A comparison of two approaches to pseudorandomness

The concept of pseudorandomness plays an important role in cryptography. In this note, we contrast the notions of complexity-theoretic pseudorandom strings (from algorithmic information theory) and pseudorandom strings (from cryptography). For example, we show that we can easily distinguish a complexity-theoretic pseudorandom ensemble from the uniform ensemble. Both notions of pseudorandom strings are uniformly unpredictable; in contrast with pseudorandom strings, complexity-theoretic pseudorandom strings are not polynomial-time unpredictable.

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