Question: A stream of cipher operates on a data stream of 6-bit characters using a simple mono-alphabetic substitution technique. Estimate and explain the number of different substitution alphabets possible. The key is effectively the substitution alphabet, which can be expressed as a $384$-bit number (i.e. $64×6$ bits).
Discuss the security of this system compared with DES/3DES and a one-time pad, providing a full justification for your conclusions.
This is a past exam question which I am struggling to solve. I am not a security expert, nor intending to move in that direction as a career path. The module is part of my MSc course and has nothing to do with my career.
Answer (what I have so far):
The number of different substitution alphabets is $26!$ (factorial), assuming use of the English alphabet. It is also assumed that letters can be in any position and cannot repeat themselves.
Why is the key suddenly expressed as a $384$-bit number? I don't understand. Why $64·6$?
We don't have $64$ characters in our alphabet...if each character within the English alphabet is represented with $6$ bit, then it should be $6·26=156$ bits. Correct?
Now I am thinking if the question says $64$, maybe the alphabet is custom (like including uppercase letters and some numbers + characters), so the number of permutations is $64!$ (factorial). Is this correct?
What does this key look like (or an example of such a key)?
I understand key substitution with a single key word. For example:
Can you help me determine what the substitution alphabet key should look like?
I went to Wikipedia's page Six-bit character code and became even more confused. Is this link even relevant?
I would appreciate examples more than answers. Thank you. If you find my question too long, please ignore the part about comparison with other encryption systems.