It's a terrible, terrible idea.
You are just being paranoid at this point.
Like someone mentioned, using this to encrypt state secrets? Stupid idea. Using it to provide some level of trust that the server never sees the plaintext data? Pretty reasonable.
The difference between traditional compilers, chips on motherboards, and so on and so forth, are that you aren't downloading and using a fresh copy every time.
If it were possible to securely store some JavaScript in your browser (trust-on-first-use), or otherwise verify that the JS hadn't changed since the last time you used it, and if that JS weren't accessible from the DOM, and if that JS were well-written and used standard practices and had been reviewed by cryptographers, then maybe it would be OK to use.
...But then again, you've just reinvented SSL.
Here's the SJCL demo: http://bitwiseshiftleft.github.com/sjcl/demo/
The users id is a sha256 hash of their public key and all we keep are the public keys.
Working so far in FF and Chrome, not even trying it in IE