Kth min Threshold Encryption for Privacy-preserving Data Evaluation.

This article introduces the |$k$|th min threshold encryption (KTE), a new cryptographic primitive designed for privacy-preserving data evaluation, particularly to determine if the |$k$|th smallest element in an attribute set exceeds a predefined threshold without revealing confidential data unless this condition is met. The proposed KTE scheme operates under a public-key setting, generating private keys based on an evaluation criterion involving the rank |$k$| and threshold |$d$|, and features optimally short private keys consisting of a single group element, enabling efficient decryption with only two pairing operations. The construction employs novel encoding techniques to transform the threshold comparison into an inner product test and is proven selectively secure under the |$n$|-Decision Bilinear Diffie-Hellman Exponent (n-DBDHE) assumption. Experimental results demonstrate that KTE outperforms related fuzzy identity-based encryption and predicate encryption schemes in terms of key size and decryption efficiency. The work also outlines open challenges, including extending security to adaptive models and supporting multi-dimensional data.