Multi-Key FHE Common Public Key for Constant-Cost Computation
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Solution Overview
Problem
Existing Multi-Key Fully Homomorphic Encryption (FHE) systems face significant challenges including high computational overhead, complex key management, and scalability issues due to the exponential increase in computational costs with the number of users, particularly in re-linearization and bootstrapping operations.
Innovation Solution
A method is introduced to generate a common public key based on local secret keys using polynomial interpolation, reducing the secret key combination to a single value, enabling efficient re-linearization and decryption processes, thereby maintaining constant computational costs regardless of the number of users.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If Multi-Key FHE is used to enable secure collaboration among multiple users, then data privacy and security are improved, but computational overhead increases exponentially with the number of users
Solution Approach 1:
The patent segments the secret key management by introducing key separation matrices that allow each user to have their own secret key while enabling collaborative computations. The public key is segmented into multiple components (first public key, second public key, third public key) that can be independently managed and combined, reducing the exponential computational overhead associated with traditional Multi-Key FHE approaches.
2Reliability
If multiple secret keys are used for encryption by different users, then data sharing security is improved, but key management complexity increases
Solution Approach 1:
The patent introduces key separation matrices as intermediary structures that mediate between multiple user secret keys and the encryption/decryption processes. These matrices serve as a systematic framework for managing multiple keys, reducing the complexity of key distribution, storage, and usage while maintaining strong security guarantees for each user's data.
3Adaptability or versatility
If traditional Multi-Key FHE re-linearization is performed with multiple users, then encrypted computations are enabled, but computational cost grows exponentially
Solution Approach 1:
The patent fundamentally changes the parameters of the re-linearization process by using a structured approach with separate public key components and key separation matrices. Instead of dealing with exponential growth in key combinations, the system uses polynomial-based constructions where the computational complexity grows polynomially with the number of users, enabling efficient re-linearization and bootstrapping operations.
Data Source
AI summary
The present application is directed towards secure data sharing and computation. In particular, the present application is directed to improvements in the use of Multi-Key Fully Homomorphic Encryption (FHE), to perform computations on encrypted data without the need for decryption, thereby providing a means for encrypted data sharing and computation. This, in turn, facilitates collaborative analysis of data while maintaining data confidentiality. This is done by generating a local secret key for the user; generating a local public key pk; based on the local secret key; sharing the local public key with the other users, receiving a local public key from each of the other users; and generating a common public key based on the N local public keys.