Question about variations on Vigenere cipher
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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 &quot;variant Beaufort&quot; of the Vigenere cipher where encryption was done by stepping backwards and encryption by stepping forwards.