  In this work, we study a generalization of hidden subspace states to hidden
coset states (first introduced by Aaronson and Christiano [STOC '12]). This
notion was considered independently by Vidick and Zhang [Eurocrypt '21], in the
context of proofs of quantum knowledge from quantum money schemes. We explore
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, it 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.
This conjecture was later proved by Culf and Vidick in a follow-up work.
  - Finally, we give a 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. This is the first
example of a copy-protection scheme with provable security in the plain model
for a class of functions that is not evasive.
