Privacy-preserving Data Splitting: A Combinatorial Approach

TL;DR

This paper introduces a new combinatorial formulation for privacy-preserving data splitting, developing algebraic and greedy algorithms to optimize data fragment distribution while satisfying privacy constraints.

Contribution

It presents a novel combinatorial framework and algebraic methods, including Gröbner bases, for solving data splitting problems with privacy considerations.

Findings

Algebraic method using Gröbner bases for optimal data splitting

Greedy algorithm for approximate solutions

New combinatorial formulation of data splitting problem

Abstract

Privacy-preserving data splitting is a technique that aims to protect data privacy by storing different fragments of data in different locations. In this work we give a new combinatorial formulation to the data splitting problem. We see the data splitting problem as a purely combinatorial problem, in which we have to split data attributes into different fragments in a way that satisfies certain combinatorial properties derived from processing and privacy constraints. Using this formulation, we develop new combinatorial and algebraic techniques to obtain solutions to the data splitting problem. We present an algebraic method which builds an optimal data splitting solution by using Gr\"{o}bner bases. Since this method is not efficient in general, we also develop a greedy algorithm for finding solutions that are not necessarily minimal sized.