Partial Signature Derivation for Constant-Size Verification
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Solution Overview
Problem
Existing electronic signature solutions that produce constant-size signatures struggle with efficiency and anonymity, as they require transmitting all signed data for verification, and recent schemes either have high verification costs or cannot prove relationships without revealing certified data.
Innovation Solution
A method for deriving a partial signature for a subset of messages, which involves calculating a first verification element from non-subset messages and a second verification element to prove its correctness, allowing for efficient verification without revealing unnecessary data, using a bilinear environment with random scalars for anonymization.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Volume of moving object
If constant-size signature schemes are used, then signature size is reduced, but verification requires transmitting all signed data
Solution Approach 1:
The patent segments the verification process into two parts: a constant-size verification proof that can be transmitted independently, and the full signed data that remains local. This allows the verification proof to be separated from the complete data set, enabling verification without transmitting all signed data.
Solution Approach 2:
The patent extracts the essential verification information from the complete signed data into a separate constant-size verification proof. This extracted proof contains only the necessary elements to verify signature validity, allowing it to be transmitted and verified independently of the full data set.
2Loss of information
If zero-knowledge proof techniques are used to conceal data, then anonymity is achieved, but verification complexity increases linearly with number of concealed elements
Solution Approach 1:
The patent changes the parameter of verification complexity from linear (in number of concealed elements) to constant. By using a specific mathematical construction based on bilinear maps and pairing-friendly elliptic curves, the verification complexity becomes independent of the number of concealed elements, achieving O(1) verification time.
3Productivity
If recent constant-size signature schemes are used, then verification efficiency improves, but ability to prove relationships without revealing data is lost
Solution Approach 1:
The patent creates a universal signature scheme that can serve multiple functions: it can verify basic signature validity, prove relationships between signed data elements, and maintain data anonymity. The scheme is designed to be adaptable to different verification needs while maintaining constant-size proofs and efficient verification.
Data Source
AI summary
A method for deriving a partial signature for a subset of a set of messages. The method is implemented by a partial signature derivation entity and includes: receiving the set of messages and a signature of the set of messages, the signature including signature elements of the set of messages; deriving a first verification element calculated from the messages of the set other than those of the subset; deriving a second verification element to prove that the first verification element is formed correctly; and sending to a verification entity a partial signature specific to the subset, the partial signature including a constant number of elements having at least the elements of the signature of the set of messages, the first verification element and the second verification element, the partial signature being verifiable with only messages of the subset.