QAP-Based Homomorphic Encryption One-Way Computational System Design
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Solution Overview
Problem
Current fully homomorphic encryption (HE) schemes face challenges in achieving practical, noise-free computations due to exponential overhead and inability to conduct blind evaluations without secret disclosure, relying on approximated solutions and high computational costs.
Innovation Solution
A method for designing a one-way computational system in quotient algebra partition-based homomorphic encryption (QAPHE) that constructs fault-tolerant encodes using tensor-product operators, correction operators, and permutations to achieve exact solutions with modest computational overhead, enabling blind evaluations and secure computations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If noise reduction methods are used in lattice-based HE schemes, then computation can be performed on encrypted data, but exponential overhead is required and only approximated solutions are obtained
Solution Approach 1:
The patent segments the computational process into distinct phases: encoding the function as a QAP instance, performing homomorphic evaluation, and decoding results. This segmentation allows each phase to be optimized independently, avoiding the exponential overhead of traditional lattice-based noise reduction while maintaining computation accuracy through structured algebraic operations.
Solution Approach 2:
The patent changes the fundamental parameters of the HE system by transitioning from lattice-based cryptography to QAP-based cryptography. This parameter change enables exact arithmetic operations on encrypted data without requiring noisy approximation corrections, thereby eliminating exponential computational overhead while maintaining reliability.
2Reliability
If traditional HE schemes are used, then encrypted computation is enabled, but algorithms and operators are revealed during computation (no blind evaluation)
Solution Approach 1:
The patent introduces QAP instances and evaluation circuits as intermediaries between the encrypted data and the computation process. These intermediaries allow the computation to be performed on encrypted representations without exposing the underlying algorithms or operators, enabling blind evaluation while maintaining security through the cryptographic structure of QAPHE.
3Measurement precision
If fault tolerant encoding is used in QAPHE, then exact solutions can be obtained, but computational complexity increases
Solution Approach 1:
The patent performs preliminary encoding of the function as a QAP instance before homomorphic evaluation. This preliminary action structures the computation in advance, allowing exact solutions to be obtained during evaluation without requiring complex fault tolerant mechanisms during the actual computation phase, thereby reducing overall computational complexity.
Data Source
AI summary
The present inventive concept discloses a method of designing a one-way computational system in QAP-based homomorphic encryption applied to the n-qubit encode operations of a k-qubit action M for public-key and semi-public-key schemes respectively, n≥k, wherein the method comprises: preparing a tensor-product operator =I2<sup2>n-k</sup2>⊗M=12 and decomposing it into two parts, wherein is composed of elementary gates, and let =1† and 2=; providing a correction operator, =12 for public-key and =I2<sup2>k </sup2>for semi-public-key, and an encoding operator, Qen†V†=W1W2 for public-key and Qp†=W1W2 for semi-public-key, both composed of elementary gates; providing appropriate permutations P, P0 and P1, while P0=P1 for semi-public-key, to obey the nilpotent condition PW1P0=I for the identity operator; through process of merging operators according to sets of identities of gates, including Id-GateELIM, Id-GateEx and Id-GateREP, there obtain the mixed encode for public-key scheme, Uen=PQen†V†=(P1†W1†21W1P1)(P1†P0)(P0†W1†2W1P0) (P0†W2), and that for semi-public key, Uen=PMQp†=(P0†W1†2W1P0)(P0†W2) with n=k, 1=2=I2<sup2>n </sup2>and P0=P1.