Encrypted Similarity Calculation With Nonlinear Weighted Distance Tables
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Solution Overview
Problem
Existing similarity calculation systems using additive homomorphic encryption struggle to perform nonlinearly weighted similarity calculations without decrypting ciphertexts, as they cannot handle nonlinear weights defined by varying weight values based on the values of elements.
Innovation Solution
A similarity calculation system that calculates nonlinearly weighted similarity by transmitting ciphertexts of vector elements and a weighted distance table, allowing the input terminal to perform element distance calculations using additive homomorphic encryption, and the similarity calculation apparatus to extract the final distance from the summed ciphertexts without decrypting the original data.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of information
If additive homomorphic encryption is used to calculate similarity while keeping rating values confidential, then data confidentiality is improved, but the ability to perform nonlinearly weighted similarity calculations is lost
Solution Approach 1:
The patent segments the similarity calculation process into multiple stages: (1) pre-calculating and storing weighted distance tables for all possible rating value combinations, (2) using homomorphic encryption to calculate only the final similarity distance without decrypting intermediate weighted differences. This segmentation allows nonlinear weighting to be pre-computed while maintaining encryption during the critical similarity calculation phase.
Solution Approach 2:
The patent performs preliminary action by pre-calculating weighted distance tables for all possible combinations of rating values before the actual similarity calculation. These pre-computed tables store the weighted distances for every possible pair of rating values, allowing the system to quickly lookup and combine results during encrypted similarity calculation without needing to perform complex nonlinear weight calculations in real-time.
2Measurement precision
If nonlinear weighting is applied to reflect stronger differences in favorable ratings, then measurement precision is improved, but computational complexity increases beyond additive homomorphic encryption capabilities
Solution Approach 1:
The patent pre-computes weighted distance tables that encode nonlinear weighting logic before the actual similarity calculation. These tables store pre-calculated weighted distances for all possible rating value pairs, allowing the system to achieve precise nonlinear weighting by simple table lookup and addition during encrypted computation, avoiding complex real-time calculations.
Solution Approach 2:
The patent introduces weighted distance tables as an intermediary structure between the raw rating values and the final similarity calculation. These tables act as a mediator that translates nonlinear weighting requirements into pre-computed lookup values, enabling precise measurement while keeping the actual computation simple and compatible with additive homomorphic encryption.
Data Source
AI summary
A similarity calculation system calculating a distance between a first vector stored in a similarity calculation apparatus and a second vector entered from an input terminal wherein the similarity calculation apparatus transmits to the input terminal a ciphertext of each element of the first vector and a weighted distance table with respect to combinations of possible values of the elements of the first vector and the second vector, and the input terminal refers to the weighted distance table to calculate a ciphertext of element distances for all combinations of the value of a single element of the second vector and possible values of elements of the first vector, calculates the ciphertexts of the sum of the element distances for each element of the second vector using additive homomorphic encryption, and transmits the ciphertext of the sum to the similarity calculation apparatus.