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.