Designing a Robust Quantum Signature Protocol Based on Quantum Key Distribution for E-Voting Applications
Abstract
:1. Introduction
1.1. Motivation and Research Contribution
- Firstly, an identity-based quantum designated verifier signature scheme for e-voting is proposed. This framework incorporates important security properties and is a unique approach.
- Secondly, a comprehensive security analysis is conducted to ensure the robustness of the proposed quantum signature framework. The framework demonstrates resilience against various cryptographic attacks.
- Thirdly, our scheme is implemented using the programming language Python and the tool Scyther, which effectively combines execution and simulation. We carefully evaluate the costs and advantages of our protocol and find that it is well suited for secure communication.
1.2. Related Work
1.3. Paper Structure
2. Quantum E-Voting System
- The election authority has many quantum resources and computational capabilities, whereas participants in the same domain have limited resources.
- Through the election authority, participants exchange distributed and correlated key strings by executing the quantum portion of quantum key distribution (QKD).
- A designated participant acts as the voter and tally clerk to start electronic voting. The election authority sends the voting content as a judgment question to the other participants.
- Other participants create pre-signatures for a one-bit answer. Bit 1 (Yes) indicates approval, while bit 0 (No) indicates disapproval, serving as their ballots.
- Participants send their pre-signatures to the election authority and ask for actual signatures to be sent to the ballot collector.
- The ballot collector gathers all signatures and counts the number of ballots issued, concluding the voting process.
3. Preliminaries
3.1. No-Cloning Theorem
3.2. Heisenberg Uncertainty Principle
- is the uncertainty in position.
- is the uncertainty in momentum.
- h is the reduced Planck constant, approximately equal to .
3.3. Quantum Key Distribution (QKD)
4. The Proposed Quantum E-Voting Scheme
4.1. Initialization Phase
4.2. Key Generation Phase
- The EA established a bulletin board and revealed specific identification numbers and for participants.
- A voter submits a registration application to EA, who confirms the voter’s identity and eligibility to vote.
- EA privately selects a hash function with equal distribution before generating the key. K is the master key of the EA, and it generates private keys for voters and tally clerks using its own master key:
- According to the quantum key distribution protocol, EA distributes the pads e and d with voter:
- EA makes public and . Then, using secret pads, the voter and tally clerk calculate their private keys:
4.3. Voting Phase
- In this step, the voter and tally clerk make use of quantum key distribution (QKD) to establish a shared secret string of n bits. Let be the vote to be signed. This string will serve as an OTP in the future. EA picks n-bit strings at random , and and defines:
- Next, EA performs and on and to obtain the sequences:
- Let and . After that, EA generates l decoy particles () chosen from the set for checking eavesdropping. EA obtains by inserting l into and obtains by inserting l into . Then, we send to the voter and to the tally clerk, respectively.
- In the quantum sequences and , the positions and states of decoy particles are revealed. The EA confirms the receipt of particles. Decoy particles are measured and compared to their initial state. The protocol continues if there are no errors; otherwise, it is resumed or restarted.
- The voter and tally clerk are able to recover the quantum sequences from and from after testing eavesdropping. For every , the voter performs the operation on and obtains :The voter measures each with the basis . If the measurement outcome is |0〉, then the voter sets ; otherwise, the voter sets and obtains .
- According to , and the voter’s private key , the voter computes and , where
- For each , the voter performs the operation for each , on on and obtains
- Let after that. To check the eavesdropping attack, the voter generates decoy particles l () at random from the set . The voter inserts these particles into |v〉 and obtains . The voter sends to the tally clerk. The tally clerk measures each decoy particle and compares the results. If there is an error, the protocol is restarted; otherwise, the next step is executed.
- After ensuring there is no eavesdropping, the tally clerk recovers the quantum sequence |v〉 from and keeps as the quantum vote.
4.4. Counting Phase
- According to the tally clerk’s private key, for that received from EA in step 5, , the tally clerk performs operation on and obtains:Next, the tally clerk measures using the basis , and if |0〉 is the measurement result, they set . In the other case, they set . The tally clerk then obtains .
- According to r, , and the secret pad s, the tally clerk calculates:
- Let . Then, for each , the tally clerk executes the operation on and finds:
- Finally, the tally clerk verifies . If , the tally clerk accepts as the valid vote of the voter; otherwise, the tally clerk rejects the vote.
- After N participants for have finished voting, the tally clerk publishes the final voting results and the corresponding on the bulletin board for further checking the availability. Finally, Bob counts all the voting results and announces the winning judgment option on the bulletin board.
5. Security Analysis
- Designated verification propertyThe proposed QDVS scheme for electronic voting ensures the fulfillment of the designated verification attribute. The tally clerk’s secret key and secret pad s play a crucial role during the counting stage, with only the tally clerk being privy to the knowledge of the secret pad s and private key . Although EA can calculate , they know nothing about the secret pad s so EA cannot compute in the counting phase step 2. So even the EA cannot verify the QDVS. Therefore, our scheme possesses the property of designated verification.
