We’re imagining that the discriminator gets to see the computation done by f—the tricky part of the Fermat test is that even if you see the computation of an(modn) you still can’t figure out whether the number was prime or Carmichael.
We are also hoping the discriminator will be no harder to learn than f, and so e.g. if gradient descent bakes some tricky secret into f then we are happy baking the same secret secret into the discriminator (and this is why obfuscated circuits aren’t a counterexample).
We’re imagining that the discriminator gets to see the computation done by f—the tricky part of the Fermat test is that even if you see the computation of an(modn) you still can’t figure out whether the number was prime or Carmichael.
We are also hoping the discriminator will be no harder to learn than f, and so e.g. if gradient descent bakes some tricky secret into f then we are happy baking the same secret secret into the discriminator (and this is why obfuscated circuits aren’t a counterexample).