Compression methods?

[Grand_Master]

I haven't done much of file compression really,
even though I know how to use the most common ones (rar, zip, 7-zip, etc).
I want to find two compression methods.

What compression method should I use for saving most diskspace and what program can accomplish this task?
I don't want to spend days or week to compress a 4 GB folder. I don't mind if it takes a half a day to compress as long as I compress it really effectively, though.

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What method should I use to get the highest available encryption?

I would prefer a method that even the police or the governement can't crack, even though that's not really necessary. But I need to know how sequre the method is.
(Maybe I should use an encryption tool, rather than a compression tool for that task, I don't really know. But it would be appreciated to save some disk space at the same time.)

[canine]

GnuPG should enable you to encrypt things that the FBI can't crack.

If you need that kind of security, or if you're paranoid, as I am, then you'd probably also need to worry about fragments of files left on your disk after the files have been deleted or encrypted. In that case, you'd need to shred the file.

http://en.wikipedia.org/wiki/Data_erasure

[Grand_Master]

Thanks for reply. I'll check your link.