Linearly Homomorphic Signatures for Zero-Knowledge Subset Proofs
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Solution Overview
Problem
Existing electronic voting systems face challenges in ensuring the privacy of individual votes, particularly against malicious voters who may attempt to send biased ballots or sell their votes, while maintaining the integrity of the tally and preventing attacks such as CS-attacks and VS-attacks.
Innovation Solution
A linearly homomorphic signature method using randomizable tags and zero-knowledge proofs is employed to create and verify ciphertexts, allowing efficient proof of subset membership without revealing vote information, even in the presence of dishonest voters, by utilizing ElGamal encryption and generating signatures on the client-side.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If encryption is applied to guarantee voter privacy, then privacy protection is improved, but verification of vote validity becomes more complex
Solution Approach 1:
The system performs preliminary actions by generating proofs of subset membership and attaching them to encrypted ballots before submission. These proofs verify that encrypted ciphertexts correspond to valid plaintexts from the authorized set without requiring decryption during verification, thus maintaining privacy while enabling efficient validation.
Solution Approach 2:
The invention introduces cryptographic intermediaries including homomorphic signatures and zero-knowledge proofs that act as mediators between the encrypted vote and the verification process. These intermediaries enable validation of vote integrity without revealing the actual vote content, resolving the contradiction between privacy protection and verification capability.
2Reliability
If mixing networks are used to permute and randomize ballots, then privacy against malicious voters is improved, but system complexity and computational overhead increase
Solution Approach 1:
The system performs preliminary randomization and proof generation at the voter端 before ballot submission. Each voter randomly selects an authorized plaintext, encrypts it, generates a proof of subset membership, and attaches the proof to the ciphertext. This preliminary action eliminates the need for complex post-submission mixing operations while maintaining privacy guarantees.
Solution Approach 2:
The invention extracts the verification function from the mixing network by incorporating proofs of subset membership directly into each ballot. This extraction allows verification to occur independently without requiring complex mixing operations, reducing system complexity while maintaining security against malicious voters.
3Measurement precision
If individual ballots are decrypted for counting, then tally accuracy is improved, but voter privacy is compromised
Solution Approach 1:
The invention replaces the mechanical decryption process with a cryptographic verification mechanism. Instead of decrypting individual ballots to verify accuracy, the system uses homomorphic signatures and zero-knowledge proofs to validate that each ciphertext corresponds to a valid plaintext from the authorized set, maintaining both privacy and tally accuracy.
Solution Approach 2:
Cryptographic intermediaries including proofs of subset membership serve as mediators between the encrypted ballots and the tallying process. These intermediaries enable accurate verification of vote validity without requiring decryption, thus preserving voter privacy while ensuring tally accuracy.
Data Source
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AI summary
The present invention relates to a method involving: a. an authority device AUT 10 configured to generate at least a set of public parameters; b. a sender device SEND 20 configured to generates at least one ciphertext with at least one proof of subset membership; c. a receiver device REC 30 configured to stores at least one final ciphertext.