Tracing Quantum State Distinguishers via Backtracking.

We show the following results: The post-quantum equivalence of indistinguishability obfuscation and differing inputs obfuscation in the restricted setting where the outputs differ on at most a polynomial number of points. Our result handles the case where the auxiliary input may contain a quantum state ; previous results could only handle classical auxiliary input. Bounded collusion traitor tracing from general public key encryption, where the decoder is allowed to contain a quantum state . The parameters of the scheme grow polynomially in the collusion bound. Collusion-resistant traitor tracing with constant-size ciphertexts from general public key encryption, again for quantum state decoders . The public key and secret keys grow polynomially in the number of users. Traitor tracing with embedded identities in the keys, again for quantum state decoders , under a variety of different assumptions with different parameter size trade-offs. Traitor tracing and differing inputs obfuscation with quantum decoders/auxiliary input arises naturally when considering the post-quantum security of these primitives. We obtain our results by abstracting out a core algorithmic model, which we call the Back One Step (BOS) model. We prove a general theorem, reducing many quantum results including ours to designing classical algorithms in the BOS model. We then provide simple algorithms for the particular instances studied in this work.