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I have a question for a class of secure communication, but I have no idea about how to proceed in order to answer it. I'll be very grateful to whom replies to me.

Assuming that brute force attack with 80bit keys is infeasible, let's compare the security of the Vigenere cipher with the security of the monoalphabetic cipher in the ciphertext-only attack model considering the encryption of 10 character messages with randomly chosen secret keys for each encryption.

  • Which cipher among Vigenere and monoalphabetic provides better security when the security criterion is only based on the size of the key space ( brute force attack )?

  • Is there any other consideration for which the answer would be different than in a)?

  • Can any of these ciphers provide absolute security? if so give a precise definition of the configuration that would allow for it.

Hint: $2^{80}=1.2 \cdot 10^{24}$ ; $26^{10}=1.4 \cdot 10^{14}$ ; $26! = 4 \cdot 10^{26}$

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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 help for Vigenère (at least not without additional methods). With that in mind Vigenère could be considered more secure than simple substitution. In fact: both are not really secure, don't rely on them.

c) Vigenère with a key that is exactly as long as the plain text could be considered absolutely secure. But then again, it would be highly unpractical. :-)

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