Encrypted Computation via Radix Decomposition and Selective Carry Reduction
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Solution Overview
Problem
Existing cryptographic methods for performing encrypted computations, such as those using homomorphic encryption, face challenges including limited precision for integer plaintexts, inefficiency, lack of parallelizability, and inflexibility, particularly when dealing with large values or values defined modulo large moduli.
Innovation Solution
The proposed solution involves encoding and encrypting values as multiple subvalues that can hold carry, allowing for efficient performance of arithmetic operations and function applications without the need for frequent carry reductions. This approach optimizes computation by selectively performing encrypted carry-reductions and enables parallelization of operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If homomorphic encryption is used to perform encrypted computations, then data privacy is preserved, but computation efficiency deteriorates and precision is limited
Solution Approach 1:
The patent divides a large encrypted value into multiple smaller subvalues (e.g., digits in a radix decomposition). Each subvalue is processed independently through encrypted operations, avoiding the need to handle large values directly. This segmentation enables more efficient computation while maintaining the encrypted state, resolving the contradiction between privacy preservation and computation efficiency.
Solution Approach 2:
The patent changes the parameter representation by using radix decomposition to express large values as combinations of smaller subvalues. This parameter transformation allows encrypted arithmetic operations to be performed on smaller components, improving computational efficiency and precision without compromising data privacy.
2Measurement precision
If carry reductions are performed frequently to maintain precision, then measurement precision is improved, but computation time increases
Solution Approach 1:
Instead of performing carry reductions after every encrypted operation, the patent applies them selectively only when necessary to maintain precision. This partial action approach reduces the overall computation time while still ensuring that precision requirements are met at critical points in the computation process.
Solution Approach 2:
The patent performs preliminary radix decomposition of large values into subvalues before encrypted operations begin. This preliminary action organizes the data structure to facilitate more efficient processing and reduces the frequency of subsequent carry reductions needed during computation.
3Adaptability or versatility
If encrypted operations are performed on large values, then computational capability is improved, but precision is lost due to noise accumulation
Solution Approach 1:
By segmenting large encrypted values into smaller subvalues through radix decomposition, the patent enables encrypted operations on manageable components. This segmentation prevents noise accumulation that would occur with large values, maintaining decryption precision while preserving computational capability on encrypted data.
Solution Approach 2:
The patent replaces direct encrypted arithmetic on large values with a systematic approach using radix decomposition and subvalue processing. This substitution of the computational mechanism allows operations to be performed on smaller units with controlled noise, then recombined to produce the final result with maintained precision.
4Reliability
If traditional encrypted computation methods are used, then security is maintained, but parallelizability is limited
Solution Approach 1:
The patent segments encrypted values into independent subvalues that can be processed in parallel. Since each subvalue in the radix decomposition can be operated on independently through encrypted operations, multiple processing units can work simultaneously on different subvalues, enabling parallelization while maintaining security through homomorphic encryption.
Solution Approach 2:
The patent creates a universal encrypted computation framework based on radix decomposition that can handle various arithmetic operations (addition, multiplication, etc.) on encrypted subvalues. This multi-functional approach allows the same encrypted processing mechanism to be applied across different operations and can be executed in parallel, enhancing both versatility and parallelizability.
Data Source
Figure 1A~2A
Figure 2B~3B
Figure 3C~3D
AI summary
Some embodiments are directed to a cryptographic method of performing an encrypted computation on a set of one or more encoded-and-encrypted values. A value is encoded- and-encrypted as encryptions of multiple respective subvalues. A subvalue has a corresponding message modulus and carry-message modulus larger than the message modulus. A value is encoded-and-encrypted without carry by non-carry subvalues smaller than the corresponding message moduli. A value is encoded-and-encrypted with carry by at least one with-carry subvalue larger than or equal to the corresponding message modulus. An encrypted operation is applied to at least an input value encoded- and-encrypted with carry to obtain an output value encoded-and-encrypted with carry. An encrypted carry-reduction is applied to the output value encoded-and-encrypted with carry to obtain a further encoding-and-encryption of the output value in which at least one with-carry subvalue is reduced to a non-carry subvalue.