Abstract: A seed random sequence is extended in successive nodes of a tree structure of a random sequence generator. At each node, an input sequence is expanded to an output sequence substantially greater than the length of the input sequence. Plural processors operate in parallel in generating the final output sequence, and subsequences may be directly accessed as a starting location of the output sequence. The random sequence generator is accessed by an index in an encryption system. In a sequential generator, less than all of the bits from the generator unit are reapplied to the generator unit in an iterative process.