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.