Threshold Digital Signatures With Verifiable Sub-Group Participation
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Solution Overview
Problem
Threshold signature schemes do not provide a way to identify which participants contributed to a given signature, allowing for potential false claims of participation.
Innovation Solution
A method where participants generate ephemeral private and public keys for unique sub-groups, using these keys to create signature shares that can be verified as coming from a specific sub-group, ensuring only the contributing participants can prove their involvement.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If threshold signature schemes are used to distribute private key shares among participants, then security is improved by requiring multiple participants to generate a signature, but the ability to identify which participants contributed is lost
Solution Approach 1:
The patent segments the signature generation process into distinct phases: key generation phase where participant identities are recorded, and signature generation phase where signatures are created. The system maintains separate tracking of participant contributions through recorded associations between participant identifiers and their generated signature shares, allowing identification without compromising the threshold security model.
Solution Approach 2:
The patent introduces an intermediary coordinator that manages the association between participant identifiers and signature shares. This coordinator records which participants contribute to each signature generation event, acting as a mediator that enables traceability without requiring participants to reveal their private key shares or compromising the decentralized security architecture.
2Ease of operation
If participants share their private key shares to generate a signature, then signature generation is simplified, but security is compromised as any participant can generate valid signatures
Solution Approach 1:
The patent segments the private key into multiple shares distributed among participants, requiring a threshold number of shares for signature generation. This segmentation maintains security by ensuring no single participant has full control, while the coordinator facilitates the aggregation process to maintain ease of operation.
Solution Approach 2:
The coordinator acts as an intermediary that collects signature shares from participants and aggregates them into a valid signature. This mediator approach simplifies the operation for participants (who only need to contribute their share) while maintaining security through the threshold requirement and centralized verification.
3Reliability
If a threshold number of participants must agree to generate a signature, then security is improved by preventing single-point control, but the complexity of tracking contributions increases
Solution Approach 1:
The coordinator serves as a central intermediary that automatically tracks which participants contribute to each signature. This centralized tracking mechanism manages the complexity of monitoring threshold compliance, participant contributions, and signature validity without requiring complex peer-to-peer verification protocols among participants.
Solution Approach 2:
The system implements feedback mechanisms where the coordinator verifies and records each participant's contribution to the signature generation process. This feedback loop ensures that the threshold requirement is met and provides a clear audit trail of contributions, managing tracking complexity through systematic verification and recording.
Data Source
AI summary
A computer-implemented method of proving that a target sub-group generated a digital signature, wherein the group is divisible into a plurality of unique sub-groups, each sub-group comprising at least the threshold number of participants. The method comprises: for each sub-group to which the first participant belongs, generating a first ephemeral private key share, wherein each other participant of each respective sub-group generates a respective ephemeral private key share; for each respective shared ephemeral private key, generating a respective shared ephemeral public key; generating a first signature share of the signature based on a first private key share, the first ephemeral private key share of a target one of the respective shared ephemeral private keys, and a message; and making the first signature share available to a coordinator for generating the signature.