Goldreich-Levin reductions are ubiquitous in cryptography: they convert an algorithm capable of guessing ⟨r,m⟩\langle r, m \rangle (mod 22) for a hidden string mm and a random challenge rr, to one that is capable of extracting the entirety of mm. Here, we describe a "simultaneous" Goldreich-Levin reduction for two entangled parties who are capable of guessing ⟨r,m⟩\langle r, m \rangle given uniformly random identical challenges rr. This allows to upgrade any unclonable encryption scheme satisfying "search" security to one satisfying the gold standard of unclonable "indistinguishability". As a corollary, we show that the simplest candidate unclonable encryption scheme from BB84 states satisfies unclonable indistinguishability.

This result was discovered by GPT-5.6 Ultra after a few interactions. Our prompts included recent results on unclonable encryption by Ananth and Sahai, and Ragavan.