Homomorphic Encrypted Text Multiplication via Quotient–Remainder Decomposition
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Solution Overview
Problem
Homomorphic multiplication operations in existing encryption methods consume excessive modulus resources, leading to reduced plain text space and inefficiencies, which can result in the need for frequent bootstrapping operations that are time-consuming.
Innovation Solution
The method involves decomposing homomorphic ciphertexts into quotient and remainder data, performing operations on these components to generate a homomorphic multiplication result, and then reassembling the result while minimizing modulus consumption.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If homomorphic multiplication operation is performed using existing encryption methods, then the operation can be executed on encrypted data, but the modulus consumption is excessive leading to reduced plain text space
Solution Approach 1:
The patent divides the homomorphic multiplication operation into two independent parts: a first homomorphic multiplication operation and a second homomorphic multiplication operation. Each operation uses a portion of the modulus, thereby reducing the total modulus consumption while maintaining the ability to perform homomorphic multiplication on encrypted data.
2Quantity of substance
If modulus consumption is reduced through operation decomposition, then plain text space is extended, but the operation complexity increases
Solution Approach 1:
The homomorphic multiplication is segmented into two operations that can be executed in parallel or sequentially. This segmentation reduces modulus consumption and extends plain text space, while the overall process remains manageable through structured decomposition into defined operational steps.
3Reliability
If bootstrapping operations are performed frequently to extend plain text space, then the encryption can maintain security, but the processing time increases significantly
Solution Approach 1:
The patent performs preliminary decomposition of the homomorphic multiplication operation into two separate operations before execution. This preliminary structuring allows the system to achieve secure encryption with extended plain text space without requiring frequent bootstrapping operations, thereby reducing processing time while maintaining security.
Data Source
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AI summary
An electronic apparatus of the present disclosure comprises: a memory for storing a plurality of homomorphic ciphertexts; and a processor for performing homomorphic multiplication operations on the plurality of homomorphic ciphertexts, wherein the processor uses the plurality of homomorphic ciphertexts decomposed into quotient data divided by a preset modulus and remainder data, so as to generate a plurality of intermediate operation results using quotient operation data using quotient data of each of the plurality of homomorphic ciphertexts, quotient data of one text among the plurality of homomorphic ciphertexts, and the remainder data of the remaining homomorphic ciphertexts, and uses the quotient operation data and the plurality of intermediate operation results so as to generate a homomorphic ciphertext according to the result of the homomorphic multiplication operations.