I take your point. But what can be done about it? There are tradeoffs to make there vis a vis how long encryption takes.

Barry.

Imagine that you've just written a twenty-character message and cubed it by hand. This involved multiplying each of twenty digits by each of twenty other digits, and then involved multiplying each of twenty digits by each of forty digits, a process that took you three and a half hours and left you with a number sixty digits long. Let's call it 'B' for Very Big Number.

Now you've got to divide that sixty digit number by some number 'M' (for modulus). This will involve subtracting multiples of M from B until you're left with a remainder that's smaller than M is.

With this in mind, how many digits long would you like for M to be?

Sixty-one.

Wait.

Fifty-nine.

Okay, the new magic number is... is there a website that tells you what a number's name is...

sixty-six octodecillion, 
five hundred ninety five septendecillion,
nine hundred fifty seven sexdecillion,
four hundred sixteen quindecillion,
eight hundred thirteen quattuordecillion,
three hundred sixty two tredecillion,
four hundred seventy two duodecillion,
six hundred forty six undecillion,
four hundred fifty one decillion,
two hundred seventeen nonillion,
three hundred ninety seven octillion,
three hundred fifty two septillion,
eight hundred sixty three sextillion,
six hundred fourteen quintillion,
five hundred ninety nine quadrillion,
six hundred ninety nine trillion,
seven hundred ninety eight billion,
three hundred sixty eight million,
two hundred twenty three thousand,
four hundred and forty-nine.

But remember to pad your message to at least twenty characters and/or include some of the letters from the second half of the alphabet because otherwise an attacker'd just take the cube root.

This fifty-nine digit public number has a fifty-nine digit secret exponent; it could take Toff weeks to decrypt with the key in front of him.

Is "Barry" willing to spend weeks of subjective time on this? Of course not. Barry doesn't care that much about this game. They must have a secret method for arithmetic, or a magic device, or a relevant class feature, or a really good mechanical calculator. Toff hopes it's an idea he can steal for himself. 

And make sure not to pad it over fifty-nine characters, because that's the maximum message size! 

Not that this is much of a concern, since writing a twenty character message would already take, per Altronus, three and a half hours...

Is this remotely practical? Twenty characters is, like, five words. 

This is a lot of a hassle for five words.

Yeah, there's a reason why no one IRL used public key cryptography for anything before the seventies. The technology wasn't mature.

If you can encrypt five words but can't encrypt messages of whatever length best pleases you, Lord Toff Ornelos is prepared to declare that a skill issue. Just cipher the key to a more easily used cipher and send the ciphered key along with the ciphered message.

But, this is interesting. Apparently Lyvina's culture uses personal code ciphers on messages much longer than five words, and takes their ability to do so for granted - they don't bother with efficiency. From this Toff infers that the planet does in fact have highly advanced and widely proliferated mechanical calculators.

Betimes five words compose the hinge of history.

Sending gives you 25.

Not everyone can cast sending!

Toff is prepared to call that a skill issue too.

Cipher the key to a Vigenère cipher, use the Vigenère to cipher the rest of your plaintext, send the ciphered key and the ciphered plaintext. Voila, now you can send as long of a message as you care to write.

Sloooooow. But fastest in the class, so, full marks.

Yes, absolutely, please adulterate your terrifying mathematics with an alphabet cipher for me to squint at until I can make out where whoever wrote it thinks the words begin and end.

That doesn't work because then your message is only as secure as the Vigenère, and you're already assuming that they have arithmeticians.

Huh. 

You learn something every day.

Say more? 

The Vigenère is period-appropriate. Some people were still calling the Vigenère unbreakable in the 20th century. 

I wasn't one of them, though.

But! You could encrypt the key to a one-time pad. That's unbreakable even in theory.

The key to a one-time pad is at least the length of the plaintext.

Arthur. That's the joke.