Bilinear Mapping Verification for Trusted Authority Associations
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Solution Overview
Problem
In cryptographic hierarchies, verifying the association between lower-level and higher-level trusted authorities without relying on digital certificates is challenging, especially when offline verification or secrecy is required.
Innovation Solution
The method employs bilinear mappings, specifically using a shared secret and verification parameters derived from elliptic curve cryptography to enable a third party to verify the association between two parties by computing and comparing cryptographic parameters, eliminating the need for digital certificate tracing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If digital certificates are used to verify associations between trusted authorities, then verification can be performed, but the process requires tracing through multiple certificates and message exchanges, increasing complexity and time consumption
Solution Approach 1:
The patent applies preliminary action by pre-computing and publishing verification parameters (a and b) by the first trusted authority before the association verification is needed. These parameters are derived from the first authority's private key and public key in advance, enabling the second authority to generate verification data that can be immediately verified without requiring real-time certificate tracing or message exchanges between authorities.
Solution Approach 2:
The patent extracts the essential verification function from the complex digital certificate chain by using bilinear mappings to create a condensed verification mechanism. Instead of requiring full certificate traversal, the system extracts only the necessary cryptographic relationship (the association between authorities) and represents it through simplified verification parameters that can be checked independently.
2Reliability
If digital certificates are used to verify associations between trusted authorities, then verification can be performed, but the process requires message exchanges and certificate tracing, increasing device complexity
Solution Approach 1:
The patent introduces an intermediary verification mechanism using bilinear mappings that mediates between the first and second trusted authorities. The verification parameters a and b act as intermediaries that encode the association relationship, allowing the third party to verify the connection without directly interacting with either authority's full certificate chain or requiring complex message exchange protocols.
Solution Approach 2:
The patent replaces the mechanical process of tracing through digital certificate chains and exchanging messages with a cryptographic substitution using bilinear mappings. This substitution transforms the verification task from a complex procedural system (certificate chaining) into a more elegant mathematical system where the association is encoded in verification parameters that can be checked through straightforward cryptographic computations.
3Reliability
If traditional cryptographic verification methods are used, then associations can be verified, but offline verification and secrecy are compromised due to required message exchanges
Solution Approach 1:
The patent enables offline verification by having the first trusted authority pre-compute and publish the verification parameters a and b before any verification is needed. These parameters are derived from the authority's private key in advance and can be stored and used later without requiring any message exchanges or online communication between authorities, allowing verification to be performed offline while maintaining security.
Data Source
AI summary
A first party has a first and a second cryptographic key. A second party has a third and a fourth cryptographic key, the fourth cryptographic key being derived from the first and third cryptographic keys thereby providing an association between the parties. To enable a third party to verify the existence of an association between the first and second parties, the second party generates a number that in association with the second cryptographic key, the third cryptographic key and the fourth cryptographic key define a first cryptographic parameter, a second cryptographic parameter and a third cryptographic parameter respectively. By using these parameters and the second and third cryptographic keys, the third party can verify if the first and second parties are associated.