Homomorphic Cyclic Operation on Encrypted Polynomial Data
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Solution Overview
Problem
Implementing cyclic operations in homomorphic encryption systems without decrypting periodic arrays of encrypted data is challenging due to computational costs and the need to shift data storage locations while maintaining order, which existing technologies have not effectively addressed.
Innovation Solution
A homomorphic cyclic operation system that encrypts periodic data by storing it in the coefficients of an indeterminate polynomial and shifts the data by applying the indeterminate raised to a power, allowing cyclic operations on encrypted data without decryption.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If cyclic operation is implemented in homomorphic encryption system, then data processing capability is improved, but computational cost increases
Solution Approach 1:
The patent replaces the mechanical approach of decrypting and shifting data with a mathematical substitution using polynomial multiplication. By representing data as coefficients of a polynomial and using homomorphic multiplication with x^s (where s is the shift amount), the system achieves cyclic shifting directly on encrypted data without decryption, thus reducing computational cost while maintaining cyclic operation capability.
Solution Approach 2:
The patent changes the parameter representation from direct data values to polynomial coefficients. By transforming the data into a polynomial form and using polynomial multiplication instead of direct data manipulation, the system achieves efficient cyclic operations. The shift operation is transformed into a parameter change (multiplication by x^s) that can be performed homomorphically.
2Reliability
If data storage location shifting is performed on encrypted data, then data privacy is maintained, but operation complexity increases
Solution Approach 1:
The patent makes the polynomial multiplication operation universal for both encryption and cyclic shifting. The same homomorphic multiplication mechanism that encrypts data also performs cyclic shifting when multiplied by x^s. This multi-functionality reduces operation complexity by eliminating the need for separate decryption and shifting operations.
Solution Approach 2:
The patent introduces the polynomial representation as an intermediary between the data and the shifting operation. By representing data as polynomial coefficients, the system can perform shifting through polynomial multiplication rather than direct data manipulation. This intermediary representation simplifies the operation by allowing homomorphic multiplication to serve dual purposes.
Data Source
AI summary
A homomorphic cyclic operation system performs a homomorphic cyclic operation on a periodic array of data using homomorphic encryption having a homomorphic operation defined with respect to at least one multiplication and comprises: an encryption apparatus that encrypts the periodic array of data by storing it in the coefficients of an indeterminate polynomial to generate a ciphertext of periodic data; and a homomorphic cyclic operation apparatus that shifts the periodic array of data in the ciphertext of the periodic data by applying the indeterminate raised to the power of a shift amount to the ciphertext of the periodic data.