Nested Threshold Signatures with Enforced Sub-Group Participation
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing threshold signature schemes require a threshold number of participants to contribute, but do not ensure that specific participants are involved in the signature generation, which can lead to security vulnerabilities.
Innovation Solution
Implement a nested threshold signature scheme that requires a sub-group of participants to contribute to generate a message-independent component (MIC), ensuring that at least one specific participant is involved by restricting MIC generation to this sub-group, using Shamir's secret sharing scheme to split the MIC into secondary shares.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a threshold signature scheme is implemented to require multiple participants to contribute, then security against single-point failure is improved, but the ability to ensure specific participants are involved deteriorates
Solution Approach 1:
The patent segments the signature generation process into two distinct components: a message-independent component (MIC) and a message-dependent component (MDC). The MIC is generated by a specific sub-group of participants using Shamir's secret sharing scheme, while the MDC is generated by any threshold number of participants. This segmentation allows the system to enforce involvement of specific participants (through MIC generation) while maintaining the flexibility of threshold signatures (through MDC generation), thereby resolving the contradiction between security through multiple participants and control over specific participant involvement.
Solution Approach 2:
The patent implements a nested structure where the MIC generation process is embedded within the overall threshold signature scheme. The MIC acts as a nested layer that requires specific participants to contribute first, and then the MDC layer allows threshold participation. This nested approach enables the system to ensure specific participant involvement at the MIC level while maintaining threshold flexibility at the signature level, thus resolving the contradiction between reliability through thresholds and adaptability for specific participant control.
2Ease of operation
If any threshold number of participants can contribute to signature generation, then ease of operation is improved, but security against unauthorized signatures deteriorates
Solution Approach 1:
The patent applies preliminary action by requiring the MIC to be generated first by a specific sub-group of participants before the actual signature generation can proceed. This preliminary step ensures that authorized participants are involved in advance, and only after this authorization is established can the threshold signature process continue with the MDC generation. This preliminary authorization step resolves the contradiction by ensuring security through pre-validated participant involvement while maintaining operational ease through the subsequent flexible threshold process.
Data Source
AI summary
A computer-implemented method of requiring at least one of a sub-group of a group of participants to contribute to a threshold-optimal signature scheme, wherein the valid signature comprises a first signature component and a second signature component, wherein each participant has a respective private key share of a shared private key, a respective ephemeral private key share of a shared ephemeral private key, and the first signature component, wherein the shared private key can only be generated with at least a first threshold number of respective private key shares.