Implementing aztec-nr library that constrains a use of fresh keys

[benesjan]

We need to have the ability to constrain the use of fresh keys from registry. Implement a fresh-key library (if you hate the name feel free to chime in with a new one) which will have the following functions:

assert_fresh_master_nullifier_public_key(account: AztecAddress, npk_m)
assert_fresh_master_incoming_viewing_public_key(account: AztecAddress, npk_m)
assert_fresh_master_outgoing_viewing_public_key(account: AztecAddress, npk_m)
assert_fresh_master_tagging_public_key(account: AztecAddress, npk_m)

It's essential that these checks can be done without calling the canonical registry contract because we can't afford another kernel iteration --> it adds a few seconds of proving and these checks will be common. For this reason we will need directly read the SharedMutable of the registry contract. Here is a separate issue to implement that functionality.

[sklppy88]

@benesjan: How do we constrain this if we aren't storing them at them moment? #5723 (comment)

Also, how do we constrain it if its not in the registry and we only pass in one of the parts of the key_hash ? There is no way to derive if it's actually valid no ?

In my eyes we need to have it in the registry to assert if it's fresh, OR to have access to the base derivation through all the inputs.

A bit confused here

[sklppy88]

Following scrum, have decided to make a lib fn to constrain only the nullifier keys (not the other 3), and if the key does not exist in registry, to only say that it does not exist as there is no way to constrain this w/out the full preimg