Integer-Wise Homomorphic Encryption Multiplication with Error Control
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Solution Overview
Problem
Existing fully homomorphic encryption techniques, such as those based on the LWE problem, face significant computational challenges due to the accumulation of errors during operations, leading to impractically long computation times and large data handling requirements, especially in bootstrapping processes.
Innovation Solution
The encryption processing device employs a processor to generate and manipulate fully homomorphic ciphertexts with added errors of predetermined variance, enabling integer-wise multiplication operations without decryption by using a combination of TLWE and TRLWE encryption techniques, including Gate Bootstrapping and Private Key Switching, to manage and reduce errors effectively.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If fully homomorphic encryption based on LWE problem is used, then all arithmetic operations can be performed on encrypted data, but computation time becomes impractically long due to error accumulation and bootstrapping requirements
Solution Approach 1:
The patent applies preliminary action by performing Gate Bootstrapping in advance to convert ciphertexts into a form suitable for efficient multiplication operations. The bootstrapping process is executed before the main computation to prepare the ciphertexts, reducing the need for repeated bootstrapping during operations and thereby decreasing overall computation time.
Solution Approach 2:
The patent changes parameters by using Integer-wise type homomorphic encryption with specific parameter settings (n, k, q, plaintext modulus) that optimize the balance between security and computational efficiency. The error variance and polynomial degree are carefully selected to minimize error accumulation while maintaining security, reducing the frequency and cost of bootstrapping operations.
2Reliability
If bootstrapping is performed to reduce error components, then decryption remains feasible, but the amount of computation and data handling becomes large
Solution Approach 1:
The patent extracts and manages error components separately through the use of specific encryption schemes that isolate error terms. By using TRLWE encryption with structured error terms and performing operations in a way that separates signal from noise, the system reduces the complexity of error management and bootstrapping operations.
Solution Approach 2:
The patent introduces intermediary structures such as key switching keys and intermediate ciphertexts that facilitate error management without requiring full bootstrapping operations. These intermediaries allow for controlled error propagation and reduction, simplifying the overall computation while maintaining decryption feasibility.
3Adaptability or versatility
If bit-by-bit computation is used in TFHE, then homomorphic operations can be performed, but processing efficiency is reduced compared to integer-wise operations
Solution Approach 1:
The patent transitions from bit-wise operations to integer-wise operations by changing the dimension of computation. Instead of processing individual bits, the system operates on entire integers as single units using Integer-wise type TLWE encryption, which processes multiple bits simultaneously and achieves significant speedup while maintaining homomorphic properties.
Solution Approach 2:
The patent creates a universal encryption framework that can perform addition, subtraction, multiplication, and division operations on integers directly without conversion to bit-wise representations. This multi-functional capability allows a single encryption scheme to handle all arithmetic operations efficiently, eliminating the need for separate bit-wise processing circuits.
Data Source
AI summary
An encryption processing device that processes a ciphertext, the ciphertext being a fully homomorphic ciphertext that has a value obtained by adding an error with a predetermined variance to a predetermined value, as a plaintext associated with an integer and that enables a predetermined operation between integers to be performed without decryption, the device including a processor which executes a process including generating, based on a first ciphertext as a multiplier, a third ciphertext having a first stepped polynomial as a plaintext and performing an operation based on the third ciphertext and a second ciphertext as a multiplicand to calculate a ciphertext corresponding to a result of multiplication between plaintexts of the first ciphertext and the second ciphertext as a fourth ciphertext of an operation result.