Basically, yes. When we talk about how fast an algorithm is, we usually talk about how much longer it will take to run when you increase the length of the input.
Encryption works because you can double the size of the encryption key and make it take [very large number] times more operations to break the encryption (twice the work to encrypt+decrypt if you have the key, but tremendously harder to crack into without the key).
Comments
A lot of widely-used cryptography relies on factoring large numbers being difficult.
Are we using "difficult" to mean "takes longer than the universe"? Since presumably that would be why we trust it for cryptography?
Basically, yes. When we talk about how fast an algorithm is, we usually talk about how much longer it will take to run when you increase the length of the input.
Encryption works because you can double the size of the encryption key and make it take [very large number] times more operations to break the encryption (twice the work to encrypt+decrypt if you have the key, but tremendously harder to crack into without the key).