Systems, methods and modulated data signals are described herein that provide an efficient way to derive a single key from which a user can extract virtually any number of data encryption keys. A database is logically divided into segments and a small prime number is associated with each segment. An encryption key is derived for each segment in the database and a key set is determined for distributing a data subset to a user. Each segment is encrypted with the corresponding encryption key. A single key is derived using the prime numbers associated with the data segments and the single key, the encrypted database, and a small amount of public information is provided to the user. The user utilizes this information to extract the encryption key set from the single key. One implementation utilizes a tree structure to significantly reduce the number of modular exponentiations that must be calculated when extracting the encryption keys. This, in turn, dramatically decreases the processing overhead that must be allocated to the processing associated with deriving the encryption keys.