Partial Signature Verification with Constant-Size Attribute Proofs
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Solution Overview
Problem
Existing electronic signature mechanisms for anonymous authentication are inefficient due to the high cost of calculating proofs of knowledge and the large size of the public key, which becomes prohibitive for large sets of attributes.
Innovation Solution
A method for deriving a partial signature that reduces the public key size to 3n elements and maintains security by using a bilinear environment with fewer scalars, allowing constant-size signatures and linear complexity verification.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If proofs of knowledge are used to conceal irrelevant attributes, then privacy is preserved, but computational cost and communication overhead increase significantly
Solution Approach 1:
The patent extracts only the necessary attributes for authentication from the complete attribute set. Instead of proving knowledge of all n-1 irrelevant attributes, the system selectively processes only the required attributes, removing unnecessary computational and communication overhead while maintaining privacy for concealed attributes.
Solution Approach 2:
The authentication process is segmented into two distinct phases: a one-time expensive setup phase that generates verification keys, and a subsequent efficient authentication phase that uses pre-computed values. This segmentation moves the heavy computational burden to the setup phase, making actual authentication operations much faster.
2Productivity
If a signature mechanism supports n attributes with constant-size signatures, then verification complexity is reduced, but public key size becomes prohibitive (n² elements)
Solution Approach 1:
The patent performs preliminary computation during key generation to create pre-computed verification keys that encode information about all n attributes. This preliminary action allows the verification phase to operate efficiently with constant-time operations regardless of the number of attributes, without requiring the public key to scale with n² elements.
Solution Approach 2:
The patent changes the parameter representation by using bilinear pairings and exponentiation-based constructions. Instead of storing n² discrete elements, the system uses a compact representation with bilinear maps where verification complexity becomes independent of the number of attributes, achieving O(1) verification time.
3Reliability
If all attributes are signed to ensure complete authentication, then security is strengthened, but signature size and verification cost increase
Solution Approach 1:
The patent extracts and processes only the subset of attributes that are actually required for authentication. By removing irrelevant attributes from the signature generation process, the signature size remains constant and verification cost is minimized, while security is maintained for the essential attributes through the use of verification keys that encode information about all attributes.
Data Source
AI summary
A method for deriving a partial signature for a subset of a set of messages. The method includes: receiving the set of messages and a signature of the set, which includes signature elements of the set; generating anonymized elements of the signature; generating a first verification element from messages other than those of the subset; generating a second verification element to prove the first verification element is well formed; and sending, to a verification entity, a partial signature specific to the subset. The partial signature includes a constant number of elements having at least the elements of the signature of the set of anonymized messages, the first verification element and the second verification element. The partial signature is verifiable with only the messages of the subset of messages. The second verification element is a function of derived values calculated from at least the other elements of the partial signature.