Monoid Algebra-Based Fully Homomorphic Encryption Scheme
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Solution Overview
Problem
Current fully homomorphic encryption schemes are inefficient due to lengthy bootstrapping procedures, making them unattractive for practical applications, and lack secure transmission methods that can withstand brute-force attacks.
Innovation Solution
The development of a family of fully homomorphic encryption schemes using monoid algebras and character theory, which enables secure encryption and decryption without requiring extensive computational power, by employing a monoid algebra-based encryption scheme that supports homomorphic operations and uses a probabilistic multiplicative homomorphic encryption scheme for secure data transmission.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If Gentry's bootstrapping transformation is used to construct fully homomorphic encryption schemes, then both addition and multiplication operations are supported on encrypted data, but the implementation becomes inefficient due to lengthy bootstrapping procedures requiring extensive computational power
Solution Approach 1:
The patent extracts the bootstrapping procedure from the encryption scheme and replaces it with a key generation mechanism. Instead of performing lengthy bootstrapping operations to refresh ciphertexts, the system generates cryptographic keys that inherently enable unlimited homomorphic operations without requiring intermediate bootstrapping steps, thus eliminating the computational bottleneck while preserving full functionality
Solution Approach 2:
The patent changes the fundamental parameters of the encryption scheme by using ideal lattices and specific module structures that allow homomorphic operations to be performed efficiently without bootstrapping. By adjusting the mathematical parameters (module size, error distribution, lattice dimension), the system achieves a balance between security, functionality, and efficiency that eliminates the need for computationally intensive bootstrapping procedures
2Reliability
If error-based encryption schemes are used to achieve probabilistic homomorphic encryption, then security is improved, but the noise accumulation limits the degree of polynomials that can be handled
Solution Approach 1:
The patent applies preliminary error management techniques during key generation and encryption setup. By carefully controlling error distribution and magnitude from the outset, and using ideal lattice structures that contain error growth, the system prevents noise accumulation from limiting polynomial degree, thereby maintaining both security and high adaptability for complex computations
3Productivity
If re-linearization technique is applied to obtain leveled fully homomorphic encryption schemes, then efficiency is improved, but the schemes still require significant computational resources and are not resistant to brute-force attacks
Solution Approach 1:
The patent combines multiple cryptographic primitives and mathematical structures (ideal lattices, module structures, error-based encryption) into a composite encryption scheme. This composite approach achieves both efficiency through optimized homomorphic operations and strong security resistance against brute-force attacks by leveraging the strengths of each component while mitigating their individual weaknesses
Data Source
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AI summary
A blueprint that produces a family of FHE schemes given any homomorphic monoidal encryption scheme. The ciphertext space is a subspace of the monoid algebra over F2 generated by the initial encryption monoid. The method can be generally applied to any monoid encryption schemes. Advantageously, monoid encryption schemes produce efficient FHE schemes with the inventive blueprint. Furthermore, the corresponding FHE scheme can correctly decrypt and efficiently compute circuits with low (polynomial in the security parameter) additive depth, a feature not realized by prior encryption methods.