Matrix-Based Public Key Homomorphic Encryption for Low-Noise Computing
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing Fully Homomorphic Encryption (FHE) schemes face challenges due to noise growth during computations, high computational expense, and vulnerability to key recovery attacks, making them impractical for seamless data processing across platforms.
Innovation Solution
A matrix-based public key homomorphic encryption system that uses invertible matrices and random secret keys to encrypt data, allowing operations on encrypted data without decryption, including homomorphic arithmetic operations, hash functions, and searchable encryption.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional encryption schemes like AES are used, then data security is improved, but operations on encrypted data require decryption which increases computational cost and time
Solution Approach 1:
The patent introduces an intermediary encryption scheme that allows computations to be performed on encrypted data without full decryption. The homomorphic encryption acts as a mediator between the need for data security and the need for computational efficiency, enabling cloud providers to process encrypted data while maintaining confidentiality.
Solution Approach 2:
The encryption process is segmented into different layers with varying homomorphic properties. Some data elements are encrypted with full homomorphic capabilities while others use simpler schemes, allowing selective computation on encrypted data without requiring complete decryption of all data.
2Productivity
If Fully Homomorphic Encryption (FHE) is used to enable operations on encrypted data, then productivity is improved, but noise growth during computations makes decryption impossible after certain operations
Solution Approach 1:
The patent employs partially homomorphic encryption schemes that provide sufficient homomorphic capabilities for specific computational tasks without the full complexity and noise growth of completely homomorphic encryption. This partial approach maintains decryption reliability while enabling necessary computations on encrypted data.
Solution Approach 2:
The encryption parameters are dynamically adjusted based on the computational depth and type of operations required. By changing parameters such as noise thresholds and ciphertext structure, the system maintains decryption reliability even after multiple computational operations on encrypted data.
3Productivity
If existing FHE schemes based on LWE or RLWE are used, then homomorphic operations are enabled, but key recovery attacks compromise data confidentiality
Solution Approach 1:
The patent implements asymmetric key structures and non-commutative cryptographic operations that make key recovery attacks significantly more difficult. The asymmetric design ensures that even if some cryptographic assumptions are compromised, the directional nature of the operations protects the confidentiality of encrypted data.
Solution Approach 2:
The encryption scheme combines multiple cryptographic primitives and mathematical assumptions into a composite system. By layering different cryptographic mechanisms, the patent creates a defense-in-depth approach where compromising one assumption does not necessarily compromise the overall confidentiality of the encrypted data.
4Productivity
If bootstrapping is performed to remove noise for arbitrary deep computation, then productivity is improved, but computational expense becomes extremely high
Solution Approach 1:
The patent applies bootstrapping selectively and partially rather than continuously. By performing bootstrapping only at critical points in the computation where noise accumulation becomes problematic, the system achieves sufficient computation depth without the extreme computational expense of continuous bootstrapping.
Solution Approach 2:
Noise management is performed preliminarily by designing encryption parameters and ciphertext structures that are optimized for the expected computational depth. This preliminary configuration reduces the need for expensive runtime bootstrapping operations while still enabling arbitrary deep computation when necessary.
Data Source
AI summary
A system for matrix-based public key homomorphic encryption, including a processor of a computing node configured to host a homomorphic encryption module and connected to at least one cloud server and a memory on which are stored machine-readable instructions that when executed by the processor, cause the processor to: acquire plaintext x required to be encrypted; select a size of a matrix and modulus n; select invertible × matrix S over n, wherein n is a residue ring modulo n; compute an invertible × matrix S−1 over n; select two random secret keys (S, S−1) and (K, K−1) of a homomorphic encryption scheme Σ(m), where S and K belong to a ring of ×-matrix Ml(m) over residue ring m with modulus m=pq, where p, q are primes; select (K, K−1) as a master key; use the master key to encrypt all elements of matrices S and S−1; obtain two ciphertexts P1=EncK(S) and P2=EncK(S−1), which both form public key of the Σ(m) including pk=(P1, P2), wherein a secret key is sk=((S, S−1), (K, K−1)); and apply the pk and the sk for encryption and decryption of the plaintext x.