A new order preserving encryption (OPE) scheme has been proposed. It encrypts data belonging to the real interval [0,1], so, if input data belong to a different set, it must be mapped into it. With this cryptosystem, encryption and decryption times are logarithmic in the number of key points, which has been demonstrated by means of an experimentation.
A security analysis has been performed in order to test the unpredictability of the obtained functions and select the best parameter configuration for the restrictions in key generation. This allowed to avoid degenerate cases, so that the desired entropy can be obtained. An attacker with access to the contents of a database with some fields using OPE can