You're just describing ordinary challenge-response. That has nothing to do with homomorphic encryption and there are plenty of examples from before homomorphic encryption became viable, for example https://www.geoffchappell.com/notes/security/aim/index.htm

Homomorphic encryption hides data, not computation. If you've been trying to learn compsci from GPT, you might have fallen victim to hallucinations. I'd recommend starting from wikipedia instead. https://en.wikipedia.org/wiki/Homomorphic_encryption

And btw most games are cracked within a week of release. You have way too much faith in buzzwords and way too little faith in bored Eastern European teenagers.

> Homomorphic encryption hides data, not computation

Data is computation.

  x = challenge_byte ^ secret_key
  if x > 64:
    y = hash_memory_range()
  else:
    y = something_else()
  return sign(y, secret_key)