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Hmm, first about your type of encryption: ...for a Caesar Cipher that encrypts each letter with a different integer as a shift... This actually describes a VigenĂ¨re Cipher. The classic approach to break this kind of cipher is by Determine the key length first Break the underlying Caesar Cipher for each letter of the key. To follow this route a ...

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I don't think there is a name for this special kind of property, but it is a clear hint for polyalphabetic substitution ciphers. It is a special kind of polyalphabetic substitution cipher. The first alphabet is a normal random key, while each successive alphabet is generated by a one-character right shift of the previous alphabet. As a result there are as ...

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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 VigenĂ¨re 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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To prove an encryption scheme to be perfectly secure, we need to prove: $$P[M=m|C=c]=P[M=m]$$ where $c$ is a cipher text and $m$ is a plain text. From Bayes theorem, we have: $$P[M=m|C=c]=\frac{P[C=c|M=m] \cdot P[M=m]}{P[C=c]}$$ It is noteworthy that: $$P[C=c|M=m]=P[K=k]$$ where $K$ is the key space and $k$ is a particular key. Now: P[C=c]=P[K=k]=\frac{...

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