HEArgmax: Secure homomorphic encryption-based protocols for Argmax function

In the current era of big data, cloud-based Machine Learning as a Service (MLaaS) – where clients send encrypted queries to the cloud and receive prediction results – has gained significant attention. However, privacy concerns arise as cloud servers typically require access to clients’ raw data, potentially exposing sensitive information. Homomorphic encryption (HE), an advanced cryptographic technique that allows computation on encrypted data without decryption, offers a promising foundation for privacy-preserving MLaaS. A critical challenge in this context is the efficient and secure evaluation of the argmax function—a key operation in classification tasks used to select the class with the highest predicted probability. Existing HE-based methods, such as Phoenix (Jovanovic et al., 2022), rely on non-interactive protocols using high-degree polynomial approximations of the sign function, which lead to significant computational overhead. This paper introduces $\mathrm{HEArgmax}$, an interactive protocol designed for efficient and secure $argmax$ evaluation under encryption. Unlike prior approaches, $\mathrm{HEArgmax}$ leverages the algebraic properties of the sign function in combination with a lightweight interactive mechanism under the standard semi-honest model, without requiring trusted setup or multi-party computation. We present two protocol variants: $\mathrm{HEArgmax}$-HT, optimized for high-throughput scenarios using batch processing, and $\mathrm{HEArgmax}$-LC, which minimizes communication by processing a single encrypted vector. Experiments show that $\mathrm{HEArgmax}$ reduces inference latency from 157 s to 8 s on the MNIST dataset, and performs well even on CIFAR-100 with 100 output classes, completing in under 4 min using 128-bit HE security parameters. Despite being interactive, our protocol achieves comparable communication costs to Phoenix. These results demonstrate that $\mathrm{HEArgmax}$ is both practical and scalable for real-world privacy-preserving MLaaS deployments.