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Recently, storage of huge volume of data into Cloud has become an effective trend in modern day Computing due to its dynamic nature. After storing, users delete their original copy of the data files. Therefore, users cannot directly control over that data. This lack of control introduce security issues in Cloud data storage, one of the most important security issue is integrity of the remotely stored data. Here, we propose a Distributed Algorithmic approach to address this problem with publicly probabilistic verifiable scheme. Due to heavy workload at the Third Party Auditor side, we distribute the verification task among various SUBTPAs. We use Sobol Random Sequence to generate the random block numbers that maintain the uniformity property. In addition, our method provide uniformity for each subtasks also. To make each subtask uniform, we use some analytical approach. For this uniformity, our protocols verify the integrity of the data very efficiently and quickly. Also, we provide special care about critical data by using Overlap Task Distribution Keys.