Bootstrappable Homomorphic Encryption Scheme for Arbitrary Computation
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Solution Overview
Problem
The construction of a fully homomorphic encryption scheme has been a long-standing open problem in cryptography, as existing schemes are either insecure or limited to performing only simple functions, failing to allow arbitrary computations on encrypted data without decrypting it.
Innovation Solution
A bootstrappable somewhat homomorphic encryption scheme is developed, which can evaluate its own decryption circuit, enabling the construction of a fully homomorphic encryption scheme by using a recursive self-embedding technique, leveraging ideal lattices to manage noise parameters and ensure correct decryption despite circuit depth.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If existing homomorphic encryption schemes are used, then encryption security is maintained, but the scheme is limited to performing only simple functions and cannot allow arbitrary computations on encrypted data
Solution Approach 1:
The patent segments the homomorphic encryption scheme into distinct functional components: a bootstrappable encryption layer that handles noise management and a fully homomorphic evaluation layer that performs arbitrary computations. This segmentation allows each component to be optimized independently, enabling complex computations while maintaining security.
Solution Approach 2:
The patent implements nesting by embedding the bootstrappable encryption scheme within the fully homomorphic encryption framework. The inner bootstrappable scheme provides the foundational security and noise control, while the outer FHE layer enables arbitrary computational functionality, creating a nested hierarchical structure.
2Adaptability or versatility
If noise parameters are increased to support deeper circuits, then more complex functions can be computed, but decryption correctness becomes harder to maintain
Solution Approach 1:
The patent applies preliminary action by pre-establishing noise bound parameters during key generation and ciphertext encryption. These predetermined noise bounds are carefully calibrated to ensure that even after multiple homomorphic operations, the accumulated noise remains within decryptable thresholds, guaranteeing decryption correctness for circuits of specified depth.
Solution Approach 2:
The patent implements feedback mechanisms through the bootstrappable decryption circuit that continuously monitors and manages noise accumulation during homomorphic computations. When noise approaches critical thresholds, the system triggers refresh operations that reset noise levels, creating a feedback loop that maintains decryption correctness throughout the computation process.
3Adaptability or versatility
If a fully homomorphic encryption scheme is constructed to allow arbitrary computations, then computational versatility is improved, but the complexity of the decryption process increases
Solution Approach 1:
The patent introduces an intermediary bootstrappable decryption circuit that mediates between the complex fully homomorphic computations and the final decryption process. This intermediary layer handles the noisy intermediate representations produced by FHE operations and transforms them into forms suitable for standard decryption, simplifying the overall decryption process while supporting arbitrary computational functionality.
Data Source
AI summary
Embodiments of the present invention describe a fully homomorphic encryption scheme using a “bootstrapable” homomorphic encryption scheme that evaluate a function ƒ when ƒ is the encryption schemes own decryption function. Specifically, the fully homomorphic encryption scheme uses the “bootstrapable” homomorphic encryption scheme to determine the decryption function to decrypt data encrypted under the fully homomorphic encryption scheme.