# Verification key generation

The constraints and trade-offs discussed in the [noise insertion](https://docs.inferix.io/inferix-whitepaper/implementation/noise-insertion) and the [noise spreading](https://docs.inferix.io/inferix-whitepaper/implementation/adaptive-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 [\[12\]](https://docs.inferix.io/references#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.