Why don't you perform some tests and see which is better *for your and
your data*.

If you are just compressing a single stream of data, then there's nothing to be
gained by using ZIP format -- that is designed specifically for packing
/several/ files (compressed) into one larger archive file.

The other two formats are not essentially different.  All three formats use the
same compression algorithm with the same parameters.  The /only/ difference
between "deflate" and "gzip" is that the two formats have different
header/trailer information around the (identical) compressed data.  "deflate"
puts slightly less (I think it's 12 bytes less), but uses a weaker checksum.
Also the "gzip" format can easily be read by external applications such as the
"gzip" command-line utility, which is universal on Unix-alike platforms and
widely available for Windows.

   -- chris

As has been pointed out, it is probably pointless to compress
encrypted data.  The whole point of encryption is to increase the
entropy of the cyphertext, which makes it less compressible.

If you wish to reduce the size of your encrypted files then you should
try compressing the plaintext first and then encrypting the compressed
file.

Two warnings:

1 Most compression formats have standard headers etc.  These may
increase the amount of structure in your file and hence make it easier
to decrypt.  Whether this is a problem depends on how much structure
there is in your uncompressed plaintext and who you are trying to
conceal it from.

2 Generaly avoid the encryption options built into compression
programs.  They are fine for stopping casual snooping but are not as
secure as a properly implemented strong encryption algorithm.

rossum