Unclonable encryption from BB84 states: a simultaneous Goldreich-Levin reduction
Abstract
Goldreich-Levin reductions are ubiquitous in cryptography: they convert an algorithm capable of guessing ⟨ r, m ⟩ (mod $2$) for a hidden string m and a random challenge r, to one that is capable of extracting the entirety of m. Here, we describe a "simultaneous" Goldreich-Levin reduction for two entangled parties who are capable of guessing ⟨ r, m ⟩ given uniformly random identical challenges r. 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.
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BibTeX
@misc{coladangelo2026unclonable,
title = {{Unclonable encryption from BB84 states: a simultaneous Goldreich-Levin reduction}},
author = {Andrea Coladangelo and Qipeng Liu and Ziyi Xie},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.17629},
eprint = {2608.17629},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.17629},
}
RIS
TY - UNPB
TI - Unclonable encryption from BB84 states: a simultaneous Goldreich-Levin reduction
AU - Andrea Coladangelo
AU - Qipeng Liu
AU - Ziyi Xie
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2608.17629
UR - https://arxiv.org/abs/2608.17629
AB - Goldreich-Levin reductions are ubiquitous in cryptography: they convert an algorithm capable of guessing ⟨ r, m ⟩ (mod $2$) for a hidden string m and a random challenge r, to one that is capable of extracting the entirety of m. Here, we describe a "simultaneous" Goldreich-Levin reduction for two entangled parties who are capable of guessing ⟨ r, m ⟩ given uniformly random identical challenges r. 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.
ER -