Augmented Zero-Knowledge Proofs with OPRF-Based Private Membership

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Solution Overview

Problem

Existing zero-knowledge proof protocols fail to provide privacy-preserving membership tests on private sets, neglecting the privacy requirements of verifiers, and do not support unlinkable user authentication in self-sovereign identity systems.

Innovation Solution

An oblivious pseudo-random function (OPRF) protocol is used to determine a pseudo-random function (PRF) result based on an input from a proving device and a PRF key, allowing verifiers to check user membership in a private verifier list without disclosing the list to the user.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Loss of information

If standard zero-knowledge proof protocols are used for user authentication, then user privacy is protected, but verifier privacy is compromised because verifiers must disclose their check lists to enable membership testing

Engineering Contradiction:
Improveverifier list privacyVSAvoidmembership test capability
Core Design Contradiction:
Loss of informationVSEase of operation

Solution Approach 1:

The patent introduces an intermediary mechanism using oblivious pseudo-random functions (OPRF) and trusted execution environments (TEEs). The verifier's check list is transformed into encrypted representations within a TEE, allowing membership testing without direct disclosure of the list contents. This intermediary computational layer enables the verifier to perform membership tests while maintaining list privacy, resolving the contradiction between verifier privacy and membership test capability.

Inventive Principle:
Principle #24Intermediary (Mediator)

Solution Approach 2:

The patent transforms the verifier's check list from plaintext identifiers into encrypted representations using OPRF with unique salts for each entry. This parameter transformation allows the system to perform membership testing on encrypted data within TEEs, enabling the verifier to maintain list privacy while still performing accurate membership tests. The change in data representation form resolves the contradiction by making the list unusable for direct inspection while preserving its functional utility.

Inventive Principle:
Principle #35Parameter changes

2Loss of information

If verifiers keep their check lists secret, then verifier privacy is maintained, but users cannot prove non-membership without the verifier disclosing list information

Engineering Contradiction:
Improveverifier list secrecyVSAvoidmembership test reliability
Core Design Contradiction:
Loss of informationVSReliability

Solution Approach 1:

The patent uses TEEs as an intermediary trusted computing environment that holds the verifier's secret check list. The TEE performs membership testing operations without exposing the list contents to either the user or external observers. This intermediary ensures that membership test reliability is maintained through cryptographic verification while the list remains secret within the trusted boundary, resolving the contradiction between list secrecy and test reliability.

Inventive Principle:
Principle #24Intermediary (Mediator)

Solution Approach 2:

The patent replaces the traditional mechanical approach of direct list disclosure and comparison with cryptographic substitution using OPRF and TEEs. Instead of mechanically comparing plaintext lists, the system uses cryptographic transformations and trusted execution to perform membership testing. This substitution maintains list secrecy while ensuring reliable membership determination through cryptographic proof mechanisms.

Inventive Principle:
Principle #28Mechanics substitution (Replace mechanical system)

3Loss of information

If existing anonymous credential systems are used, then user identity privacy is protected, but unlinkable authentication across multiple verifiers is not achieved

Engineering Contradiction:
Improveuser identity privacyVSAvoidunlinkable authentication capability
Core Design Contradiction:
Loss of informationVSAdaptability or versatility

Solution Approach 1:

The patent segments the authentication process into multiple independent cryptographic interactions using unique salts for each OPRF evaluation. Each verifier interaction uses distinct cryptographic parameters, making it computationally infeasible to link authentication events across different verifiers. This segmentation of the authentication process into isolated cryptographic sessions enables unlinkable authentication while maintaining user identity privacy.

Inventive Principle:
Principle #1Segmentation

Solution Approach 2:

The patent adds a new dimension to anonymous credential systems by integrating OPRF-based membership testing with TEEs. This dimensional extension allows the system to simultaneously achieve unlinkable authentication across multiple verifiers and private membership testing, going beyond the capabilities of traditional anonymous credential systems. The additional cryptographic layer enables these advanced privacy features without compromising user identity protection.

Inventive Principle:
Principle #17Another dimension (Dimensionality change)

Data Source

PatentUS12395341B2Augmented zero-knowledge proof with private membership test
Publication Date: 2025.08.19 NEC CORP
  • US12395341B2 patent drawing
  • US12395341B2 patent drawing
  • US12395341B2 patent drawing

AI summary

A method for performing a privacy-preserving membership test includes performing an oblivious pseudo-random function (OPRF) protocol to determine a pseudo-random function (PRF) result based on an input from a proving device and a PRF key. The input indicates a user identity of a user associated with the providing device. The method further includes determining whether the user belongs to a verifier list associated with a verifier device based on testing membership of the user using the verifier list and the PRF result.