Homomorphic Ciphertext Coordinate Transform for Large Integer Security
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Solution Overview
Problem
Existing fully homomorphic encryption techniques, such as TFHE, face challenges in maintaining security while allowing large integer values as plaintexts, leading to decreased security strength as the value of the plaintext increases, necessitating finer division of the range and smaller errors, which complicates decryption and computation.
Innovation Solution
An encryption processing apparatus transforms ciphertexts using polar coordinates through homomorphic operations and Gate Bootstrapping to ensure security and efficiency in handling large integer values without decryption, employing a processor that applies polynomials to ciphertexts to calculate distances and angles, utilizing TLWE encryption and TRLWE encryption for enhanced security and practical computation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If the range from 0 to 1 of the circle group is divided more finely to represent larger integer values, then the plaintext value range is improved, but the security strength decreases
Solution Approach 1:
The patent applies segmentation by dividing the circle group range into finer sections to represent larger integer values. This is achieved through the Gate Bootstrapping process which segments the plaintext space and uses a test vector polynomial to map finer range divisions to ciphertext representations, enabling larger integer values while maintaining security through the structured segmentation approach
Solution Approach 2:
The patent changes parameters by introducing a test vector polynomial with specific coefficients that modify the encryption behavior. The polynomial coefficients are designed to transform the fine range divisions into ciphertexts that maintain security properties. This parameter change allows the system to represent larger integers without directly compromising security, as the polynomial transformation preserves the hardness of the LWE problem
2Reliability
If the error component is reduced to maintain security, then the security strength is improved, but the computational complexity increases
Solution Approach 1:
The patent applies preliminary action by performing Gate Bootstrapping before the error component becomes too large to be decrypted. The test vector polynomial is applied in advance to prepare ciphertexts that can handle larger integer values. This preliminary processing reduces the error accumulation that would otherwise occur during subsequent homomorphic operations, maintaining security without requiring excessive computational complexity during the main computation
3Reliability
If bootstrapping is performed to reduce error component, then the decryption reliability is improved, but the computation time increases
Solution Approach 1:
The patent changes parameters by using a specific test vector polynomial with optimized coefficients that reduce the computational overhead of bootstrapping. The polynomial coefficients are designed to minimize the number of operations required during Gate Bootstrapping while still achieving sufficient error reduction. This parameter optimization allows decryption reliability to be improved without proportionally increasing computation time
Data Source
AI summary
An encryption processing apparatus processes a fully homomorphic ciphertext and includes a processor performing the following processes. The processor performs a homomorphic operation involved in an operation for transforming coordinates of a point on a plane from orthogonal coordinates to polar coordinates with respect to a ciphertext and applies a predetermined polynomial to obtain a new ciphertext. The processor obtains a new ciphertext corresponding to a square of an x-coordinate value of the point by using a first polynomial, obtains a new ciphertext corresponding to a square of a y-coordinate value of the point by using a second polynomial, and applies a predetermined polynomial to a ciphertext obtained by a homomorphic operation between the new ciphertext corresponding to the square of the x-coordinate value and the new ciphertext corresponding to the square of the y-coordinate value, to obtain a ciphertext corresponding to a distance of the point from the origin.