Unclonable Cryptography with Unbounded Collusions and Impossibility of Hyperefficient Shadow Tomography
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arXiv
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| Format: | Preprint |
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2023
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| author | Çakan, Alper Goyal, Vipul |
| author_facet | Çakan, Alper Goyal, Vipul |
| contents | Quantum no-cloning theorem gives rise to the intriguing possibility of quantum copy protection where we encode a program or functionality in a quantum state such that a user in possession of k copies cannot create k+1 copies, for any k. Introduced by Aaronson (CCC'09) over a decade ago, copy protection has proven to be notoriously hard to achieve. Previous work has been able to achieve copy-protection for various functionalities only in restricted models: (i) in the bounded collusion setting where k -> k+1 security is achieved for a-priori fixed collusion bound k (in the plain model with the same computational assumptions as ours, by Liu, Liu, Qian, Zhandry [TCC'22]), or, (ii) only k -> 2k security is achieved (relative to a structured quantum oracle, by Aaronson [CCC'09]).
In this work, we give the first unbounded collusion-resistant (i.e. multiple-copy secure) copy-protection schemes, answering the long-standing open question of constructing such schemes, raised by multiple previous works starting with Aaronson (CCC'09).
More specifically, we obtain the following results. - We construct (i) public-key encryption, (ii) public-key functional encryption, (iii) signature and (iv) pseudorandom function schemes whose keys are copy-protected against unbounded collusions in the plain model (i.e. without any idealized oracles), assuming (post-quantum) subexponentially secure iO and LWE.
- We show that any unlearnable functionality can be copy-protected against unbounded collusions, relative to a classical oracle.
- As a corollary of our results, we rule out the existence of hyperefficient quantum shadow tomography, * even given non-black-box access to the measurements, assuming subexponentially secure iO and LWE, or,
* unconditionally relative to a quantumly accessible classical oracle, and hence answer an open question by Aaronson (STOC'18). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_18318 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Unclonable Cryptography with Unbounded Collusions and Impossibility of Hyperefficient Shadow Tomography Çakan, Alper Goyal, Vipul Cryptography and Security Quantum no-cloning theorem gives rise to the intriguing possibility of quantum copy protection where we encode a program or functionality in a quantum state such that a user in possession of k copies cannot create k+1 copies, for any k. Introduced by Aaronson (CCC'09) over a decade ago, copy protection has proven to be notoriously hard to achieve. Previous work has been able to achieve copy-protection for various functionalities only in restricted models: (i) in the bounded collusion setting where k -> k+1 security is achieved for a-priori fixed collusion bound k (in the plain model with the same computational assumptions as ours, by Liu, Liu, Qian, Zhandry [TCC'22]), or, (ii) only k -> 2k security is achieved (relative to a structured quantum oracle, by Aaronson [CCC'09]). In this work, we give the first unbounded collusion-resistant (i.e. multiple-copy secure) copy-protection schemes, answering the long-standing open question of constructing such schemes, raised by multiple previous works starting with Aaronson (CCC'09). More specifically, we obtain the following results. - We construct (i) public-key encryption, (ii) public-key functional encryption, (iii) signature and (iv) pseudorandom function schemes whose keys are copy-protected against unbounded collusions in the plain model (i.e. without any idealized oracles), assuming (post-quantum) subexponentially secure iO and LWE. - We show that any unlearnable functionality can be copy-protected against unbounded collusions, relative to a classical oracle. - As a corollary of our results, we rule out the existence of hyperefficient quantum shadow tomography, * even given non-black-box access to the measurements, assuming subexponentially secure iO and LWE, or, * unconditionally relative to a quantumly accessible classical oracle, and hence answer an open question by Aaronson (STOC'18). |
| title | Unclonable Cryptography with Unbounded Collusions and Impossibility of Hyperefficient Shadow Tomography |
| topic | Cryptography and Security |
| url | https://arxiv.org/abs/2311.18318 |