Copy Protection

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Functionality Description[edit]

Copy Protection is a functionality first defined by Aaronson [1] that enables a Vendor to send a program (a circuit) to a Client so that the Client cannot duplicate it.

Classically, this functionality has been proven impossible. However, it is possible to copy protect some families of programs using quantum computation.

Tags: Quantum Functionality, Two Party Protocols, Universal Task, Computational Security

Use-cases[edit]

  • Any kind of software licence protection

Protocols[edit]

Currently, protocols for Copy Protection are only known for a few families of circuits.

  • Quantum Copy Protection for Compute and Compare functions [3] [4]
  • Quantum Copy Protection for Pseudo Random Number Generators [5]

Properties[edit]

A Copy Protection protocol for a family of circuits is made of two algorithms:

  • Protect, which takes as input a classical description of a circuit and outputs a quantum encoding of this circuit.
  • Eval, which takes as input a quantum state and an classical input, and returns a classical output.

A Copy Protection scheme for a family of circuits has - if for any circuit of this family and for any input for this circuit,

A Copy Protection scheme for a family of circuits has - if no polynomially bounded quantum adversary can efficiently copy a protected program, more formally if for any such adversary, her probability of winning the following game is lower than :

  • A Challenger samples a circuit C in the family and sends Protect(C) to the Adversary
  • The Adversary runs any polynomial computation she wants on Protect(C) and sends two quantum states, respectively and to two of her agents, respectively Alice and Bob
  • The Challenger samples two inputs for the circuit and sends to Alice and to Bob.
  • Alice sends to the Challenger and Bob sends to the Challenger.
  • The Adversary wins iff and

We assume that Alice and Bob cannot communicate with each other.

Further Information[edit]

Even with quantum computation, Copy Protection is not possible for all families of circuits. Currently, it has been proven impossible for all learnable functions and de-quantumizable functions [2] .

Knowledge Graph[edit]

References[edit]

  1. Aaronson (2009) proposed a fist definition of Quantum Copy Protection.
  2. Ananth, Prabhanjan, and La Placa (2020) constructed a family of unlearnable circuits that cannot be copy protected.
  3. Coladangelo et al. (2020) proposed a copy protection construction for Compute and Compare functions in the QROM.
  4. Broadbent et al. (2021) proposed a copy protection construction for Compute and Compare functions without assumptions but with a weaker adversary model.
  5. Coladangelo et al. (2021) proposed a copy protection construction for PRNGs based on coset states.