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report/src/sections/04-Approach.tex

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@@ -244,7 +244,7 @@ \subsection{Shuffle security}\label{subsec:approach-shuffle-security}
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The second event that can occur is related to the fact that every shuffle distributes the possibility of a certain ciphertext to be in a certain slot.
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So, if a shuffle contains a lot of ciphertexts with a larger than average chance of containing a certain ciphertext, then that would imply that there is a higher chance of that ciphertext being in that slot.
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It is theoretically possible to find an optimal number of shuffles, given the shuffle size, and a number of adversarial shufflers, to guarantee that the shuffle is secure.
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It is theoretically possible to find a number of shuffles, given the shuffle size, and a number of adversarial shufflers, to guarantee that the shuffle is secure.
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For any $0 < \delta < 1/3$, if $T \geq 20 n / k \ln(n/\delta) + \beta $ and $ k \geq 256 \ln^2(n/\delta)(1 - \alpha/n)^{-2}$.
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If $T$ and $k$ are chosen such that the above two conditions are met, then the protocol is an $(\epsilon , \delta)$-secure $(T,n,k)$-shuffle in the presence of a $(\alpha, \beta)$-adversary where $\epsilon = 2/(n-\alpha)$.
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