Homomorphic Ciphertext Rebooting via ModRaise and Error Removal
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Solution Overview
Problem
Conventional techniques face difficulties in efficiently performing operations and reboots on homomorphic ciphertexts for binary data, particularly with reduced plaintext space, and inefficient handling of Learning with Errors (LWE) ciphertexts.
Innovation Solution
An electronic device with a processor that performs ModRaise tasks, trigonometric functions, and transformation tasks to expand the plaintext space of homomorphic ciphertexts, including slot-to-coefficient and coefficient-to-slot transformations, and ring packing to efficiently operate and reboot LWE ciphertexts.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional techniques are used to perform operations on homomorphic ciphertexts for binary data, then the operations can be performed without decrypting the data, but the operations cannot be efficiently performed due to reduced plaintext space
Solution Approach 1:
The patent applies parameter changes by performing a ModRaise task that increases the modulus of the homomorphic ciphertext from an initial modulus q0 to a larger modulus q1. This parameter change expands the plaintext space, enabling efficient subsequent operations on the ciphertext while maintaining the homomorphic encryption properties and security guarantees.
2Adaptability or versatility
If the modulus of the homomorphic ciphertext is increased through ModRaise task, then the plaintext space is expanded, but errors in the ciphertext need to be removed through trigonometric functions
Solution Approach 1:
The patent converts the harmful effect of errors in the ciphertext into a beneficial process by applying trigonometric functions (such as sine or cosine) to the ciphertext after ModRaise. These functions help remove or reduce the accumulated errors while preserving the meaningful information, thereby improving ciphertext accuracy after the modulus increase.
3Productivity
If multiple ciphertexts are operated on simultaneously, then processing capability is improved, but the complexity of matching and managing ciphertexts increases
Solution Approach 1:
The patent applies segmentation by dividing multiple LWE ciphertexts into pairs and processing them independently through matching operations. Each pair of ciphertexts is handled separately with its own ModRaise and trigonometric function application, which simplifies the management complexity compared to processing all ciphertexts as a single group, while still achieving improved overall processing capability through parallel operation on multiple pairs.
Data Source
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AI summary
An electronic device for rebooting a homomorphic ciphertext is disclosed. The present device comprises a communication unit, a memory, and a processor. When a ciphertext obtained by homomorphically encrypting binary data is received from at least one external device via the communication unit, the processor stores the ciphertext in the memory, performs a ModRaise task for increasing a modulus of the ciphertext, removes an error in the ciphertext by applying a trigonometric function to the ciphertext having the increased modulus, and expands a plaintext space in the ciphertext. Accordingly, a homomorphic ciphertext of a message including binary data can be efficiently processed.