Currently, with third-party cloud providers handling data mining tasks while securely processing sensitive data has become critical. These providers may exploit intermediate data during computation, posing privacy risks. In privacy-preserving classification, we address a secure comparison problem where inputs a and b are encrypted, ensuring no plaintext is exposed to the cloud. Our protocol, designed for a semi-honest model, allows only the end user to learn whether a > b, keeping both inputs hidden from cloud parties. While initially targeting single comparisons, our protocol scales to multiple encrypted inputs to identify the maximum value securely. It thus serves as a foundational tool for secure data processing. Additionally, we introduce a second protocol utilizing homomorphic encryption’s additive property to compare encrypted values efficiently, reducing both computational and communication overhead. Both protocols avoid circuit-based methods and operate in a fixed number of rounds, enhancing performance.