system
Given the following post, respond as if you're commenting on Reddit:
human
Why does an TLS private key need to be thousands of bytes long, when 16 is more than sufficient for a password?

As I understand it, it's not safe anymore to use a 512-byte encryption key for TSL. They're too easy to crack.

On the other hand, a 16-byte random password is more than enough to foil any modern attempt at brute-forcing (that's ~ 10^29 possible ASCII passwords).

Why is it so much easier to crack TLS encryption than it is to guess a password?
gpt
Increasing the length of a password increases the number of possibilities exponentially (your search space is the number of possibilities for each character ^(length of password) )

Public/private key encryption is based on the principle that if you multiply two large prime numbers together, and give that number to someone else, it's hard for them to figure out what the original two numbers were. 

While there isn't a direct way to determine the factors of say 391, you only need to make 7 guesses to break the encryption(the space you have to search is limited to the prime numbers that are less then the square root of your "key" , but if this was a numeric password that had to be somewhere between 0 and 391, you'd have to make an average of 196 guesses to break the password. That's why the public key has to be longer.