Black-Hole Radiation Decoding as a Cryptographic Assumption

Zvika Brakerski (Weizmann Institute of Science) https://simons.berkeley.edu/talks/zvika-brakersky-weizmann-institute-science-2023-05-05 Minimal Complexity Assumptions for Cryptography (Based on https://arxiv.org/abs/2211.05491) We propose to study equivalence relations between phenomena in high-energy physics and the existence of standard cryptographic primitives, and show the first example where such an equivalence holds. A small number of prior works showed that high-energy phenomena \emph{can be explained} by cryptographic hardness. Examples include using the existence of one-way functions to explain the hardness of decoding black-hole Hawking radiation (Harlow and Hayden 2013, Aaronson 2016), and using pseudorandom quantum states to explain the hardness of computing AdS/CFT dictionary (Bouland, Fefferman and Vazirani, 2020). In this work we show, for the former example of black-hole radiation decoding, that it also \emph{implies} the existence of secure quantum cryptography. In fact, we show an existential equivalence between the hardness of black-hole radiation decoding and a variety of cryptographic primitives, including bit-commitment schemes and oblivious transfer protocols (using quantum communication). This can be viewed (with proper disclaimers, as we discuss) as providing a physical justification for the existence of secure cryptography. We conjecture that such connections may be found in other high-energy physics phenomena.