Recursive Multiplier Circuitry for Homomorphic Encryption
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Solution Overview
Problem
Current homomorphic encryption implementations are resource-intensive due to the complexity of large polynomial multiplications, particularly in performing computations on encrypted data without decrypting it, which leads to increased noise levels and computational overhead.
Innovation Solution
The implementation of a multiplier circuitry that uses a recursive multiplication process with configurable multipliers to perform polynomial multiplications efficiently, reducing the number of computations and resources required by employing techniques like the Karatsuba-Ofman algorithm and modular arithmetic.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If homomorphic encryption is used to perform computations on encrypted data without decryption, then data security is improved, but computational resource consumption increases
Solution Approach 1:
The patent segments large polynomial multiplications into smaller sub-problems that can be solved using iterative multiplication algorithms. By breaking down the computation into manageable chunks and reusing intermediate results, the system reduces overall computational resource consumption while maintaining data security through homomorphic encryption.
2Productivity
If large polynomial multiplications are performed using current implementations, then homomorphic encryption operations can be executed, but device complexity increases
Solution Approach 1:
The patent employs nested iterative multiplication processes where outer iterations handle higher-degree polynomial terms while inner iterations compute lower-degree products. This nested structure allows the system to build complex polynomial multiplications from simpler repeated operations, reducing implementation complexity while enabling homomorphic encryption operations.
Solution Approach 2:
The patent performs preliminary computations of intermediate polynomial products and stores them for reuse in subsequent multiplication steps. By pre-computing and caching these intermediate results, the system avoids redundant calculations, simplifying the overall implementation while maintaining full homomorphic encryption functionality.
3Reliability
If iterative multiplication processes are used to reduce computational overhead, then noise level increase is controlled, but computation time increases
Solution Approach 1:
The patent maintains continuous useful action by iteratively building polynomial products step-by-step, where each iteration produces intermediate results that are immediately reused in subsequent iterations. This continuous process controls noise level accumulation by avoiding large single-step multiplications, while the systematic reuse of intermediate results minimizes redundant computations and offsets the increased computation time.
Solution Approach 2:
The iterative multiplication process incorporates feedback mechanisms where intermediate results from previous iterations are fed back into subsequent computation steps. This feedback loop allows the system to control noise accumulation by adjusting computation strategies based on intermediate noise levels, while the structured feedback process ensures that computation time is optimized through intelligent reuse of intermediate results.
Data Source
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AI summary
This disclosure is directed to multiplier circuitry that includes a multiplier that is configurable to generate a plurality of subproducts by performing a plurality of multiplication operations involving values having a first precision using a recursive multiplication process in which a second multiplier of the multiplier performs a second plurality of multiplication operations involving values having a second precision that are derived from the values having the first precision.