Homomorphic Encryption for Secure Linear Algebra on Encrypted Data
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Solution Overview
Problem
Current cryptographic systems lack the capability to perform complex computations such as solving systems of linear equations and matrix inversions directly on encrypted data without decrypting, especially in untrusted environments, limiting their application in secure data processing and analysis.
Innovation Solution
A cryptographic system that includes secure protocols for matrix multiplications and solving systems of linear equations in the encrypted domain using homomorphic computation and secret sharing, allowing for operations like Gaussian elimination and iterative methods without restrictions on matrix coefficients, enabling secure data analysis and processing directly on encrypted data.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If data is decrypted to perform analysis tasks, then computational operations can be performed on the data, but security and privacy are compromised
Solution Approach 1:
The patent introduces homomorphic encryption as an intermediary that enables computational operations on encrypted data without decryption. The encryption scheme acts as a mediator between the need for secure data storage and the need for data processing, allowing the cloud server to perform computations on ciphertexts while the data remains encrypted throughout the entire process.
Solution Approach 2:
The patent transforms the data representation by encrypting it using homomorphic encryption properties, changing the parameter state from plaintext to ciphertext. This transformation allows mathematical operations to be performed on the encrypted data in such a way that the results, when decrypted, match the results of operations performed on the plaintext data.
2Reliability
If conventional cryptographic protocols are used to protect private information, then unauthorized access is prevented, but no practical system exists for secure processing against trusted parties
Solution Approach 1:
The patent creates a universal secure processing framework that works against both unauthorized third parties and trusted parties (such as cloud servers). The homomorphic encryption system provides multi-functionality by enabling not only confidentiality against outsiders but also secure computation between authorized entities, making the same cryptographic primitive effective against multiple threat models.
3Adaptability or versatility
If Gentry's cryptosystem with bootstrappable decryption is used, then full homomorphism is achieved, but practical implementation remains an open problem
Solution Approach 1:
The patent applies partial homomorphic encryption properties to solve practical problems without requiring full homomorphism. By using additive or multiplicative homomorphic properties selectively for specific computational tasks (such as linear operations, statistical analysis, or machine learning models), the system achieves practical security and functionality without the complexity of bootstrappable decryption schemes.
Data Source
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AI summary
Disclosed embodiments include a cryptographic system implemented in at least one digital computer with one or more processors or hardware such as FPGAs for performing secure computations, analysis, and signal processing directly on encrypted data in untrustcd environments. According to a basic embodiment, the proposed cryptographic system comprises: (a) at least one secure protocol for performing matrix multiplications in the encrypted domain, and (b) at least one secure protocol for solving systems of linear equations in the encrypted domain. According to a particular embodiment, the system comprises a plurality of privacy-preserving protocols for solving systems of linear equations (SLE) directly based on homomorphic computation and secret sharing.