Homomorphic Ciphertext Remainder Processing for Big Integer Security
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Solution Overview
Problem
Conventional Integer-wise TFHE requires increasing the division number of a circle group to handle big numbers, which compromises ciphertext security.
Innovation Solution
An encryption processing apparatus performs scalar remainder operations on ciphertexts to enable operations on multiple-precision integers without deteriorating ciphertext security, utilizing a processor to handle fully homomorphic ciphertexts with added errors and perform operations without decryption.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If the division number of a circle group is increased to handle big numbers in Integer-wise TFHE, then the capability to represent larger integers is improved, but the ciphertext security is deteriorated due to smaller allowable errors
Solution Approach 1:
The patent segments the representation of big integers by using multiple ciphertexts, each representing a part of the integer. Instead of increasing the division number of a single circle group to handle larger numbers, the system divides the integer into multiple parts and uses multiple ciphertexts to represent these parts, thereby maintaining security while enabling big number operations.
Solution Approach 2:
The patent transitions from a single-dimensional approach (increasing the division number of one circle group) to a multi-dimensional approach by using multiple ciphertexts in parallel. This allows the system to represent big numbers through the combination of multiple encrypted parts rather than expanding a single encryption dimension, thus preserving security parameters.
2Measurement precision
If bootstrapping is performed to reduce error components in fully homomorphic encryption, then the decryption accuracy is improved, but the computation time and complexity increase significantly
Solution Approach 1:
The patent applies partial bootstrapping by performing bootstrapping operations only when necessary and only for the extent needed to manage error growth. Instead of continuously performing full bootstrapping, the system uses error suppression techniques that provide sufficient accuracy without the full computational overhead of complete bootstrapping cycles.
Solution Approach 2:
The patent introduces error suppression as an intermediary technique between encryption and decryption. This intermediary process manages and reduces error accumulation without requiring full bootstrapping, thereby maintaining decryption accuracy while reducing the computational time and complexity associated with complete bootstrapping operations.
Data Source
AI summary
An encryption processing apparatus processes a ciphertext. The ciphertext is a fully homomorphic ciphertext that has, as a plaintext associated with an integer, a value obtained by adding an error with a predetermined variance to a predetermined value and that is able to be subjected to a predetermined operation between integers without being decrypted. The apparatus includes a processor that performs a process including a calculation process of performing a scalar remainder operation on a ciphertext of a dividend based on a first polynomial obtained from a plaintext of a divisor to obtain a new ciphertext corresponding to a remainder.