Revision History for: Dual Basis Measurement Based Quantum E-voting
- 2025-05-22 at 15:03 by JuliaM
implements Quantum Electronic Voting
Introduction
This protocol implements the functionality of Quantum E-voting. The protocol uses an entangled state with a special property as a blank ballot and is self-tallying, i.e. the voters, without the presence of any trusted authority or tallier, need to verify that they share specific quantum states.
Outline
Consider $N$ voters who wish to cast their vote secretly.
- One of the voters prepares some states in two forms, and each voter receives a specific particle of each global state.
- After voters verify that they received the correct states by the cut-and-choose technique, such as described in [2], they perform certain measurements on their qudits and cast their vote based on the measurement outcome.
- In the end, all voters simultaneously broadcast their votes in encoded form, and everyone can compute the election result by a simple summation.
Assumptions
All classical communication in the protocol takes place using pairwise authenticated channels.
The protocol assumed the ability to prepare a multipartite entangled quantum state, as well as a quantum memory that would last throughout the protocol before the final measurement.
Requirements
Network Stage: Quantum Memory
Other requirement:
- Quantum memory
- Entangled states with the dimension of the number of voters.
- Pairwise authenticated classical channel
Notation
- $V_i$: $i^{\\\text{th}}$ voter
- $c$: number of possible candidates
- $m$: dimension of qudits
- $\\\delta_0$: security parameter
- $N$: number of voters
- $v_i$: vote of the $i^{\\\text{th}}$ voter
- $P_N$: set of all possible permutations with $N$ elements
- $B_k$: $k^{\\\text{th}}$ voter’s blank ballot
Properties
NOTE: According to [3], this protocol is not secure. (doesn’t satisfy quantum privacy property.)
We can construct an adversary that violates privacy by an attack on the cut-and-choose technique of the protocol with a non-negligible advantage in $\\\delta _{0}$.Technical Description
- Setup phase:
- One of the voters prepares $N + N2^{\\\delta_0}$ states of the form:
$$
|D_1\\\rangle = \\\frac{1}{\\\sqrt{m^{N-1}}} \\\sum_{\\\sum_{k=1}^N i_k = 0 \\\mod c} |i_1\\\rangle |i_2\\\rangle \\\ldots |i_N\\\rangle
$$
and $1 + N2^{\\\delta_0}$ states of the form:
$$
|D_2\\\rangle = \\\frac{1}{\\\sqrt{N!}} \\\sum_{(i_1, i_2, \\\ldots, i_N) \\\in P_N} |i_1\\\rangle |i_2\\\rangle \\\ldots |i_N\\\rangle
$$
Each voter $V_k$ receives the $k^{\\\text{th}}$ particle from each of the states. - Voter $V_k$ randomly chooses $2^{\\\delta_0}$ of the $|D_1\\\rangle$ states.
The other voters measure half of their particles in the computational basis and half in the Fourier basis:- If the chosen basis is computational, the measurement results should sum to $0$
- If the chosen basis is Fourier, the measurement results should be equal
- All voters simultaneously broadcast their results. If any discrepancy is found, the protocol aborts.
- The $|D_2\\\rangle$ states are similarly checked.
- All voters measure their qudits in the computational basis.
Each $V_k$ now holds a blank ballot of dimension $N$, represented as:
$$ B_k = [\\\xi_k^1, \\\ldots, \\\xi_k^{s_k^k}, \\\ldots, \\\xi_k^N]^T $$
and a unique index $s_k^k \\\in \\\{1, \\\ldots, N\\\}$ from the measurement outcome of the qudit belonging to $|D_2\\\rangle$.
- One of the voters prepares $N + N2^{\\\delta_0}$ states of the form:
- Casting phase:
- $V_k$ applies the transformation: $\\\xi_k^{s_k^k} \\\rightarrow \\\xi_k^{s_k^k} + v_k $.
- All voters simultaneously broadcast their columns, forming a public $N \\\times N$ table.
- Tally phase:
- Each $V_k$ checks that its corresponding row sum equals its own vote $v_k$. If not, the protocol aborts.
- The final outcome of the election is the sum of the elements in each row of the public $N \\\times N$ table.
Experimental Implementations
No content has been added to this section, yet!
Further Information
No content has been added to this section, yet!
References
- Wang, Qingle, Chaohua Yu, Fei Gao, Haoyu Qi, and Qiaoyan Wen. “Self-tallying quantum anonymous voting.” Physical Review A 94, no. 2 (2016): 022333.
- Kashefi, Elham, Luka Music, and Petros Wallden. “The quantum cut-and-choose technique and quantum two-party computation.” arXiv preprint arXiv:1703.03754 (2017).
