A pseudo-random number generating circuit and method, comprising: a plurality of pseudo-random number generator (PRNG) units combined in a cascade structure of several layers to produce a pseudo-random output stream, the PRNG units of any given layer running more slowly than those PRNG units of more downstream layers of the cascade structure and running more quickly than those PRNG units of more upstream layers of the cascade structure, the PRNG units including a relatively slow but cryptographically very secure PRNG unit feeding the most upstream layer of the cascade structure, and very fast, but possibly cryptographically insecure PRNG unit at the most downstream layer.