‘encrypt’ and ‘compress’ data during transmission

If you have to ‘encrypt’ as well as ‘compress’ data during transmission then which would you do first and why?

Data should be transmitted over any communication network in such a way that the data integrity and authenticity should be maintained, for this first compress the data and then encrypt the data.

The reason behind it is; if you encrypt first you will have nothing but random data to work with, which will destroy any potential benefit from compression.
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