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We reconsider the black hole firewall puzzle, emphasizing that quantumerror-correction, computational complexity, and pseudorandomness are crucialconcepts for understanding the black hole interior. We assume that the Hawkingradiation emitted by an old black hole is pseudorandom, meaning that it cannotbe distinguished from a perfectly thermal state by any efficient quantumcomputation acting on the radiation alone. We then infer the existence of asubspace of the radiation system which we interpret as an encoding of the blackhole interior. This encoded interior is entangled with the late outgoingHawking quanta emitted by the old black hole, and is inaccessible tocomputationally bounded observers who are outside the black hole. Specifically,efficient operations acting on the radiation, those with quantum computationalcomplexity polynomial in the entropy of the remaining black hole, commute witha complete set of logical operators acting on the encoded interior, up tocorrections which are exponentially small in the entropy. Thus, under ourpseudorandomness assumption, the black hole interior is well protected fromexterior observers as long as the remaining black hole is macroscopic. On theother hand, if the radiation is not pseudorandom, an exterior observer may beable to create a firewall by applying a polynomial-time quantum computation tothe radiation.

The ghost in the radiation: Robust encodings of the black hole interior