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It is helpful to first define what a perfectly secure block cipher is. In the ideal case there are n different keys where each key uniquitely indexes one of the permutations mapping {0,1}^k to {0,1}^k. In this case we have n=(2^k)! Possible permutations/keys. Perfect security typically means that no information is revealed at all. Not even against an ...


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How many non-trivial*, interesting perfect secrecy systems are there other than the one-time-pad? Infinitely many. Let $\mathbb G$ be a group (written multiplicatively). Then $\operatorname{KeyGen}(1^n)=k\stackrel{\$}{\gets}\mathbb G^n$, that is the key is a vector of $n$ independently random group elements. $\operatorname{Enc}(k,m):\mathbb G^n\times \...


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