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| This type of protocol is subject to double voting and privacy attacks when several voters are colluding. | | This type of protocol is subject to double voting and privacy attacks when several voters are colluding. |
| * Double voting: A corrupted voter can apply the “yes” unitary operation many times without being detected. | | * Double voting: A corrupted voter can apply the “yes” unitary operation many times without being detected. |
| * Privacy attack: An adversary that corrupts voters <math>V_{k-1}</math> and <math>V_{k+1}</math> can learn how voter <math>V_k</math> voted with probability 1. | | * Privacy attack: An adversary that corrupts voters <math>V_{k−1}</math> and <math>V_{k+1}</math> can learn how voter <math>V_k</math> voted with probability 1. |
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| ==Protocol Description==
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| *Setup phase:
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| T prepares the state <math>|\phi_0\rangle =\dfrac{1}{\sqrt{N}}\sum_{j=0}^{N-1}|j\rangle_V |j\rangle_T</math>, keeps the second qudit and passes the first to voter <math> V_1</math> as the ballot qudit.
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| * Casting phase:
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| For k = 1, ... ,N, <math>V_k </math>receives the ballot qudit and applies the unitary <math>U^{v_{k}}=\sum_{j=0}^{N-1}|j+1\rangle \langle j|</math>, where <math>v_k = 1</math> signifies a yes vote and <math>v_k = 0</math> a no vote.
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| Then, <math> V_k</math> forwards the ballot qudit to the next voter <math>V_{k+1}</math> and <math> V_N</math> to T.
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| * Tallying phase:
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| The global state held by T after all voters have voted is:
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| <math>|\phi_N\rangle =\dfrac{1}{\sqrt{N}}\sum_{j=0}^{N-1}|j+m\rangle_V|j\rangle_T</math>
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| T measures the two qudits in the computational basis, subtracts the two results, and obtains the outcome m.
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| ==Further Information==
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| <div style='text-align: right;'>''*contributed by Sara Sarfaraz''</div>
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