Homomorphic Ciphertext Remainder Processing for Complete Integer Arithmetic
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Solution Overview
Problem
Existing fully homomorphic encryption techniques, such as TFHE, are inefficient in performing multiplicative operations due to undefined multiplicative operations on the circle group, limiting their ability to perform four arithmetic operations completely in Integer-wise type homomorphic encryption.
Innovation Solution
An encryption processing apparatus that processes fully homomorphic ciphertexts by performing subtraction and multiplication operations in a homomorphic manner to achieve complete four arithmetic operations, including division and remainder operations, by utilizing Gate Bootstrapping and TRLWE encryption to manage errors effectively.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If fully homomorphic encryption based on LWE problem is used, then both additive and multiplicative operations can be performed on encrypted data, but computation time becomes excessively long due to error accumulation requiring frequent bootstrapping
Solution Approach 1:
The patent changes the mathematical foundation from LWE problem to Ring-LWE problem, transforming the encryption scheme to operate in polynomial rings instead of vector spaces. This parameter change enables more efficient multiplication operations through polynomial multiplication while maintaining security, and allows bootstrapping to be performed more frequently without excessive computational overhead, thus resolving the time consumption issue
2Productivity
If TFHE is used for Integer-wise type homomorphic encryption, then bit-wise operations can be performed efficiently, but multiplication operations are undefined on the circle group limiting arithmetic completeness
Solution Approach 1:
The patent makes the encryption scheme universal by enabling all four arithmetic operations (addition, subtraction, multiplication, division) to be performed on Integer-wise type ciphertexts. Through the Ring-LWE framework and appropriate parameter selection, the system achieves multi-functionality where a single encryption scheme can handle complete arithmetic operations, resolving the limitation of TFHE's undefined multiplication on circle groups
3Reliability
If bootstrapping is performed frequently to reduce error components, then decryption accuracy is maintained, but the large amount of data handling in bootstrapping increases computation complexity
Solution Approach 1:
The patent substitutes the traditional bootstrapping mechanism with a more efficient error management approach based on Ring-LWE properties. By leveraging the algebraic structure of polynomial rings and carefully chosen parameters, the system maintains decryption accuracy through less computationally intensive error correction mechanisms, replacing the complex mechanical bootstrapping process with a more elegant algebraic solution
Data Source
AI summary
An encryption processing apparatus processing a hully homomorphic ciphertext includes a processor. The processor obtains, based on a subtraction result of homomorphic subtraction of a second ciphertext from a first ciphertext, a binary third ciphertext determining whether the subtraction result is positive or negative. The processor then performs a process that subtracts a result of homomorphic multiplication between the third ciphertext and the second ciphertext from the first ciphertext in a homomorphic manner to obtain a new ciphertext. The processor obtains a new third ciphertext by using a process result of the process as a new first ciphertext, and repeats the process using the new first ciphertext, the second ciphertext, and the new third ciphertext. The processor outputs the new ciphertext obtained after a predetermined number of repetitions of the process in total, as a result of a remainder operation of the first ciphertext by the second ciphertext.