Cryptographic Accumulator for Efficient Credential Verification
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Solution Overview
Problem
Existing cryptographic accumulator systems for anonymous credential verification are inefficient, particularly for resource-constrained devices, as they require substantial computational and communication costs for updates and witness generation, and may compromise user privacy.
Innovation Solution
A method using a cryptographic accumulator generated from group elements, where each group element is generated using a secret value and a group generator, allowing for efficient updates and witness computation, with witnesses being products of subsets of group elements, enabling fast and secure verification of data items like cryptographic credentials.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of information
If cryptographic accumulators are used for anonymous credential verification, then user privacy is protected, but computational and communication costs for updates and witness generation become substantial
Solution Approach 1:
The patent segments the credential verification system into distinct components: the issuer maintains the accumulator, users hold credentials with associated witnesses, and verifiers check validity. This segmentation allows each party to perform only necessary computations (users perform lightweight witness verification rather than full accumulator updates), resolving the contradiction between privacy protection and computational efficiency.
Solution Approach 2:
The patent implements preliminary action by having users obtain credentials and witnesses from the issuer before verification transactions. The issuer pre-computes and distributes valid credential-witness pairs, so users don't need to perform expensive accumulator update computations during actual verification. This preliminary preparation resolves the efficiency problem while maintaining privacy.
2Reliability
If traditional revocation checking methods are used (publishing revoked credential lists), then credential validity can be verified, but communication efficiency deteriorates due to large list sizes
Solution Approach 1:
The patent extracts the revocation information from large published lists and incorporates it into a compact cryptographic accumulator structure. Instead of publishing complete lists of revoked credentials, the system extracts essential validity information and embeds it in the accumulator, which can be represented in a compact form. This resolves the contradiction between reliable verification and reduced communication overhead.
Solution Approach 2:
The patent changes the parameter representation from explicit credential identifier lists to a cryptographic accumulator value. The accumulator transforms the set of valid credential witnesses into a single cryptographic parameter that verifiers can check against. This parameter transformation dramatically reduces communication data size while maintaining verification reliability.
3Reliability
If credential identifiers are revealed to verifiers for revocation checking, then validity can be confirmed, but user anonymity is compromised
Solution Approach 1:
The patent introduces cryptographic witnesses as intermediaries between credential identifiers and verifiers. Instead of verifiers directly seeing credential identifiers, they interact with mathematical witnesses that prove validity without revealing identity. The witness acts as a mediator that translates identity-sensitive information into privacy-preserving proof, resolving the contradiction between verification reliability and anonymity protection.
Solution Approach 2:
The patent replaces the mechanical system of direct identifier revelation with a cryptographic substitution system. Instead of verifiers mechanically checking identifier lists, the system uses cryptographic proofs (witnesses) that mathematically guarantee validity while preserving anonymity. This substitution resolves the contradiction by replacing identity-revealing mechanisms with privacy-preserving cryptographic alternatives.
Data Source
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AI summary
Methods and apparatus are disclosed for providing a cryptographic accumulator, indicative of a set of data items such as cryptographic credentials, in a data processing system (1). A plurality of group elements is generated and a mapping is defined between data items in said set and respective group elements. A cryptographic accumulator is generated, the cryptographic accumulator comprising the product of respective group elements related to the group elements mapped to the data items in the set. The cryptographic accumulator is then published in the data processing system (1) so as to be available for use by system components (6, 7) involved in verifying whether data items in use in the system (1) are members of the set indicated by the accumulator.