The spacecraft should generate the key pairs itself once it landed and send the public keys to earth to be sure no human stole the private keys.

But, while fun, your idea is not that stupid.

If the spacecraft continuously generate key pairs, you could even avoid landing it and "just" throw it in some direction, Voyager style (if you can afford rebuilding some every few decades) or on some orbit in the solar system. You don’t have to pay for the landing tech.

I wouldn’t even be surprised that this could be viable economically. It doesn’t sound that much technologically difficult