Encrypted Edit Distance via Programmable Bootstrapping
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Solution Overview
Problem
Existing fully homomorphic encryption (FHE) schemes face challenges in computational overhead, particularly due to costly polynomial multiplication and noise accumulation, which hinder efficient string similarity calculations like edit distance, especially in data-dependent branching and large input sizes.
Innovation Solution
A method for equality checking and edit distance calculation in the encrypted domain using programmable bootstrapping operations, employing negacyclic lookup tables and differential encoding values to optimize computations, allowing for efficient handling of larger input sizes and reducing the number of bootstrapping operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional FHE schemes are used for edit distance calculation, then data confidentiality is maintained, but computational overhead becomes prohibitively high
Solution Approach 1:
The patent changes the parameter space from traditional FHE schemes to TFHE (Torus Fully Homomorphic Encryption) which operates over the torus group. This parameter change enables more efficient polynomial multiplication using Toom-Cook and Karatsuba algorithms, reducing computational overhead while maintaining confidentiality
Solution Approach 2:
The patent replaces traditional arithmetic operations with homomorphic Boolean algebra operations (NAND, XOR, XNOR logic gates) in the TFHE scheme. This substitution allows for more efficient computation and enables programmable bootstrapping that reduces the number of expensive bootstrapping operations needed
2Adaptability or versatility
If polynomial multiplication is performed in FHE schemes, then string similarity calculations can be performed on encrypted data, but computational cost increases substantially
Solution Approach 1:
The patent uses Toom-Cook multiplication and Karatsuba multiplication algorithms that create intermediate copies of the polynomial representations. These algorithms break down the multiplication into smaller sub-problems, reducing the overall computational cost while maintaining the ability to perform operations on encrypted data
Solution Approach 2:
The patent performs preliminary polynomial decomposition and preparation before the main multiplication operation. By pre-processing the polynomial representations and using efficient multiplication algorithms, the actual multiplication cost is significantly reduced
3Productivity
If multiple homomorphic operations are performed sequentially, then edit distance calculation can be completed, but noise accumulates and requires frequent bootstrapping
Solution Approach 1:
The patent designs the computation to minimize interruptions for bootstrapping by continuously performing operations that keep noise levels manageable. Through optimized operation sequencing and using TFHE's properties, the system maintains useful computation continuity rather than alternating between computation and bootstrapping
Solution Approach 2:
The patent extracts and isolates the noise accumulation problem by using TFHE's specific properties where noise behaves differently than in traditional FHE. This extraction allows for longer computation sequences before bootstrapping is required, as the noise management characteristics of TFHE enable more operations between bootstrap cycles
4Reliability
If bootstrapping operations are performed frequently to manage noise, then data security is maintained, but computational overhead increases
Solution Approach 1:
The patent changes the underlying mathematical parameters from traditional FHE to TFHE over the torus. This parameter change fundamentally alters how noise accumulates and manages, reducing the frequency of bootstrapping operations needed while maintaining security and noise level control
Solution Approach 2:
The patent introduces dynamic noise management through programmable bootstrapping where the bootstrap operation can be adapted to the specific computational needs. The system can adjust when and how bootstrapping is applied based on the actual noise levels and computation progress, rather than following a fixed frequent bootstrap schedule
Data Source
Figure 1~3
AI summary
The present invention relates to a method for performing an equality checking of a first character and a second character in a cryptographic application wherein programmable bootstrapping is used, at least one of said first and said second character being encrypted, the method comprising: o checking the equality of the first character with the second character by determining a difference between said characters, and o using the difference as input for a lookup table operation through a programmable bootstrap operation, said lookup table yielding a first predetermined value if the difference equals zero and a second predetermined value different from the first predetermined value, so obtaining an equality result for the pair of characters formed by the first and the second character.