Two big events that moved cryptology forward in the 19th century. First, the telegraph. And second, the collapse of the polyalphabetic cipher, le chiffre indéchiffrable.
I suspect it is easy to understate the impact of the telegraph. The first words sent effectively shrunk the world. For cryptology, the change prompted the abandonment of the nomenclator system and its associated code books (good riddance) in favour of actual ciphers.
One reason is that the telegraph reduced the impact of errors in sending an enciphered message. If you made a mistake, you could be quickly notified and resend the corrected version immediately. This removed the main obstacle to the adoption of sophisticated ciphers.
The assault on the polyalphabetic cipher was single-handedly done by retired Prussian military major Friedrich W. Kasiski. He proposed a general approach to breaking the previously unbreakable cipher.
Some caveats to this technique:
– His approach only works if the key repeats. A short message encrypted with a long key is still out of reach.
– The solution is straightforward if the cipher text alphabet is known. If it uses made-up symbols, the cryptanalyst’s job is greatly complicated.
The attack is in two parts:
(a) Make an informed guess as to the length of the key.
If presented with decent amount of poly-alphabetically enciphered text, it is likely that some parts of the key enciphered the same plain symbols in more than one place due to the key’s repeating nature. This would lead to repeated ciphertext symbols. The distance between the repeated cipher text groups can be used to make an educated guess about the key length. Specifically, use the ‘Kasiski examination’ technique in tabular form.
(b) Treat the cipher text as groups of interwoven monoalphabetic ciphers, where each group is enciphered using the same key symbol. Solve each using frequency analysis.
The difficulty of doing this part depends on the cipher and plain text alphabets. If they are the same (e.g. the Vigenère cipher), you are in luck. The more the system strays from this, the more out of luck you are. Otherwise, this is just a matter of creating a letter frequency chart and using what you know about how likely some letters appear compared to others to make good guesses.