A similar case was google reimplementing Sun/Oracle Java APIs. Which has been deemed legal after all.

If you’re interested in that kind of problems, here’s some pointer: https://en.m.wikipedia.org/wiki/Secure_multi-party_computation

This! The prior knowledge is even fairly small, everyone can toss in a random string + key. The only drawback is that all participants need to have synchronized rounds (one for collecting the random values, one for the decryption keys), and the whole protocol fails if someone decides not send timely their decryption key