Abstract: A pseudo-random number generator is used as a pre-processing step to generating a long random bit string. The bit string is then "stretched" by performing certain one-way functions in parallel on the bit strings. In a preferred embodiment, specialized constructions based on expander graphs are also used. Preferably, the strings generated by the one-way functions and expander graphs are exclusive-ored. An embodiment may operate in the following manner. Assume a slow but secure generator G.sub.0.1. Using G.sub.0, generate random numbers x.sub.1, x.sub.2, . . . , x.sub.n.2. Using a stretch function, stretch the random numbers into R=r.sub.1, r.sub.2, . . . , r.sub.n where each r.sub.i is a predetermined amount longer than x.sub.i.3. Use R as a one-time pad for encryption.This process provides a long, random, cryptographically secure bit string.

Abstract: Methodology and concomitant circuitry to generate cryptographically strong pseudo-random bit streams utilize secure block cypher encoders. Each block cypher encoder has a random key and a first seed as an input, and the output of each encoder is fed back to connect to its input. The first seed serves as the initial input, and each subsequent input is the immediate output of the block cypher encoder. Each bit in the cryptographically strong pseudo-random bit stream is related to a first inner product between input to the block cypher encoder and a second seed and a second inner product between the random key and a third seed.