Ranking, order statistics, and sorting serve as fundamental primitives for database query processing, yet they introduce significant privacy risks when applied to sensitive data. These operations remain particularly challenging to implement under fully homomorphic encryption due to their inherent dependence on data-dependent comparisons. While the state-of-the-art solution (USENIX Security’25) achieves these operations with a minimal comparison depth of 2, it suffers from three critical limitations: approximation error in results, restriction to datasets whose size is a power of two, and substantial comparison overhead. To address these challenges, we present a novel approach that builds upon this foundation through an innovative application of (2,2)-threshold Paillier cryptography. Our experimental evaluation demonstrates that the proposed solution provides three key improvements: (1) deterministic correctness (eliminating approximation errors), (2) support for arbitrary dataset sizes, and (3) significantly reduced comparison costs compared to the SOTA baseline. Our solution ranks a 128-element vector in approximately 18.1 s, computes its argmin/argmax in 20.3 s, and sorts it in 34.3 s, in which all operations outperform the SOTA.