Homomorphic Ciphertext Sorting With a 5-Way Parallel Sorter
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Solution Overview
Problem
Existing sorting algorithms for homomorphic ciphertexts are limited to basic calculations and require numerous comparison operations, leading to inefficiencies and resource waste, especially in operations like k-means clustering and top-k data calculations.
Innovation Solution
A 5-way sorter is employed to sort five homomorphic ciphertexts in a single stage using a comparison function that calculates bigger and smaller values between input ciphertexts, with parallel processing enabled by multiple 5-way sorters and approximate sign functions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional sorting algorithms (quick sort, merge sort) are used for homomorphic ciphertexts, then sorting functionality is achieved, but the process requires numerous comparison operations leading to resource waste and time consumption
Solution Approach 1:
The patent segments the sorting process into multiple stages, with each stage performing a specific comparison and sorting function. Instead of using a single conventional sorting algorithm that requires many sequential comparisons, the patent divides the ciphertexts into groups and processes them through multiple sorting stages, where each stage handles a portion of the sorting task. This segmentation reduces the total number of comparison operations needed in the homomorphic domain.
Solution Approach 2:
The patent introduces a multi-dimensional sorting approach by creating intermediate sorted versions of ciphertexts at different stages. Rather than performing all comparisons in a single dimension (sequential comparisons), the patent creates multiple sorted dimensions through different sorting stages, allowing the final sorted result to be obtained by combining these intermediate results. This dimensional approach reduces the complexity of direct multi-way comparisons.
2Reliability
If homomorphic encryption is used to maintain security during calculations, then data protection is achieved, but sorting operations become more complex and resource-intensive
Solution Approach 1:
The patent creates multiple copies of the ciphertext data through intermediate sorted versions at different stages. Each sorting stage produces a copied and transformed version of the input ciphertexts, which are then combined to produce the final sorted result. This copying approach allows the system to work with simplified versions of the data at each stage rather than performing complex operations on the original encrypted data directly.
Solution Approach 2:
The patent uses temporary intermediate sorted ciphertexts that are discarded after each sorting stage. These intermediate results are computationally inexpensive to generate and consume, serving only as temporary helpers in the multi-stage sorting process. By using these disposable intermediate objects, the patent avoids the need for complex persistent data structures and reduces overall computational complexity.
3Manufacturing precision
If multiple comparison operations are performed to sort homomorphic ciphertexts, then accurate sorting is achieved, but resource waste increases
Solution Approach 1:
The patent performs preliminary sorting operations in earlier stages that partially organize the ciphertexts before final sorting. By pre-sorting the data into groups or ranges in initial stages, the patent reduces the search space and comparison needs for subsequent stages. This preliminary action ensures that fewer comparisons are needed in later stages to achieve the final sorted result, reducing overall computational resource waste.
Solution Approach 2:
The patent skips redundant comparison operations by using the results from previous sorting stages. Instead of performing all possible comparisons from scratch, the patent leverages the partial ordering information already established in earlier stages and skips comparisons that would yield the same result. This rushing through of unnecessary comparisons significantly reduces the total computational resources required while maintaining sorting accuracy.
Data Source
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AI summary
Disclosed is a calculation device. The present calculation device includes: a memory for storing a plurality of homomorphic ciphertexts for an approximate message including an error; and a processor for sorting the plurality of homomorphic ciphertexts by using a 5-way sorter which can sort five homomorphic ciphertexts in a single stage.