The Cloud is increasingly being used to store and process big data for its tenants and classical security mechanisms using encryption are neither sufficiently efficient nor suited to the task of protecting big data in the Cloud. In this paper, we present an alternative approach which divides big data into sequenced parts and stores them among multiple Cloud storage service providers. Instead of protecting the big data itself, the proposed scheme protects the mapping of the various data elements to each provider using a trapdoor function. Analysis, comparison and simulation prove that the proposed scheme is efficient and secure for the big data of Cloud tenants.