Question about variations on Vigenere cipher

Question

I'm new here and by no means an expert on cryptography. I like to dabble, and one of my favorite classical ciphers is the Vigenere. I understand that the normal method of Vigenere encrypting is to add the corresponding number of the letter of the key to the number of the letter of the message, thus producing the cipher text for that particular letter. My question is, regardless of key length, is it advantageous to alter the order in which the key is applied to the message? For example, instead of moving forward through the alphabet to obtain the cipher text, what if I started off by going backwards? Or if I alternated by going forward with the first key letter, then backwards with the second, and so on. Or if I alternated by going backward with the first two key letters, then forward with the next two. Would this make it any harder to decipher the message or make it more difficult to use letter frequency analysis to obtain the key?

I can provide examples if my question isn't clear. Thank you in advance for any insight you are able to provide.

Answer 1

Welcome to Cryptography Stack Exchange!

Your variation would not make cryptanalysis significantly harder.

Stepping forward through the alphabet by $n$ steps is the same as stepping backwards through the alphabet by $26-n$ steps and vice-versa. Thus the Vigenere stage S forward (+18) is the same as the variant H backward (-8). The net effect is that the encryption is equivalent regular Vigenere encryption with a garbled codeword and the same cryptanalysis applies. For example, if we used your variant Vigenere with the codeword EXAMPLE and the direction BFBFBBB it would look like Vigenere with the codeword WXAMLPW.

Your idea is related to the "variant Beaufort" of the Vigenere cipher where encryption was done by stepping backwards and encryption by stepping forwards.