> If you're transmitting any data that could be illegal, your safest bet is to use some kind of encryption that would take longer than the statute of limitations for whichever crime you're committing to break (you'd probably also have to factor Moore's law into your calculation and pray that quantum computing doesn't become viable in the next x years).

Not all crypto algorithms are breakable by quantum computers. Just use one of the ones that is not. (Because the most common algorithms are based on integer factorization, which can be done efficiently with quantum computers, there seems to be a widespread belief that quantum computing makes encryption with normal computers impossible.)