Color mixing game

Now that you understand how this type of secret key exchange works, try to attack it from a bad actor's perspective. We've randomly selected the private and public colors for a secret key exchange between Alvin and Barb. Here's the information they trade over the public network:

Alvin's public mix
Barb's public mix
Public color

Can you find Alvin or Barb's private color using just this information?

Difficulty: