We have two communication points in an information system, call them A(lice) and B(ackup).

B has to store encrypted data received from A. The storage of B is encrypted, but not compressed¹.

B should have no option to decrypt the data of A².

However, the data channel between A and B are too narrow, compared to the data volume, making the compression of the communication a requirement. However, encryption maximizes the entropy of the content, making it incompressible.

Another option would be to compress the data, and then encrypt it, but then B should be able to decrypt the data to decompress it.

My first idea was that these requirements are contradicting, as it seems with the practical tools known to me. But I am not sure, how does it look from a theoretical view?

Is an encryption possible, what does not worsens the compressibility of the data in it, despite that it is "enough" secure?

¹_{The reason is here data safety and the support of incremental backups, if it matters (I think, it doesn't).}

²_{It has obvious security reason - a backup storage having all data of a complex network becomes a security bottleneck.}