Homomorphic Ciphertext Comparison via Signum Approximation
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Solution Overview
Problem
Conventional homomorphic encryption techniques face inefficiencies when comparing the sizes of encrypted real-number data, as they require bit-by-bit comparison, which is inefficient and not applicable to various fields.
Innovation Solution
A method using homomorphic encryption that involves generating a ciphertext for size comparison by performing homomorphic evaluation of subtraction between encrypted real-number data and an approximation function approximating the signum function, allowing efficient comparison of encrypted real numbers.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional homomorphic encryption technique is used to compare ciphertexts, then comparison can be performed on encrypted data, but the comparison process is inefficient due to bit-by-bit analysis
Solution Approach 1:
The patent transforms the comparison problem from bit-by-bit analysis to a mathematical function evaluation problem. By changing the parameter representation from individual bits to a continuous approximation function (such as a polynomial or rational function that approximates the signum function), the comparison efficiency is dramatically improved while maintaining encryption security.
Solution Approach 2:
The patent replaces the mechanical bit-by-bit comparison process with a mathematical substitution approach. Instead of mechanically comparing each bit position sequentially, the system uses homomorphic evaluation of an approximation function to directly obtain the comparison result, substituting a complex mechanical process with a more efficient mathematical operation.
2Productivity
If approximation function is used to approximate signum function, then size comparison of encrypted real numbers becomes efficient, but requires homomorphic evaluation capability
Solution Approach 1:
The patent performs preliminary action by pre-defining the approximation function that will be used for comparison. The function is designed in advance to approximate the signum function behavior, and its parameters are prepared beforehand, so that during actual comparison operations, only simple homomorphic evaluation is needed rather than complex real-time computation.
Data Source
Figure 1~2
AI summary
Disclosed are a ciphertext comparison method using homomorphic encryption and an apparatus for performing the same. The ciphertext comparison method using homomorphic encryption includes acquiring a first ciphertext obtained by encrypting first real-number data using a homomorphic evaluation algorithm and a second ciphertext obtained by encrypting second real-number data using the homomorphic evaluation algorithm, and generating a ciphertext for a result for comparison in size between the first real-number data and the second real-number data using homomorphic evaluation for the first ciphertext, the second ciphertext, and an approximation function for approximating a signum function.