Revision History for: Travelling Ballot Based Quantum E-Voting
- 2025-06-24 at 21:54 by JuliaM
implements Quantum Electronic Voting
Introduction
This protocol implements the functionality of Quantum Electronic Voting. The protocol uses two entangled qudits, one as a blank ballot that travels from voter to voter and the second one for computing the election result. The first quantum scheme in this category was introduced by Vaccaro[1] and later improved by[2,3] .
Related Paper(s)
Outline
We consider $N$ voters who wish to cast their vote secretly.
- The election authority prepares an entangled state, keeps one of the qudits, and passes the other one as the ballot qudit.
- Each voter receives the ballot qudit from the previous voter, casts her vote by applying a unitary and then forwards the qudit to the next voter.
- In the end, the authority obtains the election outcome by measuring the two qudits.
Assumptions
The protocol relies on being able to share a high-dimensional entangled state.
Local parties are assumed to be able to perform local qudit unitaries
Requirements
Network Stage: Quantum Memory
Other requirements:
- Quantum channel for qudit communication
- Qudit Measurement Device for the election authority
- Quantum memory to store qudits
Notation
- $V_i$: $i^\\\text{th}$ voter
- $c$: number of possible candidates
- $N$: number of voters
- $v_i$: vote of the $i^\\\text{th}$ voter
- $T$: election authority
- $m$: number of yes votes
Properties
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.
- Privacy attack: An adversary that corrupts voters $V_{k-1}$ and $V_{k+1}$ can learn how voter $V_{k}$ voted with probability 1.
Technical Description
- Setup phase:
$T$ prepares the state $|\\\phi_0\\\rangle = \\\dfrac{1}{\\\sqrt{N}} \\\sum_{j=0}^{N-1} |j\\\rangle_V |j\\\rangle_T$,
keeps the second qudit and passes the first to voter $V_1$ as the ballot qudit. - Casting phase:
For $k = 1, \\\ldots, N$,- $V_k$ receives the ballot qudit and applies the unitary $U^{v_k} = \\\sum_{j=0}^{N-1} |j+1\\\rangle \\\langle j|$,
where $v_k = 1$ signifies a yes vote and $v_k = 0$ a no vote. - Then, $V_k$ forwards the ballot qudit to the next voter $V_{k+1}$ and $V_N$ forwards it to $T$.
- $V_k$ receives the ballot qudit and applies the unitary $U^{v_k} = \\\sum_{j=0}^{N-1} |j+1\\\rangle \\\langle j|$,
- Tallying phase:
The global state held by $T$ after all voters have voted is:
$$|\\\phi_N\\\rangle = \\\dfrac{1}{\\\sqrt{N}} \\\sum_{j=0}^{N-1} |j+m\\\rangle_V |j\\\rangle_T$$$T$ measures the two qudits in the computational basis, subtracts the two results, and obtains the outcome $m$.
Experimental Implementations
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Further Information
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References
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- 2025-05-16 at 16:59 by Mina Doosti
implements Quantum Electronic Voting
Introduction
This protocol implements the functionality of Quantum Electronic Voting. The protocol uses two entangled qudits, one as a blank ballot that travels from voter to voter and the second one for computing the election result. The first quantum scheme in this category was introduced by Vaccaro[1] and later improved by[2,3] .
Related Paper(s)
Outline
We consider $N$ voters who wish to cast their vote secretly.
- The election authority prepares an entangled state, keeps one of the qudits, and passes the other one as the ballot qudit.
- Each voter receives the ballot qudit from the previous voter, casts her vote by applying a unitary and then forwards the qudit to the next voter.
- In the end, the authority obtains the election outcome by measuring the two qudits.
Assumptions
The protocol relies on being able to share a high-dimensional entangled state.
Local parties are assumed to be able to perform local qudit unitaries
Requirements
Network Stage: Quantum Memory
Other requirements:
- Quantum channel for qudit communication
- Qudit Measurement Device for the election authority
- Quantum memory to store qudits
Notation
- $V_i$: $i^text{th}$ voter
- $c$: number of possible candidates
- $N$: number of voters
- $v_i$: vote of the $i^text{th}$ voter
- $T$: election authority
- $m$: number of yes votes
Properties
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.
- Privacy attack: An adversary that corrupts voters $V_{k-1}$ and $V_{k+1}$ can learn how voter $V_{k}$ voted with probability 1.
Technical Description
- Setup phase:
$T$ prepares the state $|phi_0rangle = dfrac{1}{sqrt{N}} sum_{j=0}^{N-1} |jrangle_V |jrangle_T$,
keeps the second qudit and passes the first to voter $V_1$ as the ballot qudit. - Casting phase:
For $k = 1, ldots, N$,- $V_k$ receives the ballot qudit and applies the unitary $U^{v_k} = sum_{j=0}^{N-1} |j+1rangle langle j|$,
where $v_k = 1$ signifies a yes vote and $v_k = 0$ a no vote. - Then, $V_k$ forwards the ballot qudit to the next voter $V_{k+1}$ and $V_N$ forwards it to $T$.
- $V_k$ receives the ballot qudit and applies the unitary $U^{v_k} = sum_{j=0}^{N-1} |j+1rangle langle j|$,
- Tallying phase:
The global state held by $T$ after all voters have voted is:
$$|phi_Nrangle = dfrac{1}{sqrt{N}} sum_{j=0}^{N-1} |j+mrangle_V |jrangle_T$$$T$ measures the two qudits in the computational basis, subtracts the two results, and obtains the outcome $m$.
Experimental Implementations
No content has been added to this section, yet!
Further Information
No content has been added to this section, yet!