FHE Key Generation via CRT and LWE Modulus Design
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing fully homomorphic encryption (FHE) schemes require bootstrapping, which is computationally expensive and slow, limiting their practical application due to high computational and temporal costs.
Innovation Solution
A FHE scheme that utilizes the Chinese Reminder Theorem (CRT) and learning with errors (LWE), eliminating the need for bootstrapping by enabling arbitrary number of additions and multiplications on encrypted data without decryption.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If bootstrapping is used in existing FHE schemes, then security and correctness are maintained, but computational cost and execution time increase significantly
Solution Approach 1:
The patent extracts and removes the bootstrapping step from the FHE computation process. By using a specific modulus relationship (q = p × p') and carefully controlling noise growth through modular arithmetic properties, the scheme eliminates the need for bootstrapping while maintaining security, thus resolving the contradiction between security and computational speed.
Solution Approach 2:
The patent changes the parameter structure by introducing a specific relationship between moduli (q = p × p') and adjusting noise distribution parameters. This parameter transformation allows the system to maintain security guarantees without requiring the computationally expensive bootstrapping operation, thereby improving computational speed.
2Reliability
If bootstrapping is performed to maintain noise bounds, then ciphertext correctness is preserved, but execution time and computational resources are excessively consumed
Solution Approach 1:
The patent performs preliminary noise control by designing the encryption scheme with specific modulus relationships and noise distribution constraints from the outset. By pre-configuring the system to naturally bound noise growth through modular arithmetic (q = p × p'), the need for later bootstrapping operations is eliminated, preserving ciphertext correctness without time loss.
Solution Approach 2:
The bootstrapping step is extracted and removed from the computation flow. The scheme achieves noise bound maintenance through inherent mathematical properties of the modular arithmetic system rather than through explicit bootstrapping operations, thus preserving correctness while eliminating time consumption.
3Reliability
If FHE operations are performed on encrypted data, then data privacy is maintained, but computational efficiency decreases due to noise accumulation
Solution Approach 1:
The patent transforms the noise management approach by changing key parameters (modulus relationships, noise distribution). This parameter transformation allows multiple homomorphic operations to be performed before noise becomes problematic, improving computational efficiency while maintaining data privacy through the encrypted domain operations.
Solution Approach 2:
The patent removes the need for periodic decryption-and-re-encryption cycles (bootstrapping) that were required to manage noise accumulation. By extracting this bottleneck step and replacing it with noise-resistant mathematical structures, the system achieves better computational efficiency while preserving data privacy.
Data Source
AI summary
The present application is directed towards a new system for performing FHE and includes a method, system, program and storage medium configured for generating keys for fully homomorphic encryption, wherein generating the keys comprises: obtaining a first set of numbers, wherein the first set of numbers is a set of pairwise coprime numbers p1, ... , pk+1; obtaining a second set of prime numbers r1, r2, ..., rk+1; obtaining a third set of numbers, wherein the third set of numbers is a set of random or pseudo random numbers s1, ..., sn; calculating a secret key, sk, based on the first set of numbers, the second set of numbers, and third set of numbers; and calculating a public parameter, q, based on the first set of numbers and the second set of numbers.