Hidden Cosets and Applications to Unclonable Cryptography

Abstract

In 2012, Aaronson and Christiano introduced the idea of hidden subspace states to build public-key quantum money [STOC ’12]. Since then, this idea has been applied to realize several other cryptographic primitives which enjoy some form of unclonability. In this work, we propose a generalization of hidden subspace states to hidden coset states. We study different unclonable properties of coset states and several applications: We show that, assuming indistinguishability obfuscation (iO ), hidden coset states possess a certain direct product hardness property, which immediately implies a tokenized signature scheme in the plain model. Previously, a tokenized signature scheme was known only relative to an oracle, from a work of Ben-David and Sattath [QCrypt ’17].Combining a tokenized signature scheme with extractable witness encryption, we give a construction of an unclonable decryption scheme in the plain model. The latter primitive was recently proposed by Georgiou and Zhandry [ePrint ’20], who gave a construction relative to a classical oracle.We conjecture that coset states satisfy a certain natural (information-theoretic) monogamy-of-entanglement property. Assuming this conjecture is true, we remove the requirement for extractable witness encryption in our unclonable decryption construction, by relying instead on compute-and-compare obfuscation for the class of unpredictable distributions. As potential evidence in support of the monogamy conjecture, we prove a weaker version of this monogamy property, which we believe will still be of independent interest.Finally, we give the first construction of a copy-protection scheme for pseudorandom functions (PRFs) in the plain model. Our scheme is secure either assuming iO, OWF and extractable witness encryption, or assuming iO, OWF, compute-and-compare obfuscation for the class of unpredictable distributions, and the conjectured monogamy property mentioned above.