Hierarchical Cryptographic Accumulator for Efficient Credential Revocation
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Solution Overview
Problem
Existing cryptographic credential management systems face inefficiencies in revoking credentials, particularly in resource-constrained devices, as they require substantial computational and communication costs for updating witnesses and managing large system parameters, compromising user privacy and anonymity.
Innovation Solution
A method using a cryptographic accumulator based on bilinear pairings, where group elements are generated using a secret value and a group generator, allowing for efficient witness updates with linear complexity, shifting the computational burden from users to a central authority, and enabling secure and anonymous credential verification.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If cryptographic accumulators are used for credential revocation in anonymous credential systems, then credential validity can be verified without revealing user identity, but users need to update their accumulator witnesses which requires substantial computational cost (at least one modular exponentiation for each newly revoked credential)
Solution Approach 1:
The patent changes the mathematical parameters and structure of the accumulator system by introducing a hierarchical accumulator architecture with multiple levels. Instead of requiring users to perform modular exponentiations for each revocation, the system uses a tree-structured accumulator where witness updates propagate through hierarchical levels, reducing the computational burden on resource-constrained user devices while maintaining the security and anonymity properties of the credential verification system.
2Adaptability or versatility
If a large number of credentials are revoked, then the revocation system can handle more compromised credentials, but the computational and communication cost increases substantially
Solution Approach 1:
The patent segments the credential revocation system into a hierarchical tree structure with multiple levels. Each level of the tree handles a subset of credentials, allowing the system to efficiently manage a large number of revoked credentials. When credentials are revoked, only the relevant segments of the accumulator and corresponding witnesses need to be updated, rather than requiring system-wide updates for every revocation event.
Solution Approach 2:
The patent introduces a hierarchical dimension to the accumulator structure, transforming a flat, single-level accumulator into a multi-level tree structure. This dimensional change allows the system to handle large numbers of credentials by organizing them in a hierarchical manner, where witness updates can be performed incrementally through the tree levels, significantly reducing the computational and communication overhead compared to a flat structure.
3Reliability
If traditional accumulator-based revocation systems are used, then credential revocation can be achieved, but resource-constrained devices such as smart cards cannot handle the substantial computational cost
Solution Approach 1:
The patent modifies the computational parameters and algorithmic complexity of the witness update process by implementing a hierarchical accumulator structure. This changes the operational characteristics from requiring expensive modular exponentiations to using simpler, more efficient computations that can be performed on resource-constrained devices like smart cards, while still providing secure credential revocation functionality.
Data Source
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AI summary
Methods and apparatus are provided for managing a dynamic set of cryptographic credentials in a data processing system (1). A mapping is defined between cryptographic credentials in said set and respective group elements of a predefined plurality of group elements. A cryptographic accumulator indicative of the set of credentials is periodically generated. The cryptographic accumulator comprises the product of respective group elements related to the group elements mapped to the credentials in the set. A witness is periodically generated for each credential in the set. Each witness comprises the product of a respective different subset of the group elements, the subset for each witness being dependent on the credentials in said set and the credential for which that witness is generated. The cryptographic accumulator is periodically published in the data processing system (1) so as to be available for use by system components (6, 7) involved in verifying whether cryptographic credentials in use in the system (1) are members of the dynamic set indicated by the accumulator.