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jdege
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Yes.

It's a matter of how long the ciphertext has to be in order for the statistics to show through clearly enough. For a standard Vig, using ordinary alphabets, the longer the keyword the greater the security. Using a mixed alphabet adds more security, but truthfully not all that much. I remember seeing an estimate that it was equivalent to adding five more letters to the key, so that a mixed-alphabet Vig using a key of seven letters would be about as Secure as an ordinary-alphabet Vig using a key of 12 letters.

In your case, you could take the ciphertext encrypted with the first alphabet, attack it as an ordinary mixed-alphabet Vig, and recover the keyword. Then you could subtract the key from the ciphertext encrypted with each of the other three alphabets, and have three ordinary substitution ciphers to solve.

The trick is that it is quite hard to crack a mixed-alphabet Vig with only 36 characters unless the key is very short, so your cipher would probably be safe against classical methods for messages of less than 144 characters. Theoretically, there should be a way to pull information from the parts of the text encrypted with the other alphabets, but I can't see one right now.

OTOH, dictionary attacks always work, if you use a keyword that's in the dictionary, and there's nothing in your system that would hinder a hill-climber. So it's vulnerable to the usual computer attacks.

One thing you might ponder. What happens if the enemy gets his hands on the plaintext of one of your messages? He'd very easily be able to retrieve the keyword and all four alphabets. If you've sent other messages using the same keyword and alphabets, they'd all be compromised. If you'd been changing the keyword daily, but keeping the same alphabets for a longer period, knowing the alphabets allows the enemy to convert messages into an ordinary Vig encrypted by just the keyword, which is easily attacked.

The standard, these days, is for a cipher from which the enemy cannot recover the key, even if he has both plaintext and ciphertext. Few of the classical ciphers could offer that protection.
When cryptography is outlawed, bayl bhgynjf jvyy unir cevinpl.
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