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Program obfuscation asks whether a program can be transformed into a protected form that preserves its behavior while hiding the details of its implementation. For quantum computation, achieving such a guarantee for general quantum circuits has long been a major challenge, with prior progress limited to special classes of quantum programs.

In this talk, I will present new constructions that move beyond restricted quantum programs toward fully general quantum computation. I first give an obfuscation scheme for unitary quantum programs with quantum inputs and outputs, going beyond previous pseudo-deterministic settings. Building on this result, and combined with the subspace-preserving pseudorandom unitaries we introduce, we obtain a quantum ideal obfuscation scheme for arbitrary quantum circuits computing general completely positive trace-preserving (CPTP) maps. The constructions are proven secure assuming post-quantum one-way functions in the classical oracle model.

We revisit a natural paradigm for public-key encryption, whereby the public key is an obfuscated block cipher,  and the ciphertext is the result of applying the cipher directly to the message along with a short random nonce.  We show that if the block cipher is a permutable pseudorandom permutation [Shmueli--Zhandry, Crypto~'25] and the obfuscator is indistinguishability-secure, then the resulting  scheme is CCA2 secure.  Further, augmenting the scheme with the capability to generate obfuscated decrypt-then-apply-f circuits (for any given function f), yields a functional encryption scheme that is simulation-secure against adaptive chosen-ciphertext attacks. Even further, for any length-preserving function g, augmenting the public key with an obfuscated decrypt-apply-g-reencrypt circuit allows anyone to homomorphically apply g to encrypted data, for an unbounded number of times, while preventing any other homomorphisms or malleability. (This part relies on subexponential security.)

Formulating this powerful combination of controlled homomorphism, functional decryption, and CCA2 security within a single encryption scheme requires some care and may be of independent interest. Our definition extends that of Prabhakaran and Rosulek (PKC'08).

We finally  show, under the Split-Circuit Pseudorandomness assumption of  (Canetti, Chamon, Mucciolo, Ruckenstein, TCC '24), that an obfuscated version of a random reversible circuit is a permutable pseudorandom permutation, along with a reversible-circuit-only version of the obfuscation process leading to the actual encryption scheme. Combined with the heuristic obfuscation scheme of Canetti et al,  this suggests a potential avenue to realistic instantiations of this general template for public-key encryption. 

Joint work with Ran Canetti  and Yiding Zhang.