:"Captain Picard. There's a subspace message for you from Starfleet command. It's on [dramatic pause] a secure channel."
:"A secure channel?!? What could be so important?"
:"Good question, number one. Let's just hope it doesn't delay our rendezvous at Rigal 7. Lieutenant Worf, I'll take it in my ready room."
: Generates a 256 bit public key, exchanges public keys over subspace, calculates a session key, checks validity of web certificate "Handshake protocol complete. Connection is secure."
Me: "Computer, log into Proton Mail."
Computer voice acted by Majel Barrett: "Proton Mail connection establish. Please enter user name and password."
Me: enters user name and password
Computer voice: "Warning, this connection is not secure. Hackers may be able to intercept your private information."
Me: "Computer, establish a secure connection."
Computer voice: "Unable to comply. A secure connection requires level 4 or above access."
I guess because computational power is near unlimited and they are well past quantum computing... maybe the security scheme involves more than mathematical encryption, maybe the transmission medium? Could also be expensive because they have to use one-time pad encryption for every secure transmission. It's the only encryption scheme that cannot be cracked regardless of advances in computing but requires every transmission use a unique one-time cypher that is expended upon use.
https://en.wikipedia.org/wiki/One-time_pad
In some science fiction secure encryption ends up returning to one-time pad encryption because computational capabilities have become so advanced. An entire economic niche is created where interstellar ships travel in-between star systems delivering shipments of one-time pad keyrings that are used for secure transmissions. Any transmissions using public-private key schemes or any scheme with reusable cyphers is considered crackable by state actors and large corporations who care enough to task the necessary computational resources. As a result secure transmissions of a sensitive nature become extremely expensive.
I sorta imagine that it's due to Roddenbury being in his 70s when TNG started, the internet wasn't a thing, and lots of earlier military encryption was a variation of private key encryption, where a book of keys or cipher methods would chill on the flagship until a message was sent.
I guess that quantum computing could be a thing in the 24th century. Supposedly quantum cryptography (using light waves as keys) is literally impossible to crack, but now I'm just being pedantic.
In the 1970s they didn't have encrypted live audio video communication in outer space which is what they're showing in Star Trek. It was literally future technology until the last couple decades. And now we can do it all the time since our computer CPUs have it built in.