What are some unbreakable ciphers

Could public key cryptography like RSA be useful and secure without a computer in the late Middle Ages?

Cryptography has a long history. Really long.
Needless to say, there was no need to say how important the security of secret messages was between rulers and generals.
In ancient times, the ciphers used were pretty simple, but they evolved into more complex ones.

Old ciphers had one big flaw: they were symmetrical, which made it possible to crack them.

But what about asymmetric key encryption (for example RSA)? It is the most important encryption technique today. One might think that the Middle Ages would create a completely unbreakable cipher.

But mathematical calculations associated with encoding and decoding RSA messages require a lot of work. That's why we use computers for this. In the Middle Ages there were no computers and no way to create one, even with knowledge from the future.

Of course, it would still be possible - just train some scholars (and accidentally bring up some big math theories, but who cares?) And use small enough keys.

But would keys be small enough that a scholar (for security reasons only one) at the royal court could decrypt messages in a few hours and still be powerful? Maybe such small keys don't offer enough protection?

Question:

Is it really safe to use asymmetric key encryption in these terms?

Clarification: All calculations in the encryption and decryption process are done by hand or using techniques available in the late Middle Ages and should not take more than a day for a man to finish.

RSA is just one example of asymmetric key encryption. If RSA turns out to be useless but another type is fine, I'll accept the answer.

For security reasons, I expect something similar to our time definition: Nobody knows a quick way to break, and brute force solutions take at least years.

TO EDIT:
Not a duplicate of cryptography in a world without a computer as this question is about a special family of ciphers, while the above question is about cryptography as a whole.

Galastel

For the less tech-savvy of us, could you please add an explanation on RSA so we can try to find an answer?

a CVn ♦

Remember that it doesn't matter whether a cipher is symmetrical or asymmetrical, which makes it fragile or not. AES is symmetrical but is considered fairly secure. RSA, especially "Textbook RSA" can be trivially broken by an opponent with the appropriate knowledge, especially if it is used with hot keys. The value of encryption is usually to keep a message secure until its value has dropped enough that there is no point in spending resources on breaking the message. In a world where opponents are not particularly powerful (messengers with physical parchment from A to B), you don't need much.

Michael Kutz

I don't think a general would want to wait an entire day to decipher a message from the king. King probably doesn't want to waste an hour deciphering a message from his general. The encode / decode time seems to be too long for usable use.

AlexP

By nature, symmetric ciphers are no easier to crack than asymmetric ones. In reality, you need common asymmetric ciphers much longer keys to be as secure as good symmetric ciphers. For medieval cryptanalists, a simple cipher like an ordinary three-rotor Enigma would be way beyond its ability to crack because of the number of operations required.

Jacob Lovern

It is entirely possible that your problem occurs while trying to encrypt the message.

Let's go through the RSA algorithm:

  1. Choose two prime numbers, p and q.
  2. set n = p ∗ q
  3. find ϕ (n) that is equal to (p-1) (q-1)
  4. choose a number, 1
  5. solve for d in view of which d ∗ e≡1 (mod n)

Let us now consider each step individually.

Choose two prime numbers, p and q.

Pretty easy to do; I learned about the Eratosthenes screen in middle school.

set n = p ∗ q and find ϕ (n) that is equal to (p-1) (q-1)

Easy again. A multiplication by hand is entirely possible.

choose a number, 1