So for Playfair, we choose a keyword and put that in the keytable with no duplicates. Then, we fill the rest of the table with alphabets in order that are not in the keyword without 'J'.
Does the length of the keyword matter? I am wondering because I wanted to know whether having just a random 25 characters long word for the keytable would be more secure than choosing a word that is less than 25 characters long and filling the rest of the table with the rest of the alphabets in order.
Possibly?
The idea behind this keyword-style cipher is that this key should be easy enough to use by the both the sender and recipient, but difficult enough not to be guessed (or brute-forced). Well, that may be the case for ciphers in general, but this one (devised in the 1800s) didn't benefit from the technological advances we have nowadays. For example, sending someone a message using the key "let's be safe" would be far better to remember/convey than a similar length garble of letters "pdkr heso lf" (say).
The keyword is not meant to have control over the keytable; it does, but that is secondary to the process, but to be shareable enough in a convenient way.
Sure, having full control over the keytable and therefore choosing the layout of the entire set of 25 characters is likely more secure. But this only holds if you're trying to break the Playfair cipher by finding the key. And, solving for one key only works until a new key is chosen. General cryptanalysis of the Playfair cipher, however, could rely entirely on diphthong/bi-gram resolution for the underlying language and is therefore independent of the key.
Because the keyword and the resulting keytable are intrinsically linked, more reliance on the keyword choice could make the ciphertext more secure, rather than relying on the algorithmic completion of the keytable based on the keyword - a process that is well-known. But remember, different keywords/key phrases may result in the same keytable ("racecar" and "racer care", for example).
