Homomorphic Plaintext Encoding With RMFE for Dense Ciphertext Packing
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Solution Overview
Problem
Existing homomorphic encryption schemes face challenges with high computational expense, memory requirements, and limitations in performing fast general arithmetic circuit-based computations, especially when using SIMD techniques with composite moduli, which increase noise and restrict interactions between messages encoded under different prime factors.
Innovation Solution
A method is introduced to encode plaintext data into a finite extension field, utilizing a reverse multiplication-friendly embedding (RMFE) scheme to pack more data into each plaintext slot, enabling efficient homomorphic computation with finite extension field operations and supporting high-degree extension fields, while using a composite RMFE scheme for complex recode operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If SIMD technique is used to pack multiple plaintexts in a single ciphertext, then computational efficiency is improved, but memory requirements and processing overhead increase
Solution Approach 1:
The patent changes the parameter of plaintext encoding by using finite extension fields instead of traditional integer encoding. This allows for more efficient packing of plaintext elements into ciphertext slots, improving computational efficiency while reducing memory requirements through optimized parameter selection
Solution Approach 2:
The patent employs composite encoding schemes that combine multiple encoding techniques (including RMFE and finite field arithmetic) to create a hybrid approach that leverages the advantages of each method while mitigating their individual disadvantages, achieving better memory efficiency
2Quantity of substance
If composite moduli are used to increase data packing capacity, then more data can be packed in a single ciphertext, but noise increases and interactions between messages encoded under different prime factors are restricted
Solution Approach 1:
The patent segments the encoding process into distinct stages: first encoding plaintext elements into finite extension fields, then packing these encoded elements into ciphertext slots. This segmentation allows for independent optimization of each stage, managing noise levels while maximizing data capacity
Solution Approach 2:
The patent introduces finite extension field elements as an intermediary representation between plaintext and ciphertext. This intermediary layer enables efficient packing while maintaining control over noise accumulation, as the finite field structure provides mathematical guarantees about error propagation
3Quantity of substance
If high-degree extension fields are used to exploit complete plaintext vector space, then memory usage efficiency is improved, but computational complexity increases
Solution Approach 1:
The patent carefully selects parameters for the finite extension fields, choosing degrees that balance memory efficiency with computational feasibility. By optimizing these parameters, the system achieves high memory usage efficiency while keeping computational complexity within acceptable bounds
Data Source
AI summary
In some aspects, a method for generating encoded plaintext data in a plaintext vector space includes obtaining a plurality of vectors of plaintext elements, where each plaintext element is an element of a first finite field. The method further includes encoding the plurality of vectors of plaintext elements to a vector of field elements, where each vector of plaintext elements is encoded to a respective field element of the vector of field elements, each of the field elements is an element of a second finite field, and the second finite field is a finite extension field of the first finite field. The method additionally includes encoding the vector of field elements into an element of the plaintext vector space to produce the encoded plaintext data for homomorphic encryption and computation.