- Arapinis, Myrto, Nikolaos Lamprou, Elham Kashefi, and Anna Pappa. “Definitions and security of quantum electronic voting.” ACM Transactions on Quantum Computing 2, no. 1 (2021): 1-33.
- 2025-05-16 at 17:29 by Mina Doosti
implements Quantum Electronic Voting
Introduction
This protocol implements the functionality of Quantum E-voting. The protocol uses an entangled state with a special property as a blank ballot and is self-tallying, i.e. the voters, without the presence of any trusted authority or tallier, need to verify that they share specific quantum states.
Outline
Consider $N$ voters who wish to cast their vote secretly.
- One of the voters prepares some states in two forms, and each voter receives a specific particle of each global state.
- After voters verify that they received the correct states by the cut-and-choose technique, such as described in [2], they perform certain measurements on their qudits and cast their vote based on the measurement outcome.
- In the end, all voters simultaneously broadcast their votes in encoded form, and everyone can compute the election result by a simple summation.
Assumptions
All classical communication in the protocol takes place using pairwise authenticated channels.
The protocol assumed the ability to prepare a multipartite entangled quantum state, as well as a quantum memory that would last throughout the protocol before the final measurement.
Requirements
Network Stage: Quantum Memory
Other requirement:
- Quantum memory
- Entangled states with the dimension of the number of voters.
- Pairwise authenticated classical channel
Notation
- $V_i$: $i^{text{th}}$ voter
- $c$: number of possible candidates
- $m$: dimension of qudits
- $delta_0$: security parameter
- $N$: number of voters
- $v_i$: vote of the $i^{text{th}}$ voter
- $P_N$: set of all possible permutations with $N$ elements
- $B_k$: $k^{text{th}}$ voter’s blank ballot
Properties
NOTE: According to [3], this protocol is not secure. (doesn’t satisfy quantum privacy property.)
We can construct an adversary that violates privacy by an attack on the cut-and-choose technique of the protocol with a non-negligible advantage in $delta _{0}$.Technical Description
- Setup phase:
- One of the voters prepares $N + N2^{delta_0}$ states of the form:
$$
|D_1rangle = frac{1}{sqrt{m^{N-1}}} sum_{sum_{k=1}^N i_k = 0 mod c} |i_1rangle |i_2rangle ldots |i_Nrangle
$$
and $1 + N2^{delta_0}$ states of the form:
$$
|D_2rangle = frac{1}{sqrt{N!}} sum_{(i_1, i_2, ldots, i_N) in P_N} |i_1rangle |i_2rangle ldots |i_Nrangle
$$
Each voter $V_k$ receives the $k^{text{th}}$ particle from each of the states. - Voter $V_k$ randomly chooses $2^{delta_0}$ of the $|D_1rangle$ states.
The other voters measure half of their particles in the computational basis and half in the Fourier basis:- If the chosen basis is computational, the measurement results should sum to $0$
- If the chosen basis is Fourier, the measurement results should be equal
- All voters simultaneously broadcast their results. If any discrepancy is found, the protocol aborts.
- The $|D_2rangle$ states are similarly checked.
- All voters measure their qudits in the computational basis.
Each $V_k$ now holds a blank ballot of dimension $N$, represented as:
$$ B_k = [xi_k^1, ldots, xi_k^{s_k^k}, ldots, xi_k^N]^T $$
and a unique index $s_k^k in {1, ldots, N}$ from the measurement outcome of the qudit belonging to $|D_2rangle$.
- One of the voters prepares $N + N2^{delta_0}$ states of the form:
- Casting phase:
- $V_k$ applies the transformation: $xi_k^{s_k^k} rightarrow xi_k^{s_k^k} + v_k $.
- All voters simultaneously broadcast their columns, forming a public $N times N$ table.
- Tally phase:
- Each $V_k$ checks that its corresponding row sum equals its own vote $v_k$. If not, the protocol aborts.
- The final outcome of the election is the sum of the elements in each row of the public $N times N$ table.
Experimental Implementations
No content has been added to this section, yet!
Further Information
No content has been added to this section, yet!
References
- Wang, Qingle, Chaohua Yu, Fei Gao, Haoyu Qi, and Qiaoyan Wen. “Self-tallying quantum anonymous voting.” Physical Review A 94, no. 2 (2016): 022333.
- Kashefi, Elham, Luka Music, and Petros Wallden. “The quantum cut-and-choose technique and quantum two-party computation.” arXiv preprint arXiv:1703.03754 (2017).
- Arapinis, Myrto, Nikolaos Lamprou, Elham Kashefi, and Anna Pappa. “Definitions and security of quantum electronic voting.” ACM Transactions on Quantum Computing 2, no. 1 (2021): 1-33.