Quantum copy-protection of compute-and-compare programs in the quantum random oracle model
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866911969734295552 |
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| author | Coladangelo, Andrea Majenz, Christian Poremba, Alexander |
| author_facet | Coladangelo, Andrea Majenz, Christian Poremba, Alexander |
| contents | Copy-protection allows a software distributor to encode a program in such a way that it can be evaluated on any input, yet it cannot be "pirated" - a notion that is impossible to achieve in a classical setting. Aaronson (CCC 2009) initiated the formal study of quantum copy-protection schemes, and speculated that quantum cryptography could offer a solution to the problem thanks to the quantum no-cloning theorem. In this work, we introduce a quantum copy-protection scheme for a large class of evasive functions known as "compute-and-compare programs" - a more expressive generalization of point functions. A compute-and-compare program $\mathsf{CC}[f,y]$ is specified by a function $f$ and a string $y$ within its range: on input $x$, $\mathsf{CC}[f,y]$ outputs $1$, if $f(x) = y$, and $0$ otherwise. We prove that our scheme achieves non-trivial security against fully malicious adversaries in the quantum random oracle model (QROM), which makes it the first copy-protection scheme to enjoy any level of provable security in a standard cryptographic model. As a complementary result, we show that the same scheme fulfils a weaker notion of software protection, called "secure software leasing", introduced very recently by Ananth and La Placa (eprint 2020), with a standard security bound in the QROM, i.e. guaranteeing negligible adversarial advantage. Finally, as a third contribution, we elucidate the relationship between unclonable encryption and copy-protection for multi-bit output point functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_13865 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Quantum copy-protection of compute-and-compare programs in the quantum random oracle model Coladangelo, Andrea Majenz, Christian Poremba, Alexander Quantum Physics Cryptography and Security Copy-protection allows a software distributor to encode a program in such a way that it can be evaluated on any input, yet it cannot be "pirated" - a notion that is impossible to achieve in a classical setting. Aaronson (CCC 2009) initiated the formal study of quantum copy-protection schemes, and speculated that quantum cryptography could offer a solution to the problem thanks to the quantum no-cloning theorem. In this work, we introduce a quantum copy-protection scheme for a large class of evasive functions known as "compute-and-compare programs" - a more expressive generalization of point functions. A compute-and-compare program $\mathsf{CC}[f,y]$ is specified by a function $f$ and a string $y$ within its range: on input $x$, $\mathsf{CC}[f,y]$ outputs $1$, if $f(x) = y$, and $0$ otherwise. We prove that our scheme achieves non-trivial security against fully malicious adversaries in the quantum random oracle model (QROM), which makes it the first copy-protection scheme to enjoy any level of provable security in a standard cryptographic model. As a complementary result, we show that the same scheme fulfils a weaker notion of software protection, called "secure software leasing", introduced very recently by Ananth and La Placa (eprint 2020), with a standard security bound in the QROM, i.e. guaranteeing negligible adversarial advantage. Finally, as a third contribution, we elucidate the relationship between unclonable encryption and copy-protection for multi-bit output point functions. |
| title | Quantum copy-protection of compute-and-compare programs in the quantum random oracle model |
| topic | Quantum Physics Cryptography and Security |
| url | https://arxiv.org/abs/2009.13865 |