Extending random number summation as an order-preserving encryption scheme

A method and system for cryptographically indexing, searching for, and retrieving documents is provided. In some embodiments, an encryption system is provided that generates a document index that allows users to retrieve documents by performing encrypted queries for keywords associated with the documents. In some embodiments, each keyword maps to the same number of encrypted document identifiers. In some embodiments, an extractor graph is employed to map an indication of each keyword to a number of buckets storing encrypted document identifiers. In some embodiments, an order-preserving encryption system is provided. The encryption system uses an ordered index that maps encrypted instances of ordered attribute values to documents that are associated with those values. The ordered index enables queries containing query operators that rely on order, such as less than (""), to be successfully performed on encrypted attribute values.