Homomorphic Encryption Modular Reduction Error Variance
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Solution Overview
Problem
Fully homomorphic encryption methods face issues with increasing error variance and coefficient magnitude during modular reduction in bootstrapping, particularly when approximating high-degree polynomials, which affects data privacy and security in processing encrypted data.
Innovation Solution
A processor-implemented method using homomorphic encryption that determines a coefficient for an approximating polynomial based on error variance, adjusting a weight-constant vector to minimize variance and perform modular reduction, thereby optimizing the approximation of modular reduction functions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the degree of approximating polynomial is increased to improve modular reduction accuracy, then the approximation precision is improved, but the coefficient magnitude increases causing error variance to increase
Solution Approach 1:
The patent changes the parameter of polynomial degree in the approximating polynomial used for modular reduction. By selecting an appropriate degree (not necessarily the highest possible), the patent balances approximation precision with coefficient magnitude control, thereby managing error variance in homomorphic encryption operations.
Solution Approach 2:
The patent dynamically adjusts the approximating polynomial based on the specific ciphertext and operation context. Rather than using a fixed high-degree polynomial, the system adapts the polynomial degree and coefficients to minimize error variance while maintaining sufficient approximation accuracy for the given computational task.
2Measurement precision
If the degree of approximating polynomial is increased to improve modular reduction accuracy, then the approximation precision is improved, but the coefficient magnitude increases affecting security
Solution Approach 1:
The patent modifies the polynomial degree parameter to prevent coefficient magnitude from becoming excessively large. This parameter adjustment ensures that while approximation precision is maintained at sufficient levels, the coefficient magnitude remains bounded, thereby preventing security degradation in the homomorphic encryption scheme.
3Reliability
If error variance is reduced by optimizing approximating polynomial, then data privacy protection is improved, but the computational complexity increases
Solution Approach 1:
The patent optimizes parameters of the approximating polynomial (degree, coefficients) to reduce error variance, thereby improving data privacy protection. The optimization is performed once during key generation or parameter setup, rather than during each encryption operation, which limits the increase in computational complexity to a one-time cost.
Solution Approach 2:
The patent performs preliminary optimization of the approximating polynomial parameters before actual encryption operations. By pre-computing optimal polynomial coefficients and degrees, the system reduces error variance for privacy protection without incurring high computational complexity during time-critical encryption and decryption operations.
Data Source
AI summary
A processor-implemented encryption method using homomorphic encryption includes: receiving data; generating a ciphertext by encrypting the received data; determining a coefficient of an approximating polynomial for performing a modular reduction on a modulus corresponding to the ciphertext, based on an error between the approximating polynomial and a modular reduction function; and performing bootstrapping on the ciphertext by performing the modular reduction based on the determined coefficient of the approximating polynomial.