Quantum copy-protection of compute-and-compare programs in the quantum random oracle model
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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 𝖢𝖢[f,y] is specified by a function f and a string y within its range: on input x, 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.
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