Cryptology ePrint Archive: Report 2021/946

Hidden Cosets and Applications to Unclonable Cryptography

Andrea Coladangelo and Jiahui Liu and Qipeng Liu and Mark Zhandry

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 study a generalization of hidden subspace states to hidden coset states. 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, 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. 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.

Category / Keywords: cryptographic protocols / quantum cryptography, copy-protection, coset state

Original Publication (with minor differences): IACR-CRYPTO-2021

Date: received 12 Jul 2021, last revised 9 Jan 2022

Contact author: andrea coladangelo at gmail com, jiahui at utexas edu, qipengl at cs princeton edu

Available format(s): PDF | BibTeX Citation

Version: 20220109:021129 (All versions of this report)

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