I've looked at a few previous posts on this site but I'm still struggling with the concept of keyspace. Specifically I'm following a coursera course but I think it's probably too advanced for me as I'm failing to understand some numbers.
In the course it talks about a substitution cypher in an alphabet of 26 letters. There is then a question
What is the size of key space in the substitution cipher assuming 26 letters?
The answer is 26! (I get this bit) but the instructor then says this is roughly equivalent to 2^88 which I don't get as the numbers don't seem close to me at all.
Furthermore it talks about the enigma machine and how a 4 rotor machine which would have the following
keys = 26^4 = 2^18
This is equating to 26^4 combinations (4 rotors with 26 keys - again I get this (though should it not be 26!^4?) but then I don't get how this gives a key space of 2^18 . I think it's the equality signs throwing me off as I'm thinking it's 'equal to' as opposed to it 'equates to or resolves to'.
I just don't get these numbers if I'm honest.
Can someone break it down in it's simplest terms for me? As I say, based on this evidence I think the course might be beyond me mathematically, but I really want to understand at least this part now I've gone through it!