Homomorphic Permutation Using Noise-Assisted Client Re-Encryption
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Solution Overview
Problem
Homomorphic rotation operations in an encrypted state are time-consuming and memory-intensive due to the need for multiple arithmetic keys, and complex permutations require significant processing time.
Innovation Solution
Perform homomorphic permutations by generating a first ciphertext with added noise, transmitting it to a client, performing a predetermined operation on the decrypted ciphertext, and extracting the basic ciphertext by removing the noise, without requiring an arithmetic key.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If homomorphic rotation is performed in an encrypted state, then data security is maintained, but operation time significantly increases
Solution Approach 1:
The patent segments the homomorphic permutation operation into two distinct phases: (1) the server performs encryption and noise addition on ciphertext without decryption, and (2) the client performs decryption, permutation operation, and re-encryption. This segmentation allows the time-consuming decryption step to be performed only once by the client rather than repeatedly during encrypted operations, significantly reducing total operation time while maintaining security.
Solution Approach 2:
The patent introduces noise as an intermediary element that enables the server to perform operations on encrypted data without requiring arithmetic keys. The noise is added to the ciphertext by the server, allows the client to perform the permutation after decryption, and is then removed by the server from the re-encrypted ciphertext. This intermediary mechanism eliminates the need for traditional homomorphic rotation keys while maintaining security.
2Adaptability or versatility
If multiple arithmetic keys are used for different rotation steps, then permutation flexibility is improved, but memory management becomes difficult
Solution Approach 1:
The patent makes the noise element universal across all permutation operations. Instead of requiring separate arithmetic keys for each rotation step, a single noise element is added by the server and can support any permutation operation the client needs to perform. The client can decrypt, perform any desired permutation, and re-encrypt, with the server simply removing the noise from the result. This universal noise mechanism eliminates the need for multiple arithmetic keys while maintaining full permutation flexibility.
3Adaptability or versatility
If complex permutations are realized by synthesis of multiple homomorphic rotation operations, then permutation capability is achieved, but processing time significantly increases
Solution Approach 1:
The patent segments the complex permutation operation to be performed entirely within the client's decrypted data space rather than through multiple sequential homomorphic rotation operations. The server adds noise once, the client decrypts and performs the complete permutation in one operation, then re-encrypts. This segmentation reduces processing time from multiple sequential encrypted operations to a single decryption-permutation-re-encryption cycle.
Data Source
AI summary
A method of performing a homomorphic permutation by a server includes: generating, via a ciphertext generation portion, a first ciphertext by adding noise to the basic ciphertext; transmitting, via a transmission portion, the first ciphertext to a client; performing, via an operation portion, a predetermined operation on the noise; receiving, via a reception portion, a second ciphertext from the client; and extracting, via an extraction portion, the basic ciphertext on which the predetermined operation is performed, by removing, from the second ciphertext, the noise on which the predetermined operation is performed, wherein the second ciphertext is a ciphertext that is re-encrypted by the client after decrypting the first ciphertext and performing the predetermined operation on the decrypted first ciphertext.