We present a construction for a family of pseudo-random generators that are very fast in practice, yet possess provable statistical and cryptographic unpredictability properties. Such generators are useful for simulations, randomized algorithms, and cryptography.Our starting point is a slow but high quality generator whose use can be mostly confined to a preprocessing step. We give a method of stretching its outputs that yields a faster generator. The fast generator offers smooth memory-time-security trade-offs and also has many desired properties that are provable. The slow generator can be based on strong one-way permutations or block ciphers. Our implementation based on the block cipher DES is faster than popular generators.

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