Kth min Threshold Encryption for Privacy-preserving Data Evaluation

Abstract

Abstract The $k$th min threshold is to judge whether the $k$th smallest element of an attribute set along with a confidential file is greater than a predefined threshold, which is a fundamental, primitive operation in data evaluation, such as risk evaluation in business investment. However, it will compromise the privacy of the confidential files when proceeding with such a data evaluation because there is often a large amount of sensitive information involved in them, which the organizations/individuals are reluctant to expose due to the risk of losing a competitive advantage. Motivated by the issue how to preserve the privacy of the confidential files during data evaluation, in this research, we first present a new encryption notion called $k$th min threshold encryption (KTE) for serving privacy-preserving data evaluation. In this notion, the confidential file will be encrypted under an attribute set for its privacy protection prior to being sent to a receiver, and a decryption key is generated from a threshold $d$ and a rank $k$ of element, both selected by the receiver. The decryption will be successful if and only if the $k$th smallest element of the attribute set is greater than $d$. We then describe a concrete construction of KTE in the public-key setting. In particular, our construction features optimally short private keys, which only consists of one group element. By virtue of this advantage, it is quite practical because of only two pairing operations for decryption computation.