Question: I can imagine that finding $p,q,n$ are easy, but my text book also says the $e$ can be found rapidly, so how does modern RSA find this $e$?

![RSA as a Public Key System](https://i.stack.imgur.com/LBR7F.png)

Answer: 
A simple way to achieve this with common algorithms would be to do the following:

1. Choose a random key (key)
2. Encrypt the data using the random key (encrData)
3. Hash the encrypted data (encrHash)
4. Xor the key and the hash (xorKey)
5. The result data would be the encrypted data + the Xor key (encrData+xorKey)

To reverse:

1. Split the data into encrData+xorKey
2. Hash the encrypted data (encrHash)
3. Xor the xorKey with the encrHash Because the way xor works this reverses the process above (key)
4. Decrypt the data with the key

If needed base64 the encrypted data to produce string form

With this scheme you will need the entire string to decrypt the data and can use any secure algorithm (ex AES and SHA256)
Let's take the simplest cipher I can think of which the key is not obvious: [ROT13](https://en.wikipedia.org/wiki/ROT13). You replace a letter with the 13th letter after it, in the alphabet. Because there are 26 letters in the alphabet, you don't need to inverse the algorithm for decryption. Is ROT13 an example of keyless encryption, a very weak one of course? No, because 13 is your key. I don't think any algorithm that can be expressed with a computer can be keyless.

Another bizarre example of which the key is not obvious is a language. Obscure languages have been used as a form of encryption. The most famous example are the [code talkers](https://en.wikipedia.org/wiki/Code_talker) of World War II. Navajo was an unwritten language at that time and the only way to encrypt a message was using your language skills and your mouth. You decrypted a message using your ears, your language skills, and pen and paper. So is this form of encryption keyless? To answer that question, we have to know if this algorithm can be expressed by a computer. There is no way for a computer to translate English to Navajo right now, but there are services that can translate English to Chinese and vice versa. If we trained a language model that could automatically translate English to Navajo using a computer, that model would be your key.

So this answer doesn't ultimatively exclude any form of keyless encryption might exist. I just had a look at some encryption topics not covered by RFC or NIST and I don't think it's possible for keyless encryption to exist.