Incomplete Hypercube-based Algorithms for Privacy-Preserving Data Aggregation Using Zero-Knowledge Proofs

The privacy-preserving data aggregation is a challenging task in decentralized networks (e.g. blockchain) where multiple distinct contributors need to collaborate in order to perform a shared task (e.g. arithmetic operations) by preserving the privacy of each individual data. The existing protocols for the privacy-preserving data aggregation in the literature may require the fully-complete hypercubes over the Ethereum blockchain where it supports limited number of contributors at a certain time (i.e. exactly 2<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sup> nodes in k-dimension). Therefore, we theoretically analyze the security of such protocols from the perspective of underdetermined systems and identify the potential root problem so that any arbitrary number of nodes could be supported. For this problem, we propose three novel decentralized techniques (i.e. node multiplexing, topological recursing and data splitting) by comparing their relative advantages and disadvantages.