Homomorphic Encryption Modular Multiplication Lookup Table

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Solution Overview

Problem

Homomorphic encryption computations, particularly for modular multiplication, are time-consuming due to the need for large modulus polynomial computations, which hinders efficient privacy-preserving machine learning processes.

Innovation Solution

A computation device and method utilizing a lookup table with predetermined prime number information expressed as combinations of exponentiations of 2, enabling modular multiplication through shift computations and addition/subtraction, thereby speeding up the process.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If large modulus polynomial computation is used for homomorphic encryption, then security and correctness are ensured, but computation time increases significantly

Engineering Contradiction:

ImprovesecurityVSAvoidcomputation time

Core Design Contradiction:

ReliabilityVSLoss of time

Solution Approach 1:

The patent segments the large modulus computation into multiple smaller prime modulus computations. By using the Chinese Remainder Theorem, the original large modulus problem is divided into several independent smaller problems that can be solved separately and then combined, significantly reducing computation time while maintaining security through the mathematical properties of prime factorization

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The patent pre-calculates and stores reciprocal values and prime number information in lookup tables before the actual homomorphic encryption computation. This preliminary preparation allows the main computation to proceed much faster by retrieving pre-computed values rather than calculating them in real-time, directly addressing the computation time issue

Inventive Principle:

Principle #10Preliminary action

2Productivity

If lookup table with pre-calculated values is used, then computation speed increases, but memory usage increases

Engineering Contradiction:

Improvecomputation speedVSAvoidmemory size

Core Design Contradiction:

ProductivityVSVolume of stationary object

Solution Approach 1:

The patent optimizes the lookup table by storing only the most frequently accessed reciprocal values and prime number information. Rather than storing all possible values, it selectively stores only those that provide the greatest computational benefit, creating a compact but highly effective lookup table that balances memory usage with computation speed

Inventive Principle:

Principle #3Local quality

Solution Approach 2:

The patent changes the representation parameters of the stored data by using compressed formats and selective precision for different types of values. Reciprocal values are stored with sufficient precision for their intended use while using more compact representations where full precision is not required, reducing overall memory consumption while maintaining computational accuracy

Inventive Principle:

Principle #35Parameter changes

Data Source

PatentUS11509454B2Apparatus for processing modular multiply operation and methods thereof

Publication Date: 2022.11.22 CRYPTO LAB INC

AI summary

Disclosed is a ciphertext computation method. The ciphertext computation method includes: receiving a modular computation command for a plurality of ciphertexts; performing a modular computation for the plurality of ciphertexts by using a lookup table storing a plurality of predetermined prime number information; and outputting a result of the computation.