Matrix-Based Homomorphic Encryption for Cloud Data Privacy
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Solution Overview
Problem
Existing Fully Homomorphic Encryption (FHE) schemes face challenges due to noise growth during computations, high computational expense for bootstrapping, and vulnerability to key recovery attacks, making them impractical for real-world applications.
Innovation Solution
The proposed system employs matrix-based homomorphic encryption, where a processor hosts a homomorphic encryption module connected to cloud servers. It involves acquiring plaintext, selecting matrix sizes and modulus, choosing invertible matrices as secret keys, and encoding plaintext using an envelope matrix to enable efficient and secure computations on encrypted data.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional encryption (AES) is used for data security in cloud infrastructure, then data confidentiality is improved, but operational capability on ciphertext is lost and computational cost increases
Solution Approach 1:
The patent transforms the encryption scheme from conventional AES to homomorphic encryption, changing the cryptographic parameters to enable operations on ciphertext. This allows addition and multiplication operations to be performed directly on encrypted data without decryption, resolving the contradiction between maintaining confidentiality and enabling operational capability.
Solution Approach 2:
The patent introduces homomorphic encryption as an intermediary between conventional encryption and plaintext processing. This intermediary encryption scheme preserves the security properties of conventional encryption while adding the capability to perform computations on ciphertext, thus bridging the gap between confidentiality and operational capability.
2Duration of action of moving object
If bootstrapping is performed to remove noise in FHE schemes, then arbitrary deep computation is enabled, but computational expense becomes extremely high
Solution Approach 1:
The patent replaces the expensive bootstrapping operation with cheaper alternative techniques for noise management. By using different cryptographic constructions and noise reduction methods that do not require full bootstrapping, the system enables sufficient computation depth at a fraction of the computational expense.
Solution Approach 2:
The patent segments the computation process into multiple stages with intermediate noise management techniques. Instead of requiring a single expensive bootstrapping operation to handle all computation depth requirements, the system uses multiple smaller noise management steps that are collectively less expensive than one full bootstrapping.
3Adaptability or versatility
If existing FHE schemes are used with small noise added to encryption, then homomorphic operations are enabled, but noise growth during computation makes decryption impossible
Solution Approach 1:
The patent applies beforehand cushioning by pre-managing noise growth through careful cryptographic parameter selection and intermediate noise reduction techniques. By anticipating noise accumulation during computation and applying corrective measures before noise becomes critical, the system maintains decryption feasibility while enabling extensive homomorphic operations.
Solution Approach 2:
The patent changes the noise management parameters by using different error distribution schemes and noise scaling techniques. These parameter changes allow the system to tolerate greater noise accumulation during computation while still maintaining the ability to decrypt, thus resolving the contradiction between homomorphic operations capability and decryption feasibility.
4Productivity
If matrix-based homomorphic encryption is implemented, then computational efficiency is improved, but system complexity increases
Solution Approach 1:
The patent achieves universality by designing a matrix-based homomorphic encryption system that can perform multiple cryptographic operations (encryption, decryption, addition, multiplication, hashing) within a unified mathematical framework. This multi-functionality improves computational efficiency by leveraging the same matrix operations across different cryptographic primitives while managing system complexity through a coherent design.
Data Source
AI summary
A system for matrix-based 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 M required to be encrypted; select a size of a matrix and modulus n; select invertible × matrix S1 over n, wherein n is a residue ring modulo n; compute an invertible × matrix S2 over n; set a secret key (S1, S2); and encode the plaintext M by an integer m over n, wherein m is encoded by an envelope matrix comprising a formV(m)=(α0βm),wherein α and β are numbers chosen at random α, β∈n.