And if you have your own computer then they will soon argue that you used the network in an un-authorised way. So you need a handheld with 3G network, but they'll probably not let that in the door. ;)
No, seriously. This gets at the whole point of encryption. When this guy went into court, they showed the jury all of this bdsm porno, pictures of the guy naked, showed that he was committing other crimes like solicitation, etc, and that's why he's going to jail. A bunch of random bits don't have the same impact, especially if the defense implies that he was checking up on his ebay auctions.