Cloud-assisted image classification enables many mobile AI applications, but transmitting raw images to the cloud raises significant privacy concerns. Homomorphic encryption (HE) allows computation over encrypted data; however, existing end-to-end HE-based inference pipelines incur prohibitive latency and computational overhead, limiting their feasibility for latency-sensitive mobile systems. This paper addresses how to enable efficient encrypted image classification in mobile edge-cloud environments without sacrificing accuracy. We propose PRICE, a three-tier edge-cloud architecture that partitions deep neural network inference between a trusted edge and an untrusted cloud. The edge performs lightweight feature extraction in plaintext, while only compact embeddings are encrypted using the Cheon-Kim-Kim-Song (CKKS) scheme and offloaded to the cloud for encrypted final-layer inference. This design avoids homomorphic evaluation of deep backbone layers, significantly reducing computation depth, ciphertext size, and end-to-end latency. To further improve efficiency, we develop RowHyDiag, a row-packed hybrid diagonal encoding with hoisted-rotation-aware encrypted matrix-vector computation, which minimizes rotation operations and improves slot utilization. Extensive experiments on real devices across five datasets demonstrate that, under the evaluated 128-bit-security configurations, RowHyDiag achieves up to 31.8$\times$ faster cloud inference, 85.3$\times$ fewer rotations, and 83.0$\times$ lower setup payload than the conventional Halevi-Shoup diagonal method. RowHyDiag also outperforms the PEGASUS linear-transformation baseline, providing 1.1-4.5$\times$ faster cloud inference and 1.2-3.4$\times$ lower setup payload. The results show that PRICE enables deployment-ready, low-latency encrypted inference for mobile edge-cloud systems under a trusted-edge threat model.

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