Secret Sorting via Parallel Random ID Generation
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Solution Overview
Problem
The existing secret sorting technique requires a large number of communication stages due to repeated production of random ID columns and secret random permutations, leading to inefficiencies in secret calculation processes.
Innovation Solution
A method that generates sort permutations by parallelly generating random ID columns and performing secret random permutations using permutation data, reducing the number of communication stages through optimized steps such as random ID column generation, secret random permutation, flag creation, order table creation, and alignment, while utilizing permutation functions to efficiently align and sort data.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If random ID columns and secret random permutations are repeatedly produced in sequence, then secret sorting can be performed, but the number of communication stages becomes large
Solution Approach 1:
The patent combines multiple sequential operations (random ID column generation, permutation data generation, and sorting operations) into a unified parallel process. By generating sort permutations parallelly and using a single random ID column for multiple sorting operations, the patent merges what were previously separate communication stages into one coordinated operation, thereby reducing the total number of communication stages while maintaining secret sorting correctness
Solution Approach 2:
The patent performs preliminary generation of a single random ID column and sort permutations before the actual sorting operations. By preparing these components in advance and in parallel, the patent eliminates the need for repeated sequential generation during the sorting process, thus reducing communication stages while ensuring the reliability of secret sorting
Data Source
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AI summary
Secret calculation including secret sorting is performed at high speed. Permutation data generation step S10 generates permutation data <πi> and <π'i> so as to generate permutation data <πL>. Random ID column generation step S12 generates a random ID column [r→i] so as to generate a random ID column [r→L]. Secret random permutation step S14 performs secret random permutation of a set composed of a random ID column [r→i-1], a key column [k→i], and the random ID column [r→i] with the permutation data <πi>. Flag creation step S16 sets a flag [fj,h] by using a key [kj]=([kj,0],...,[kj,L-1]). Order table creation step S18 creates an order table [s→] by using the flag [fj,h]. Sort permutation generation step S20 generates sort permutation σπ-1L by using the random ID column [r→i], the order table [s→], a post-permutation key column [πik→i], and a post-permutation random ID column [πir→i].