- Hiding sourceThe proposed QDVS scheme satisfies the feature of the hiding source. In our scheme, both the signer and the designated verifier can generate the same QDVS. Given a signature, no one can judge who the original signer is in between the voter and tally clerk. Even if both confidential keys and are revealed, an attacker will still not be able to determine the true identity of the original voter, whether it is the voter or the designated verifier tally clerk. This characteristic guarantees that both the voter and designated verifier can generate identical QDVS. No external entity, including EA, can decide who the signer is since
- Unconditional securityOur proposed scheme ensures security through the incorporation of two approaches: the integration of the BB84 protocol to securely establish cryptographic keys between the eligible voters and the election authority by using quantum key distribution, in conjunction with the use of the one-time pad (OTP) for encryption. The security of OTPs lies in the fact that each key is used only once and is never reused. In QDVS, this means that for each voting session, new quantum-generated keys are used to encrypt the votes, which ensures that if an attacker intercept the ciphertext, they cannot derive any meaningful information without the one time pad. The unconditional security of both of these features has been established through empirical demonstrations. Therefore, our proposed QDVS scheme is unconditionally secure.
- Message privacyThe execution of a one-way hashing function for the purpose of generating secret keys enhances the level of security. The utilization of XOR operations in both the fourth and fifth steps of Section 4.2 serves to safeguard the quantum keys and during the process of distribution. The involvement of public permutation functions adds complexity to the scheme.
- Non-transferability propertyAccording to Section 4.3, we know that the voter and tally clerk can create an identical QDVS for the vote. The signature created by the voter is indistinguishable from the signature generated by the tally clerk. Hence, the designated verifier cannot prove to any third party that the signature is generated by the voter or by himself. Therefore, the QDVS is non-transferable.
- Security of secret keys and sensitive parametersFirstly, an attacker cannot compute the private keys and of the voter and tally clerk from the public identities and . These secret keys are shared securely by using the quantum key distribution protocol.Note thatSecondly, an outside attacker cannot decrypt the private keys from the OTP cipher text and . The OTPs e and d are only known to the voter and tally clerk.
- Non- repeatability:Each voter can only vote once and cannot vote again because it holds the property of the no-cloning theorem [19]. The election authority distributes random voter’s IDs to prevent forgery and easily detect repeated voting.
- Untraceability:The trace EA should be used to accurately determine the true identify of the target voter who was engaging in malicious communication. Exclusive access to the genuine identities of voters should be limited to the electoral authority alone. The employment of OTP pad with voter IDs and random quantum strings by EA ensures that the original identity cannot be traced by unauthorized individuals, effectively preventing many identity assaults.
5.1. Security Features
5.2. SCYTHER Tool
Scheme | The Third Participant | Entanglement | Swapping Test | QKD Algorithm | Verification Result |
---|---|---|---|---|---|
[11] | Trusted | ✓ | ✓ | ✓ | probabilistic |
[23] | Trusted | ✓ | × | × | Accurate |
[24] | Trusted | × | × | × | Accurate |
[25] | Trusted | × | × | ✓ | probabilistic |
[26] | - | ✓ | ✓ | × | probabilistic |
[27] | Trusted | × | ✓ | × | Accurate |
Proposed | Semi-Trusted | × | × | ✓ | Accurate |
6. Performance Analysis
6.1. Experimental Environment
- Hardware environment: We conduct experiments on a machine using 11th Gen Intel® Core™ i7-1165G7 laptop @ 2.80 GHz processor.
- Software environment: We utilize Python 3.8.11 for coding, employing GMP, and compiling with optimization options. We also employ the “Qiskit” and “pylatexenc” packages to carry out quantum simulations with suitable parameters. The “AerSimulator” backend functions by emulating the operation of an actual device. Performing a quantum circuit with measurements will result in the return of a “count dictionary” that contains the final values of any classical registers in the circuit. The circuit may contain a specialized instruction set, documented in a separate notebook, which includes gates, measurements, resets, conditionals, and other components.
6.2. Experiment Analysis
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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Symbol | Description |
---|---|
H | Hadamard Operator |
I | Identity operator |
⊕ | XOR operator |
Permutation function | |
Inverse permutation function | |
l | Decoy Particle |
d | Logarithmic function |
K | Cryptographic one-way function |
Private Key | |
N | No. of Voters |
Voter’s Identities | |
Broadcasting Question |
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Prajapat, S.; Gautam, U.; Gautam, D.; Kumar, P.; Vasilakos, A.V. Designing a Robust Quantum Signature Protocol Based on Quantum Key Distribution for E-Voting Applications. Mathematics 2024, 12, 2558. https://doi.org/10.3390/math12162558
Prajapat S, Gautam U, Gautam D, Kumar P, Vasilakos AV. Designing a Robust Quantum Signature Protocol Based on Quantum Key Distribution for E-Voting Applications. Mathematics. 2024; 12(16):2558. https://doi.org/10.3390/math12162558
Chicago/Turabian StylePrajapat, Sunil, Urmika Gautam, Deepika Gautam, Pankaj Kumar, and Athanasios V. Vasilakos. 2024. "Designing a Robust Quantum Signature Protocol Based on Quantum Key Distribution for E-Voting Applications" Mathematics 12, no. 16: 2558. https://doi.org/10.3390/math12162558