Homomorphic Ciphertext Operations With Rational Rescaling and Sprout Moduli
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Solution Overview
Problem
Existing implementations of the Cheon-Kim-Kim-Song (CKKS) scheme in homomorphic encryption face inefficiencies due to the conflicting requirements of minimizing the number of RNS moduli and maximizing multiplication depth, leading to computational inefficiencies and resource waste in modulus management.
Innovation Solution
An electronic apparatus and method that uses a Residue Number System (RNS) modulus with moduli corresponding to machine word size, employing rational rescaling and sprout moduli to perform operations on homomorphic ciphertexts, allowing for efficient key switching and rescaling to optimize computational speed.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If the number of RNS moduli is minimized by filling modulus budget with word-sized NTT primes, then device complexity is reduced, but computational efficiency deteriorates due to inability to optimize scaling factor
Solution Approach 1:
The patent segments the modulus budget into two independent parts: word-sized NTT primes for computational efficiency and sprout moduli for flexible scaling factor support. This segmentation allows each component to serve its specific purpose without compromising the other, resolving the contradiction between minimizing modulus count and maintaining computational efficiency.
Solution Approach 2:
The patent introduces sprout moduli as a new parameter type that can be dynamically adjusted based on the scaling factor requirements. By changing the modulus composition from fixed word-sized primes to a hybrid system with adjustable sprout moduli, the system achieves both low complexity and high computational efficiency.
2Loss of substance
If the scaling factor is minimized to reduce modulus waste, then loss of substance is reduced, but computational efficiency deteriorates because RNS modulus must match scaling factor size
Solution Approach 1:
The patent separates the scaling factor function from the RNS modulus structure by introducing sprout moduli. The word-sized NTT primes handle the computational efficiency requirements while sprout moduli manage the scaling factor, allowing independent optimization of both modulus waste reduction and computational efficiency.
Solution Approach 2:
Sprout moduli act as an intermediary between the scaling factor and the RNS modulus structure. They enable the scaling factor to be independently optimized without forcing the RNS moduli to match its size, thus reducing modulus waste while maintaining computational efficiency.
3Productivity
If RNS modulus is selected close to machine word size to maximize efficiency, then productivity is improved, but adaptability deteriorates due to conflict with scaling factor minimization strategy
Solution Approach 1:
The patent segments the modulus system into word-sized NTT primes for fixed computational efficiency and sprout moduli for adaptive scaling factor support. This segmentation provides both high productivity through word-sized operations and adaptability through flexible sprout modulus configuration.
Solution Approach 2:
The hybrid modulus system achieves universality by combining two types of moduli that serve different functions: word-sized NTT primes for efficient computation and sprout moduli for flexible scaling. This multi-functional approach allows the system to adapt to various computational requirements while maintaining high efficiency.
Data Source
AI summary
Provided are an electronic apparatus and a control method thereof. The apparatus includes: a memory for storing at least one instruction; and a processor, wherein the processor may be configured to acquire the homomorphic ciphertext by using a Residue Number System (RNS) modulus including a plurality of moduli each having a size corresponding to a machine word size, and perform an operation on the homomorphic ciphertext by using rational rescaling.