FHE Scale Initialization via Weighted Geometric Mean
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Solution Overview
Problem
Fully-homomorphic encryption schemes face challenges in managing ciphertext scales during modulus chain operations, leading to computationally impractical magnitudes and inaccuracies, especially in deep modulus chains where scales grow exponentially or become too low to handle.
Innovation Solution
Initializing the highest level of the modulus chain scale to a weighted geometric mean of prime numbers, with weights based on the location of each prime, ensures that subsequent scales remain within manageable ranges, preventing excessive growth or decay, and allowing for accurate rescaling across levels.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional scale initialization methods are used in deep modulus chains, then the encryption scheme can operate, but the scales grow exponentially or become too low, leading to computationally impractical magnitudes and inaccuracies
Solution Approach 1:
The patent applies preliminary action by pre-calculating and storing optimal scale values for each level of the modulus chain before execution. The scale at each level is determined in advance based on the prime factorization and modular arithmetic properties, eliminating the need for dynamic scale adjustment during computation and preventing exponential growth or decay of scales
Solution Approach 2:
The patent changes the parameter initialization approach by setting the scale at the highest level to a specific value derived from the product of primes in the modulus chain, rather than using traditional initialization methods. This parameter change ensures that subsequent scales at lower levels remain within computationally practical ranges through the relationship defined by the modulus chain structure
2Measurement precision
If scales are maintained at manageable ranges through weighted geometric mean initialization, then computation accuracy is preserved, but the initialization calculation becomes more complex
Solution Approach 1:
The complex weighted geometric mean calculation is performed in advance during system setup or key generation. The optimal scale values are pre-computed and stored in lookup tables, transforming a complex runtime calculation into a simple retrieval operation during actual homomorphic computations
Solution Approach 2:
The patent introduces an intermediary computation layer that translates the complex weighted geometric mean formula into a structured initialization procedure. The scale at each level is computed as a function of the primes and the scale at the next level, creating a systematic intermediate step that simplifies the overall initialization process
Data Source
AI summary
A computer-implemented method including, in a fully-homomorphic encryption (FHE) scheme that employs ciphertext rescaling at different levels of a modulus chain of prime numbers: initializing a scale of the highest level of the modulus chain to a value that equals a weighted geometric mean of all the prime numbers, wherein, in the weighted geometric mean, the weight for each of the prime numbers is two to the power of: a location of the respective prime number in the modulus chain, minus one.