1. A cryptographic system, comprising: a data stream receiving device configured to receive a modified data stream, said modified data stream comprising an input data stream representing a plurality of data entries encrypted using a chaotic sequence of digits; a user processing device configured to receive user access information specifying an initial value for said chaotic sequence of digits and data field location information identifying at least one data field of a plurality of data fields of a database in which a selected one of said plurality of data entries is stored; a chaotic sequence generator coupled to said user processing device, said chaotic sequence generator configured to directly generate at least one decryption sequence based on said initial value and said data field location information specified in said user access information, said decryption sequence comprising a replicated portion of said chaotic sequence of digits that was used to encrypt data stored in a respective one of said plurality of data fields of said database; and a decrypter coupled to said chaotic sequence generator and said data stream receiving device, said decrypter configured to generate an output data stream from said modified data stream by applying said decryption sequences to said modified data stream.