Homomorphic Ciphertext Comparison Using Composite Functions
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Solution Overview
Problem
Existing homomorphic encryption methods support only basic computations like addition and multiplication, lacking the ability to perform non-polynomial computations such as comparison operations efficiently.
Innovation Solution
A method and apparatus that utilize composite functions with complexity θ(α) or θ(αlogα) to perform comparison computations on homomorphic ciphertexts, enabling operations like maximum value calculation, minimum value calculation, and size comparison with increased accuracy and reduced computational complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If homomorphic encryption is used to perform computation on encrypted messages, then communication security is improved, but computational capability is limited to basic operations only
Solution Approach 1:
The patent transforms the computational approach by changing the mathematical parameters and representation of comparison operations. It converts non-polynomial comparison operations into polynomial operations by using specific parameter transformations and modular arithmetic, enabling comparison computations within the constraints of homomorphic encryption while maintaining security.
Solution Approach 2:
The patent introduces intermediary computational steps and auxiliary variables to bridge the gap between encrypted data and comparison operations. By using intermediate polynomial representations and auxiliary computations, the system enables comparison functionality without directly decrypting the data, thus maintaining security while expanding computational capability.
2Adaptability or versatility
If decryption is performed to enable comparison computation on messages, then computational versatility is improved, but security is compromised and resources are wasted
Solution Approach 1:
The patent extracts the essential comparison functionality from the decryption process. Instead of decrypting messages to perform comparisons, it extracts and implements comparison logic directly in the encrypted domain using homomorphic properties, thereby eliminating the security risk and resource waste associated with decryption while maintaining computational versatility.
Solution Approach 2:
The patent inverts the traditional approach by performing comparison operations on encrypted data rather than decrypting first. This inversion allows the system to maintain security while achieving computational versatility, as comparisons are conducted in the ciphertext domain using specially designed polynomial operations.
3Measurement precision
If traditional comparison methods are used on decrypted data, then computational accuracy is improved, but security is compromised during the decryption process
Solution Approach 1:
The patent uses intermediary polynomial representations and auxiliary computational variables to maintain accuracy in the encrypted domain. These intermediaries allow precise comparison operations to be performed on ciphertexts without decryption, preserving both security and computational accuracy simultaneously.
Solution Approach 2:
The patent changes the mathematical parameters and operational framework to enable accurate comparisons in the encrypted domain. By transforming comparison operations into polynomial operations with specific parameter choices, the system achieves measurement precision equivalent to decrypted operations while maintaining security throughout the process.
Data Source
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AI summary
Disclosed is a ciphertext calculation method. The ciphertext calculation method comprises the steps of: receiving a comparative calculation command for a plurality of ciphertexts of the same type; performing a calculation by reflecting the plurality of ciphertexts of the same type on a synthesis function corresponding to the comparative calculation command; and outputting the calculated ciphertexts of the same type.