Threshold-based secret voting scheme

Threshold-based secret voting scheme

Keyword list

Term definitionBlockchainA decentralized, distributed ledger maintained by computers in blocks. Secret sharingSplit a secret value into multiple parts (called shares) and distribute them to multiple participants. Only participants who meet certain conditions can jointly recover the original secret. Threshold secret sharingA secret sharing scheme in which only participants exceeding a predetermined number (threshold) can jointly recover the original secret. Polynomial interpolationA method of constructing a polynomial function from known data points, often used to recover secret values ​​in secret sharing schemes. Shamir secret sharingA threshold secret sharing scheme based on polynomial interpolation. Public key encryptionAn asymmetric encryption algorithm that uses a pair of keys: a public key and a private key. The public key can be made public and is used to encrypt information; the private key must be kept secret and is used to decrypt information. Blind signatureA digital signature scheme in which the signer signs a message without knowing the content of the message. Homomorphic encryptionA form of encryption that allows specific algebraic operations to be performed on ciphertext, and the decrypted result corresponds to the result of performing the same operation on the plaintext. BitcoinA digital currency created and managed in a decentralized manner, using blockchain technology to record transactions. Multi-signature is a digital signature scheme that requires multiple users to sign a message with their private keys in order to verify a transaction. Short Answer Question

Explain the basic principle of Shamir's secret sharing scheme.

Shamir's secret sharing scheme is based on the principle of polynomial interpolation. To share a secret value, first construct a t-degree polynomial with it as a constant term, where t is a threshold. Then, generate n different data points (x, f(x)) for n participants and distribute each data point to the corresponding participant. Only at least t+1 participants can recover the original polynomial through polynomial interpolation to obtain the secret value.

Why is privacy important in the context of electronic voting?

Privacy is crucial in electronic voting because it ensures that a voter's choice cannot be revealed to anyone else, including other voters, candidates, or third parties. This prevents coercion, vote buying and selling, and other forms of election fraud.

Explain how blind signatures can be used to enhance the privacy of electronic voting.

Blind signatures allow voters to have their votes signed by voting administrators without revealing the content of their votes. Voters first "blind" their votes using a blinding factor and then send them to an administrator for signature. The administrator signs the blinded vote without knowing the content of the vote. Finally, the voter removes the blinding factor and gets a valid vote signed by the administrator, but the administrator cannot associate the vote with a specific voter.

What role can homomorphic encryption play in electronic voting?

Homomorphic encryption allows encrypted votes to be counted without decrypting individual votes. This makes it possible to calculate election results without revealing the content of individual votes, thereby enhancing the privacy and security of voting.

Explain the "double voting" problem in electronic voting systems and explain how to solve it.

The "double voting" problem refers to a voter voting multiple times in an election. This problem can be solved in a variety of ways, such as: using a voter registration system to track who has voted; requiring voters to provide proof of identity; using blockchain technology to create a tamper-proof voting record.

Describe the advantages and disadvantages of using blockchain for electronic voting.

Advantages:

Transparency: All transactions are recorded on a public ledger and can be verified by anyone.

Immutability: Once recorded on the blockchain, data cannot be tampered with.

Decentralization: No single point of failure, reducing the risk of manipulation.

Disadvantages:

Scalability: Processing large numbers of transactions can be slow and expensive.

Privacy issues: Additional measures are needed to protect voter privacy.

Technical complexity: Implementing and maintaining a blockchain system can be complex.

Explain how voting data is stored in a Bitcoin transaction script.

Bitcoin transaction scripts can use multi-signature functionality to store voting data. For example, a 2-of-2 multi-signature script can be used, with one signature from the voter and another from the election administrator. Voting data can be stored in the script's public key field, which can store arbitrary data.

What does "threshold" refer to in a threshold-based secret voting scheme?

In a threshold-based secret voting scheme, "threshold" refers to the minimum number of shares required to recover the secret value. For example, in a 3-of-5 scheme, at least 3 shares are required to recover the original secret value.

Explain how key sharing is used in a threshold-based secret voting scheme to protect the confidentiality of the vote.

In a threshold-based secret voting scheme, each voter's vote is encrypted using the candidate's public key. The encrypted vote is then split into multiple shares and distributed to multiple voting administrators. Only when a predetermined number of voting administrators cooperate can the vote be decrypted and the election results calculated.

In the TSSV scheme, how can we verify that the participants have received the correct key shares?

The TSSV scheme uses a technique called "public key verifiable secret sharing" (PVSS) to verify that the participants have received the correct key shares. In PVSS, each participant receives an encrypted key share and a public information that can be used to verify the share. Anyone can use this public information to verify the validity of the share without knowing the actual key share.

Essay Question

Discuss the social and political impact of using blockchain technology for electronic voting.

Compare and contrast several existing electronic voting schemes, such as those based on hybrid networks, those based on homomorphic encryption, and those based on blockchain.

Analyze the security of threshold-based secret voting schemes and discuss how to defend against various attacks, such as collusion attacks, denial of service attacks, and quantum attacks.

Design a blockchain-based electronic voting system and describe its architecture, functional modules, security mechanisms, and user experience in detail.

Explore the potential and challenges of blockchain technology in the future development of electronic voting, and look forward to its application prospects.