A method enables prefix search of cloud stored encrypted files that are encrypted using an order preserving encryption (OPE) algorithm. The encrypted text prefix search method generates a minimum possible plaintext string and a maximum possible plaintext string of the same character length including the search term as the prefix. The minimum and maximum possible plaintext strings are encrypted using the same order preserving encryption algorithm for the encrypted text. The method determines from the minimum ciphertext and the maximum ciphertext a set of common leading digits. The set of common leading digits is used as an OPE encrypted prefix search term and provided to a cloud storage service to search in the cloud stored encrypted files for encrypted text matching the OPE encrypted prefix search term.