RSA Encryption message Length

Question

So i know that to encrypt a message in RSA we use cipher = m^e % n where m is the plain text transformed to an integer of size {0,..,n -1} and n is the modulus. Let's say that the size of n is 8192bit and e = 65537 and m (as an integer) = n - 4. So the question is wouldn't be (2^(8192-4))^65537 impossible to calculate ?

Answer 1

Not impossible at all - the exponentiation is performed modulo n, which means that the result will always be less than n. This not only limits the output size, but makes the calculation easier as intermediate stages can be reduced modulo n to keep the numbers involved "small". The Wikipedia page on modular exponentiation provides more detail on how the calculation can be performed.