The paper introduces a quantum copy-protection scheme for a large class of evasive functions known as "compute-and-compare programs". A compute-and-compare program CC[f, y] is specified by an efficiently computable function f and a string y in its range, where CCf, y outputs 1 if f(x) = y, and 0 otherwise.
The key idea is to "hide" the marked input y by encoding it in a quantum state using a random choice of basis, and then provide the evaluator with a classical hash of the encoded string. To evaluate the program on an input x, the evaluator attempts to "decrypt" using x and checks if the resulting hash matches the provided one.
The authors prove that this scheme achieves non-trivial security against fully malicious adversaries in the quantum random oracle model, making it the first copy-protection scheme to enjoy any level of provable security in a standard cryptographic model. As a complementary result, the authors show that the same scheme fulfills a weaker notion of software protection, called "secure software leasing", with a standard security bound in the QROM.
The technical core of the security proof involves a search-to-decision reduction, which allows the authors to overcome the inherent difficulty in the security analysis of copy-protection schemes, where security is based on a distinguishing game rather than a guessing game.
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