Blind Rotation in Homomorphic Encryption via Internal Products
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Solution Overview
Problem
Existing blind rotation techniques in homomorphic encryption incur significant performance overhead due to sequential updating of accumulators, limiting parallelization and efficiency in encrypted computations.
Innovation Solution
The method employs internal products instead of external products for blind rotation, allowing parallel computation of decryption ciphertexts and reducing the depth of the computation from linear to logarithmic, enabling concurrent processing on multiple cores or processors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If external products are used for blind rotation with sequential accumulator updating, then the computation can be performed correctly, but the performance overhead is significant and parallelization is limited
Solution Approach 1:
The patent divides the blind rotation computation into multiple independent decryption ciphertext computations that can be performed in parallel. Instead of sequentially updating an accumulator, the method segments the computation into parallel branches that process different components of the decryption key simultaneously, thereby reducing the overall computation depth from linear to logarithmic.
Solution Approach 2:
The patent transitions from a sequential one-dimensional computation process to a parallel multi-dimensional computation structure. By organizing the computation in terms of polynomial products and using internal products across multiple dimensions, the method enables concurrent processing on multiple cores or processors, effectively adding a parallelism dimension to the computation.
2Productivity
If sequential accumulator updating is used, then the computation structure is simple, but the performance is limited due to inability to parallelize
Solution Approach 1:
The patent performs preliminary organization of the decryption key into multiple components that can be processed in parallel. By pre-structuring the computation into independent polynomial product operations that can be executed concurrently, the method reduces the overall computation time while maintaining correctness, allowing encrypted computations to complete more efficiently.
3Productivity
If parallel processing is enabled, then the computation speed increases, but the noise growth may increase
Solution Approach 1:
The patent changes the computational parameters and structure by using internal products instead of external products, and by organizing the parallel computation around polynomial multiplications with controlled noise properties. This parameter change allows parallel processing to be performed while keeping noise growth manageable, as the internal product structure inherently controls noise accumulation compared to traditional external product approaches.
Data Source
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AI summary
Some embodiments are directed to a cryptographic method (500) of performing an encrypted computation that involves a blind rotation. Based on an encrypted input and based on the key ciphertexts of a bootstrapping key, a set of decryption ciphertexts for evaluating a decryption-under-encryption of the encrypted input is determined. An encrypted output is determined by determining an encrypted polynomial product of the decryption ciphertexts. The encrypted polynomial product is determined by computing multiple internal products. The internal products are computed at least in part in parallel.