i\theta_i </math> (mod 2) | ||
===Protocol 4 : Voting=== | ===Protocol 4 : Voting=== | ||
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# Repeat <math>\Sigma</math> times from step 4: each time repeat with <math>p_k</math> as new inputs | # Repeat <math>\Sigma</math> times from step 4: each time repeat with <math>p_k</math> as new inputs | ||
# If at least once in the <math>\Sigma</math> repetitions for the various orderings <math>y = 1</math>, this is the output of the protocol, otherwise it is <math>y = 0</math> | # If at least once in the <math>\Sigma</math> repetitions for the various orderings <math>y = 1</math>, this is the output of the protocol, otherwise it is <math>y = 0</math> | ||
===Protocol 6 : RandomBit=== | ===Protocol 6 : RandomBit=== | ||
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* ''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. | * ''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. | ||
==Further Information== | ==Further Information== | ||
<!-- theoretical and experimental papers including requirements, security proof (important), which protocol does it implement, benchmark values... --> | <!-- theoretical and experimental papers including requirements, security proof (important), which protocol does it implement, benchmark values... --> | ||
* Proofs of the protocol properties can be found in [https://arxiv.org/abs/2107.14719 Centrone et al. (2021)] | |||
* Protocols 5-7 are classical anonymous protocols taken from [https://arxiv.org/abs/0706.2010 Broadbent and Tapp(2007)] and used in [https://arxiv.org/abs/1811.04729 Unnikrishnan et al.(2018)] | |||
* Protocol 3 is the same as that of [https://arxiv.org/abs/1112.5064 Pappa et al.(2011)] | |||
= | <div style='text-align: right;'>''*contributed by Chirag Wadhwa''</div> | ||