Vigenère and transposition:

Suppose a Vigenère cipher is constructed with a key that is three letters long. The result of this first encryption is further encrypted with a Vigenère cipher, with another three-letter key.

(a) How many possible keys are embodied in the final cipher text?

(b) Suppose that after the first Vigenère encipherment, the resulting text is transformed by a transposition code that reads the text into a three by three matrix row by row and reads it out column by column after the columns are permuted. Effectively how many possible keys are embodied in the resulting double-encrypted cipher text?

(c) Suppose that after the Vigenère encryption and the transposition encryption, the text is subjected to another Vigenère cipher with a key of length 3. How many possible keys are embodied in this final result?

(d) Suppose that after the first Vigenère cipher, the transposition cipher, and the second Vigenère cipher, the transposition is reversed (perhaps because the transposition key is discovered). The result is then equivalent to a compound Vigenère cipher. What is the length of the keyword in this compound Vigenère cipher?

(e) How many possible keys are embodied in this compound Vigenère cipher?