Zip uses the same algorithm as Gzip, DEFLATE. The main difference is Zip uses it individually on each file, whereas Gzip uses it on the entire archive collectively, making Gzip better. I don't think there's really a good reason to use Zip, except to give something to a Windows user (since Windows only supports Zip archives out-of-the-box).

For password protection, as far as I know the best choice is 7-zip. Install the p7zip package to get full support for that format. The 7-zip format encrypts archives with the strongest form of AES, which from my understanding is OK (the U.S. government trusts it for top-secret stuff, for instance).

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