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a) The question seems to be about a comparison of the size of the key spaces. The hint already shows the key spaces for Vigenère with a 10-letter key ($26^{10}$) and for simple substitution ($26!$). Simple substitution has the much bigger key space. b) Using frequency analysis simple substitution is much easier to solve. Basic frequency analysis does not ...

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The first thing you should do is estimate the key length. While you may be able to do this using Kasiski examination, in this modern era of computers I very much recommend instead using the index of coindicence, which you can compute very easily, e.g. with this Python program: import sys msg = sys.stdin.read() # read ciphertext from standard input for ...

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AFAIK vigenere cipher is a plain subsitution algorithm with arbitrary key length, destroying statistical patterns (f.e. of natural languages) but not conducting any transposition. Btw. a classic approach to crack a vigenere cipher is the Kasiki-Test (https://en.wikipedia.org/wiki/Kasiski_examination) which might give you information reagrding the key ...

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