Homomorphic Ciphertext Bootstrapping for Modulus Recovery
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Solution Overview
Problem
Existing homomorphic encryption methods face challenges in performing high-dimensional matrix multiplications efficiently, leading to resource-intensive processing and prolonged times, with the modulus used for calculations potentially decreasing, causing noise to resemble the modulus size and resulting in decryption failures or operations becoming impossible.
Innovation Solution
An electronic apparatus and method that performs bootstrapping to expand the modulus of a ciphertext using different scaling factors, employing Slots-to-Coefficients (StC) and Coefficients-to-Slots (CtS) conversions to maintain operation precision and efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If homomorphic encryption is used to perform operations on encrypted data without decryption, then communication security is improved, but processing time and resource consumption increase
Solution Approach 1:
The patent performs bootstrapping operations in advance to refresh ciphertexts before they are used in subsequent homomorphic computations. By proactively managing ciphertext validity and refreshing them before the modulus decreases too much, the system prevents decryption failures and avoids the need for re-computation, thereby reducing overall processing time while maintaining security.
Solution Approach 2:
The patent implements a feedback mechanism that continuously monitors the modulus of ciphertexts during homomorphic operations. When the modulus approaches a threshold value that would cause noise to resemble the modulus size, the system triggers a bootstrapping operation to refresh the ciphertext. This feedback control ensures optimal balance between security and processing efficiency.
2Reliability
If high-dimensional matrix multiplication is performed using ciphertext-ciphertext operations, then data privacy is maintained, but resource consumption and processing time increase significantly
Solution Approach 1:
The patent performs preliminary bootstrapping operations to ensure ciphertexts are in optimal state before initiating high-dimensional matrix multiplications. By pre-refreshing ciphertexts and ensuring their modulus is sufficiently large, the system avoids intermediate decryption failures that would waste computational resources, thereby improving overall processing efficiency while maintaining data privacy.
Solution Approach 2:
The patent dynamically adjusts operational parameters based on ciphertext modulus conditions. When monitoring indicates that the modulus is approaching critical thresholds, the system changes parameters to trigger bootstrapping operations. This adaptive parameter management optimizes the balance between maintaining data privacy through homomorphic encryption and achieving acceptable processing efficiency for high-dimensional matrix operations.
3Speed
If the modulus is kept small to reduce computational complexity, then processing speed improves, but noise becomes indistinguishable from the modulus causing decryption failures
Solution Approach 1:
The patent performs bootstrapping operations in advance to refresh ciphertexts before they are consumed in computations. By proactively increasing the modulus and reducing noise levels before operations begin, the system ensures that even if the modulus decreases during processing, it remains sufficiently large to distinguish noise from the actual message, thereby maintaining decryption reliability while allowing for efficient processing.
Solution Approach 2:
The patent creates a buffer or cushion by performing bootstrapping operations that increase the modulus well before it would naturally decrease to critical levels. This beforehand cushioning ensures that there is sufficient margin between the noise level and the modulus size throughout the computation process, preventing decryption failures while allowing the system to operate at higher speeds with smaller effective moduli during actual computations.
Data Source
AI summary
An electronic apparatus includes at least one processor including processing circuitry, and memory, wherein the at least one processor is configured to, based on an instruction for an operation for a first ciphertext, perform an operation action for the first ciphertext, obtain a second ciphertext including a noise based on the operation action, and based on identifying a predetermined event on the basis of a modulus of the second ciphertext, obtain an output ciphertext having a bigger modulus than the modulus of the second ciphertext by performing bootstrapping on the basis of a first scaling factor, a second scaling factor, and a third scaling factor different from one another, and perform an additional operation action based on the output ciphertext.