I am learning about the RSA algorithm. I perform the algorithm on very small prime numbers and use online Big Integer calculators to perform the encryption and decryption and everything works just fine.
My question is about the size of the exponent we create and when it comes to bigger numbers, it seems infeasible to calculate.
For example, the algorithm starts with picking two prime numbers p and q. You compute n=pxq and then the totient of n. Next you pick a number 'e' such that 1
Then to perform an encryption you take say like the ASCII character 'A' which is 65 and you raise it to the power of e. (65^e)
The online big integer calculator started getting very slow and sluggish (over a minute to calculate) when e was bigger than about 100,000 (6 digits)
My question is then, for the working RSA algorithm, what size (number of digits) number does that algorithm pick?