Your security requirements could be nice intros to attack models. For example, you're almost describing 

Anyone who has your public key can now encrypt a message and send it to you in the form of a ciphertext.

An important requirement here is that an attacker cannot figure out 

.  That is, they cannot decipher the message with just the ciphertext and the public key.  They need the secret key to do so.

math

bitcoin_beginners

Cryptography Primer:  Keygen, Encrypt, Decrypt, Sign, Verify

SimpleStacker

Nice!

Your security requirements could be nice intros to attack models. For example, you're almost describing [IND-CPA](https://en.wikipedia.org/wiki/Chosen-plaintext_attack) here:

> Anyone who has your public key can now encrypt a message and send it to you in the form of a ciphertext.
>
> An important requirement here is that an attacker cannot figure out `m`, even if they have access to `c` and `pk`.  That is, they cannot decipher the message with just the ciphertext and the public key.  They need the secret key to do so.