Re: Rainbow tables
Unless elcom have made some amazing breakthroughs in maths that the NSA/CIA/KGB/MMB are unaware of - they cannot 'break' the encryption they can only brute force it by guessing your password.
Bitlocker almost certainly has a backdoor, and given Microsoft's history of security it is probably "NSA123".
Currently Truecrypt is probably your safest bet for keeping things secret. Don't worry they will just convict you of something else instead or accidentally shoot you on the tube if they can't break it.
Truecrypt is open source and can be built entirely from source. The binary download most people use is signed so that it can be loaded as a device driver on MSFT. The source does contain a binary blob which contains the initiialisation vectors of some of the crypto routines but you are free to replace them with your own.
There is a project underway to validate Truecrypt's source. Even if there are no deliberate backdoors it is still possible that mistakes have been made in the implementation.