If we need to both encrypt and compress a file, what must we do first?

Once you encrypt the file you will generate a stream of seemingly random data, which will be not be compressible. The compression process depends on finding compressible patterns in the data. It’s not really random.
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In general, it is recommended to compress the file first and then encrypt it. This is because compression reduces the size of the file, making it faster to transfer over a network or to store on a disk, while encryption makes the file unreadable without a decryption key.

If we encrypt the file first and then compress it, the resulting compressed file will not be much smaller than the original file because the encryption will randomize the data and prevent compression algorithms from identifying patterns that can be compressed. Additionally, compressing an encrypted file may even make it larger, as the compression algorithms will add some overhead to the encrypted data.

Therefore, it is a better practice to compress the file first, and then encrypt it using a secure encryption algorithm like AES or RSA, along with a strong encryption key or passphrase.