Integer-Wise TFHE Arithmetic Using Polynomial Range Reduction
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Solution Overview
Problem
Existing fully homomorphic encryption techniques, such as TFHE, face challenges in performing multiplication operations between ciphertexts efficiently due to the accumulation of errors, leading to impractical computation times and large data handling requirements.
Innovation Solution
An encryption processing apparatus that applies a first polynomial to the operation result of homomorphic operations between ciphertexts to determine the plaintext position and reduces the range of the plaintext, enabling efficient multiplication between Integer-wise TFHE ciphertexts using Gate Bootstrapping and TRLWE encryption.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If fully homomorphic encryption based on LWE problem is used, then arithmetic operations can be performed on encrypted data, but computation time becomes impractical due to large data handling requirements in bootstrapping
Solution Approach 1:
The patent changes the parameter of plaintext representation from integer to real number in the range of 0 to 1, enabling more efficient homomorphic operations. This parameter change allows TFHE to achieve faster computation while maintaining the ability to perform arithmetic operations on encrypted data
Solution Approach 2:
The patent transitions from bit-wise type homomorphic encryption to Integer-wise type homomorphic encryption by operating on real numbers in the range of 0 to 1. This dimensional change enables four arithmetic operations to be performed more efficiently, reducing computation time while maintaining versatility
2Reliability
If bootstrapping is performed to reduce error component, then decryption becomes possible, but computation time and data handling requirements increase significantly
Solution Approach 1:
By changing the plaintext parameter to real numbers in the range of 0 to 1, the patent reduces the magnitude of error accumulation. This allows bootstrapping to be performed more efficiently with smaller data sizes, maintaining decryption capability while reducing data handling complexity
Solution Approach 2:
The patent uses the property that multiplying a ciphertext by a polynomial with all coefficients equal to 1/4 creates a new ciphertext representing the same plaintext. This copying mechanism enables error reduction through polynomial multiplication without requiring large data handling
3Adaptability or versatility
If multiplication operation is defined for circle group ciphertexts, then four arithmetic operations can be performed, but the operation becomes complex and time-consuming
Solution Approach 1:
The patent defines multiplication for circle group ciphertexts by representing plaintexts as real numbers in the range of 0 to 1. This parameter change enables four arithmetic operations to be performed efficiently through polynomial multiplication, achieving both versatility and computational efficiency
Solution Approach 2:
The patent merges the operations for four arithmetic operations into a unified approach using polynomial multiplication with specific coefficients. This combining strategy enables efficient computation while maintaining the ability to perform addition, subtraction, multiplication, and division on encrypted data
Data Source
AI summary
In order to realize four arithmetic operations in Integer-wise type TFHE, an encryption processing apparatus that processes a ciphertext is provided, the ciphertext being a fully homomorphic ciphertext that has, as a plaintext associated with an integer, a value with an error having a predetermined variance added thereto within a predetermined value range and that is able to be subjected to a predetermined operation between integers without being decrypted. The apparatus includes applying a first polynomial in which all coefficients are the same to an operation result of a homomorphic operation between a ciphertext based on a first ciphertext (ca) and a ciphertext based on a second ciphertext (cb), to obtain a third ciphertext (cd) indicating a position of a plaintext in the operation result, and applying a predetermined polynomial to a ciphertext obtained by reducing a range of plaintext to a predetermined range in the value range by homomorphic addition of the third ciphertext to the operation result, to perform an operation between the first ciphertext and the second ciphertext.