The effect of encryption on compression ratios

Which of the following statements is true:

1) Encrypting data makes it less "compressable"
2) Encrypting data makes it more "compressable"
3) Encrypting data has no effect on its compression ratio


It seems to me that #1 *should* be true, because the encrypted data should
have few (if any) recurring patterns that a compression algorithm could
exploit. However, I'm not sure if I could prove this to be true.

In particular, I'm talking about lossless (zlib) compression.

Essentially what I'm debating is what in order to compress and encrypt my
data.

Thanks,
Adam
.

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