Is the uncompressibility of encrypted data a necessary property for a good crypt

Question

Is the uncompressibility of encrypted data a necessary property for a good cryptographic algorithm?

To make a crude experiment, I encrypted an 8K file with all 'A' and then compressed both the encrypted and the unencrypted file.

The compressed unencrypted file went down to less than 200 bytes while the conpressed encrypted file became larger than the encrypted file.

I think that while this result says nothing about the goodness of the encryption, the opposite result (i.e. if the encrypted file would shrink after compression) would have revelead a weakness of the encrypting algorithm.

Am I correct or am I missing something about the relation between encryption and compression?

Explanation / Answer

Yes, a ciphertext of a bulk encryption algorithm normally should not be compressible to less than the plaintext size

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