Multi-Key FHE Re-Linearization for Scalable Encrypted Sharing
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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 exponential growth in computational costs with the number of users, making them unsuitable for large-scale collaborative data analysis and computation.
Innovation Solution
A method is introduced to generate a public key for each user based on a set of predetermined random numbers and polynomial interpolation, allowing for the calculation of a re-linearization key using auxiliary keys, which reduces the secret key combination to a single value, maintaining computational efficiency equivalent to single-key FHE systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If multi-key FHE is used to enable secure collaboration among multiple users, then data privacy and collaborative capability are improved, but computational overhead increases exponentially with the number of users
Solution Approach 1:
The patent segments the secret key into multiple shares distributed among users, and segments the decryption process into multiple partial decryption operations. Each user holds a share of the secret key and performs partial decryption, with results combined to obtain the final plaintext. This segmentation allows multi-user collaboration while maintaining computational efficiency comparable to single-key FHE.
Solution Approach 2:
The patent implements a nested structure where secret key shares are nested within a hierarchical key management framework. The common public key is derived from all user public keys, and each user's private key share is nested within this structure, enabling secure collaborative decryption without requiring exponential computational resources.
2Adaptability or versatility
If the number of users in multi-key FHE system increases to enable broader data sharing, then privacy preservation and collaboration scope are improved, but key management complexity increases
Solution Approach 1:
The patent creates a universal common public key that can be used by all users in the system for encryption, regardless of the number of participants. This single common public key serves multiple users simultaneously, eliminating the need for users to manage multiple public keys or understand complex key distribution protocols, thereby simplifying key management while enabling scalable data sharing.
Solution Approach 2:
The patent introduces a common public key as an intermediary that mediates between multiple users' private key shares. This intermediary key allows any user to encrypt data that can subsequently be decrypted by any combination of users holding the appropriate secret key shares, simplifying the key management structure and enabling flexible collaborative access.
3Reliability
If traditional multi-key FHE is used to perform encrypted computations, then security and confidentiality are maintained, but scalability is limited due to exponential computational growth
Solution Approach 1:
The patent performs preliminary actions by pre-distributing secret key shares to users and pre-establishing the common public key before any encrypted computations occur. This preliminary key setup enables subsequent encrypted operations to proceed with computational complexity similar to single-key FHE, allowing the system to scale to many users without exponential performance degradation while maintaining strong confidentiality guarantees.
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 kj, 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.