Multi-Party Exact Homomorphic Encryption Without Noise Accumulation
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Solution Overview
Problem
Existing homomorphic encryption technologies face scalability and noise accumulation issues, particularly in quantum computing environments, limiting their ability to perform secure and efficient computations on encrypted data.
Innovation Solution
A system for secure multi-party exact homomorphic encryption (SMPEHE) involving a key generation module, message encryption module, and computation module, utilizing multivariate polynomial sets and elementary gates to encrypt and compute on ciphertexts, ensuring quantum resilience and hyper quantum resilience.
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 accumulation occurs exponentially with multiplications limiting computation depth
Solution Approach 1:
The patent extracts and eliminates the noise accumulation problem by using exact homomorphic encryption based on multivariate polynomial sets. Instead of working with noisy approximate results from traditional HE, the invention uses exact polynomial evaluation and arithmetic operations that maintain precision throughout the computation process, removing the fundamental noise limitation.
Solution Approach 2:
The patent changes the mathematical foundation from traditional lattice-based HE with inherent noise to exact polynomial-based HE. By transforming the computational framework to use multivariate polynomial sets with exact arithmetic operations, the system achieves unlimited computation depth while maintaining security, fundamentally changing the noise parameter from exponential growth to zero accumulation.
2Productivity
If quantum computing resources are increased to improve QHE performance, then computation capability is improved, but the number of physical qubits required becomes prohibitively large
Solution Approach 1:
The patent replaces quantum mechanical systems with classical computational systems. By using classical multivariate polynomial evaluation and arithmetic operations, the invention achieves homomorphic encryption functionality without requiring quantum hardware, thereby eliminating the need for large numbers of physical qubits while maintaining computation capability.
3Reliability
If Clifford+T circuits are used for fault-tolerant quantum computation, then error correction is improved, but the overhead of physical to logical qubit ratio reaches several hundred times
Solution Approach 1:
The patent substitutes quantum fault-tolerance mechanisms with classical exact computation. By using deterministic polynomial arithmetic over finite fields, the system achieves computational reliability without quantum error correction overhead, eliminating the need for hundreds of physical qubits per logical qubit.
4Reliability
If existing HE schemes are adapted to quantum versions, then quantum security is improved, but the schemes inherit all demerits of classical HE including noise accumulation and high qubit consumption
Solution Approach 1:
The patent extracts the security functionality from quantum-specific implementations and implements it through classical exact polynomial-based HE. By separating the security requirement from quantum hardware dependencies, the invention achieves quantum-level security without inheriting the noise accumulation and qubit consumption problems of quantum HE schemes.
Solution Approach 2:
The patent replaces quantum mechanical implementations with classical polynomial arithmetic. This substitution maintains the security properties needed for quantum-resistant cryptography while eliminating the physical constraints and noise issues inherent in quantum hardware-based HE schemes.
Data Source
AI summary
A system and a method for secure multi-party exact homomorphic encryption (SMPEHE) comprising a first participant, a second participant and a third participant, wherein the system further comprises: a key generation module within the first participant to produce an encryption mapping comprising an ordered product of elementary gates; to generate a multivariate polynomial set, serving as a public encryption key, via the encryption mapping; to form an encryption operator serving as a private key; and to create an encrypted polynomial set representing a computational instruction based on an encrypted action; a message encryption module within the second participant to encode a plaintext message into a first ciphertext by the public key provided by the first participant; and to transmit the first ciphertext to the third participant; and a computation module within the third participant to receive the first ciphertext; and to perform a computation on the received first ciphertext by evaluating the encrypted polynomial set. The structure of SMPEHE is a multipartite extension of the framework EHE and protects information for multiple users across all stages from transmission, to processing and to storage. All attributes of EHE are inherited and generalized in SMPEHE, including the safeguard of both data and operations, exact encrypted computations as well as exact decryptions, blind computation, the fulfillments of quantum resilience and hyper quantum resilience, and the capabilities of performing large-scale and sophisticated encrypted computations. This structure is also deployable on CPU and GPU environments.