Exact Homomorphic Encryption Using Quantum Gates Against Noise Accumulation
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Solution Overview
Problem
Existing homomorphic encryption methods face scalability and noise accumulation issues, particularly in quantum computing environments, limiting secure data processing and computation.
Innovation Solution
A computer-implemented method using a framework of exact homomorphic encryption (EHE) based on quantum fault-tolerant computation, employing multivariate polynomials and quantum gates to encrypt and compute on encrypted data, ensuring invertibility and noncommutativity for secure, exact computations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional homomorphic encryption is used to enable computation on encrypted data, then data security is improved, but noise accumulates exponentially with multiplications limiting computation depth
Solution Approach 1:
The patent extracts and eliminates the noise accumulation problem by transitioning from traditional noisy homomorphic encryption to quantum homomorphic encryption, where the quantum mechanical properties inherently prevent noise buildup that plagues classical approaches
Solution Approach 2:
The patent replaces the classical mechanical computation system with quantum mechanical operations, using quantum gates and quantum states to perform homomorphic encryption computations, thereby fundamentally changing the underlying physical mechanism from classical to quantum domain
2Productivity
If quantum computing resources are increased to improve quantum homomorphic encryption, then computation capability is improved, but the number of physical qubits required becomes prohibitively large
Solution Approach 1:
The patent segments the quantum computation into modular components using quantum circuits with controlled gates, allowing the system to achieve complex computational capabilities through composition of smaller, manageable quantum operations rather than requiring a monolithic large-scale quantum computer
Solution Approach 2:
The patent transitions from considering only the number of qubits as the resource metric to utilizing the dimensional space of quantum circuit depth and gate sequences, thereby achieving enhanced computation capability through temporal and structural dimensions rather than merely increasing qubit count
3Reliability
If fault-tolerant quantum computation is implemented to improve reliability, then error correction is improved, but the overhead of encoding increases resource requirements
Solution Approach 1:
The patent applies preliminary error correction encoding to the quantum states before they enter the homomorphic encryption computation pipeline, preparing them in advance to be resilient against errors during subsequent quantum gate operations and measurements
Data Source
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AI summary
A computer-implemented method based on a framework of Exact Homomorphic Encryption, EHE, protecting information from transmission, to processing and to storage. The EHE framework consists of the message encryption and the computation encryption, safeguarding both data and operations. A crucial step toward the construction of EHE is replacing classical logic gates with quantum gates, which acting on variables to generate multivariate polynomials alongside operating on quantum states conventionally. The generated polynomial sets serve as public keys for encrypting message and computation. Two fundamental traits of quantum gates, invertibility and noncommutativity, establish the success of EHE. As an isomorphism conducting with invertible gates, EHE naturally performs exact encrypted computation in full homomorphism as well as exact decryption. Grounded on a combinatorially high complexity offered by retrieving a circuit of noncommuting gates, EHE not only surpasses the security 2128 of the post-quantum standard, but also straightforwardly reaches 21024 for hyper quantum resilience. Blind computation is attained further, thus sheltering data and operations concurrently. The EHE framework can be regarded as a substantive manifestation of noncommutative cryptography. EHE has been deployable on CPU and GPU, showcasing the capability of exercising encrypted computations of large sizes and high complications over diverse functions.