Verification key generation

The constraints and trade-offs discussed in the noise insertion and the noise spreading are to ensure the fidelity of rendered results and the robustness of the verification, but they do not concern the security. Indeed, any attacker knowing the algorithm and parameters including trade-offs, can straightforwardly generate (without rendering the graphics scene) forged images with the same spectral characteristics, finally bypasses the verification. The security is supported using verification keys.

Each rendering task has a secret key, in current implementation, this key is also the task identification number $J_{\mathtt{id}}$. When embedding the noise vector $W$ into the scene $G$, this number is used to compute distortion regions $k_i$ for all $1 \leq i \leq n$, the vector $\left(k_i\right)_{1 \leq i \leq n}$ is called verification key. The computation is modeled as a function:

$$K_{\mathtt{verif}} \colon \left(S,W,J_{\mathtt{id}}\right) \mapsto \left(k_i\right)_{1 \leq i \leq n}$$

In the operation of the rendering network, the leak of used verification keys is unavoidable. For instance, a worker may register itself to become a verifier node; when got accepted, it will be assigned verification tasks containing verification keys, then will be able to collect used keys. Even worse, colluding workers may exchange collected keys so that each of them will possess a much larger collection [12]. Another possibility is the malicious workers may get verification keys from some compromised verifiers.

Hence $K_{\mathtt{verif}}$ must be designed so that the knowledge about used keys does not leak any information about the next generated keys. The following proposition is necessary for the security of ANGV.

Proposition 3. $K_{\mathtt{verif}}$ is a cryptographic hash function.