384- and 512-bit foreign fields

[mitschabaude]

Why

Signature schemes used for passports, by number of country:

{
  "rsa": 608,
  "brainpoolP384r1": 54,
  "secp256r1": 19,
  "secp384r1": 34,
  "brainpoolP256r1": 51,
  "brainpoolP512r1": 12,
  "secp521r1": 18
}

As we see here, there are curves from the secp*r1 and brainpool family with 384 or 512 bit base fields. These aren't currently supported in o1js, our foreign field arithmetic only allows up to 256 bits curves.

How

Anything other than leveraging dedicated custom gates is probably much too inefficient. A question might be if the existing foreign field gates could be tweaked to being combined to do multiplications in larger fields