Exact Homomorphic Encryption Using Quantum-Gate Polynomials
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Solution Overview
Problem
Existing homomorphic encryption technologies face scalability and noise accumulation issues, particularly in quantum computing environments, limiting secure data processing and computation.
Innovation Solution
A framework of exact homomorphic encryption (EHE) using quantum gates to generate multivariate polynomials for encryption and computation, leveraging invertible and noncommutative properties to ensure precise decryption and secure computation.
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 changes the fundamental parameter of encryption from traditional noisy homomorphic encryption to quantum-inspired exact homomorphic encryption using multivariate polynomials over finite fields. This parameter change eliminates noise accumulation while maintaining security through the hardness of polynomial factorization and evaluation problems.
Solution Approach 2:
The patent substitutes the mechanical noise accumulation mechanism of traditional HE with an algebraic structure based on multivariate polynomials and finite fields. The computation is performed through polynomial evaluation and manipulation rather than through noisy cryptographic operations, replacing the problematic mechanical process with an algebraic one.
2Productivity
If quantum computing resources are increased to improve quantum homomorphic encryption, then computation capability is improved, but device complexity and scalability are worsened due to requiring hundreds of times more physical qubits than logical qubits
Solution Approach 1:
The patent creates a classical computational model that copies the essential algebraic structure of quantum homomorphic encryption without requiring actual quantum hardware. By using multivariate polynomials over finite fields, it replicates the mathematical properties needed for quantum-inspired HE while running on classical computers.
Solution Approach 2:
The patent segments the quantum computation problem into classical algebraic components - specifically polynomial rings and finite field arithmetic. This segmentation allows the computation to be performed using classical algorithms on polynomial manipulation rather than requiring quantum gate operations.
3Reliability
If more quantum operations are used to achieve fault-tolerant quantum computation, then computation reliability is improved, but the number of required physical qubits increases making the system less accessible
Solution Approach 1:
The patent substitutes quantum mechanical fault tolerance mechanisms with classical algebraic error-correcting codes based on polynomial structures. The reliability is achieved through mathematical properties of polynomial rings and finite fields rather than through quantum error correction, eliminating the need for massive physical qubit overhead.
Data Source
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.