Polynomial Approximation for FHE Branching Operations
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Solution Overview
Problem
Existing fully homomorphic encryption (FHE) systems cannot perform branching operations, such as 'if' statements, which are essential for many algorithms, leading to security risks when data is decrypted for processing.
Innovation Solution
Approximate branching operations using polynomial approximations, allowing computations to be performed directly on FHE encrypted data without decryption.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If data is decrypted for processing to enable branching operations, then computational functionality is improved, but data security deteriorates
Solution Approach 1:
The patent introduces an intermediary mechanism (homomorphic encryption system with approximation algorithms) that enables branching operations to be performed on encrypted data without decryption. The encrypted data acts as an intermediary representation that preserves security while allowing computational functionality through polynomial approximation of branch operations.
Solution Approach 2:
The patent changes the parameter state of the data from decrypted plaintext to encrypted ciphertext, allowing branching operations to be performed through polynomial approximations. By operating in the encrypted domain with modified parameters (encrypted values instead of plaintext), the system achieves both security and computational functionality.
2Reliability
If polynomial approximation is used to enable branching operations on encrypted data, then data security is improved, but computational precision deteriorates
Solution Approach 1:
The patent applies partial approximation rather than exact representation of branching operations. By using polynomial approximations that are sufficiently accurate for the intended applications but not necessarily exact, the system achieves a practical balance between security preservation and computational precision.
Solution Approach 2:
The patent accepts a change in the precision parameter as a trade-off for achieving data security. The polynomial approximation introduces controlled imprecision, but this parameter change enables the critical security improvement by allowing operations on encrypted data without decryption.
3Ease of operation
If branching operations are performed on encrypted data using polynomial approximation, then ease of operation is improved, but device complexity increases
Solution Approach 1:
The patent extracts the branching operation capability from the decryption process. By taking out the ability to perform conditional logic from the plaintext domain and implementing it in the ciphertext domain through polynomial approximation, the system simplifies the operational flow (no decryption needed) while adding complexity to the underlying computational mechanism.
Data Source
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AI summary
Systems and methods that approximate and use branching operations on data encrypted by fully homomorphic encryption (FHE). The systems and methods may use polynomial approximation to convert "if" statements into "soft if" statements that may be applied to the FHE encrypted data in a manner that preserves the security of the systems and methods.