This document proposes an algorithm called ID-PUIC for remote data uploading and integrity checking in public clouds. It aims to address security issues when clients store sensitive data in public clouds, which they do not fully control. The proposed system uses a proxy to upload client data and perform remote integrity checks with the public cloud server. It introduces a protocol for the proxy to generate tags for file blocks and upload them along with the data for integrity verification. The ID-PUIC algorithm is more efficient for integrity checking than existing solutions as it ignores certificate management and uses bilinear pairings for security. The document outlines the system model, data flow, modules including key generation, tag generation and proofs to check integrity remotely between the client and public cloud server