Update the docs for decider circuits

[winderica]

In privacy-scaling-explorations/sonobe#145, we will have a slightly improved design of decider, where the decider circuit will handle a bit more checks that were previously done by the verifier.

More specifically, the current decider circuit for Nova only checks the generation of challenge $ r $, while the rest of NIFS.V is done by the verifier, including the computation of random linear combinations of $u, x, \overline{E}, \overline{W}$.

privacy-scaling-explorations/sonobe#145 follows the approach in the DeciderEthCircuit of HyperNova, which verifies the field operations in NIFS.V in-circuit. In other words, now the Nova decider circuit additionally computes the random linear combinations of $u, x$, and the verifier only needs to check $\overline{E}, \overline{W}$.

This PR updates the docs for the decider circuit and includes the changes described above. Furthermore, it also provides more details about the design, which hopefully will make the docs clearer to readers.

[arnaucube]

Nice! The Decider high level checks new organization makes much more sense now ^^

I understand that those updates come together with the updates of privacy-scaling-explorations/sonobe#145, right?

[winderica]

I understand that those updates come together with the updates of privacy-scaling-explorations/sonobe#145, right?

Yes, the updates in this PR reflect the changes in privacy-scaling-explorations/sonobe#145.