RNS-Based CKKS Scaling Alignment for Lower Decryption Noise
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Solution Overview
Problem
Homomorphic encryption schemes like CKKS suffer from significant noise growth during operations, leading to inaccurate decryption results due to exponential error accumulation, especially when using residue number systems (RNS) for efficient computations.
Innovation Solution
The method adjusts scaling factors of ciphertexts to match before operations and applies modified rescaling techniques to minimize error, using prime moduli in the RNS system to maintain accurate decryption by controlling noise growth linearly.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional CKKS homomorphic encryption is used with residue number systems for efficient computations, then computational efficiency is improved, but noise growth becomes exponential leading to inaccurate decryption results
Solution Approach 1:
The patent applies preliminary action by adjusting the scaling factor of ciphertexts before performing homomorphic multiplication operations. When ciphertexts have different scaling factors, the method pre-adjusts them to have matching scaling factors before the operation, preventing noise growth issues during computation and maintaining decryption accuracy while preserving computational efficiency
2Adaptability or versatility
If homomorphic multiplication operations are performed on ciphertexts with different scaling factors, then operational flexibility is improved, but noise accumulation increases exponentially
Solution Approach 1:
The method performs preliminary scaling factor adjustment before homomorphic multiplication. By ensuring both ciphertexts have the same scaling factor prior to operation, the system maintains operational flexibility while preventing exponential noise accumulation that would occur if operations were performed on mismatched scaling factors
3Measurement precision
If rescaling operations are applied to reduce noise, then decryption precision is improved, but computational complexity increases
Solution Approach 1:
The patent applies rescaling operations as a preliminary step before homomorphic multiplication when ciphertexts have different scaling factors. By normalizing scaling factors in advance, the method reduces noise and improves decryption precision while avoiding the need for complex rescaling operations during the main computation
Data Source
AI summary
Methods and systems for reducing noise in homomorphic multiplication include: receiving a plurality of ciphertexts, each having a corresponding level; receiving data specifying a homomorphic multiplication on two ciphertexts; for two ciphertexts having different levels: adjusting a scaling factor of a first ciphertext so that the respective scaling factors of the two ciphertexts are the same; performing the homomorphic multiplication; and rescaling a result of the homomorphic multiplication; for two ciphertexts having the same level: performing the homomorphic multiplication; rescaling a result of the homomorphic multiplication; and using the scaling factors of the two ciphertexts during a decryption process.