Verifiable Quadratic Computation Over Encrypted Data

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Solution Overview

Problem

Existing methods for computing functions over encrypted data do not guarantee the integrity of the computation results, allowing malicious servers to provide incorrect results without detection.

Innovation Solution

Utilizing a linearly homomorphic encryption scheme and a homomorphic message authentication code to enable verifiable computation of quadratic functions over encrypted data, ensuring that clients can verify the correctness of the computation results.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If homomorphic encryption is used to compute functions over encrypted data, then data privacy is protected, but computation integrity cannot be verified

Engineering Contradiction:

Improvecomputation integrityVSAvoidverification mechanism complexity

Core Design Contradiction:

ReliabilityVSDevice complexity

Solution Approach 1:

The patent introduces homomorphic message authentication codes (MACs) as an intermediary mechanism. These MACs are computed over the encrypted data alongside the homomorphic computation, allowing the client to verify computation integrity without decrypting the data. The MAC serves as a mediator that provides verification capability while maintaining the privacy guarantees of homomorphic encryption.

Inventive Principle:

Principle #24Intermediary (Mediator)

Solution Approach 2:

The verification mechanism is segmented into distinct components: the homomorphic encryption layer for privacy protection, the homomorphic MAC layer for integrity verification, and the verification protocol layer for client-side validation. This segmentation allows each component to perform its specific function independently, making the overall system more manageable and verifiable.

Inventive Principle:

Principle #1Segmentation

2Reliability

If a malicious server provides computation results without verification, then computation speed is fast, but result correctness cannot be ensured

Engineering Contradiction:

Improveresult correctnessVSAvoidverification time

Core Design Contradiction:

ReliabilityVSLoss of time

Solution Approach 1:

The homomorphic MACs are computed in advance alongside the homomorphic encryption operations. This preliminary computation of authentication tags allows for rapid verification later, as the verification process simply requires comparing the computed MAC with the provided MAC rather than performing complex computational validation.

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The patent replaces traditional mechanical verification methods (such as re-computing the entire function or decrypting to verify) with cryptographic verification using homomorphic MACs. This substitution enables verification to be performed through efficient cryptographic operations rather than computationally intensive re-computation.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Data Source

PatentEP4133679B1A method and computation entity for performing computation of a function over encrypted data

Publication Date: 2025.11.26 NEC LAB EURO GMBH

Figure 1

AI summary

For obtaining a reliable computation result by simple means a corresponding method for performing computation of a function (f) over encrypted data by a computation entity are provided, wherein the computation of a quadratic function (f) is performed by the computation entity, wherein the encrypted data are encrypted by means of a linearly homomorphic encryption scheme, and wherein a homomorphic message authentication code is used for providing verifiable computation on encrypted data. Further, a corresponding computation entity is provided.