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Diffstat (limited to 'tex-stuff')
| -rw-r--r-- | tex-stuff/math.tex | 13 |
1 files changed, 10 insertions, 3 deletions
diff --git a/tex-stuff/math.tex b/tex-stuff/math.tex index b575d75..2d2c1f7 100644 --- a/tex-stuff/math.tex +++ b/tex-stuff/math.tex @@ -77,14 +77,21 @@ the price $p_{b_a}$ bidder $a$ is willing to pay. $\forall j: p_j < p_{j+1}$. \subsubsection{Round 1: Encrypt bid} +The message has $k$ parts, each consisting of $10$ Points plus an additional $3$ +Points for the last proof. Therefore the message is $10k*32 + 3*32 = 320k + 96$ +bytes large. + \begin{enumerate} - \item Set $b_{aj}=\begin{cases}g & \mathrm{if}\quad j=b_a\\0 & \mathrm{else}\end{cases}$ and publish $\alpha_{aj}=b_{aj}+r_{aj}y$ and $\beta_{aj}=r_{aj}g$ for each j. - \item Prove that $\forall j:(\alpha_{aj}, \beta_{aj})$ decrypts to either $0$ or $g$. - \item Prove that $\forall j: ECDL_y\left(\left(\sum_{j=1}^k\alpha_{aj}\right) - g\right) = ECDL_g\left(\sum_{j=1}^k\beta_{aj}\right)$ + \item $\forall j:$ Set $b_{aj}=\begin{cases}g & \mathrm{if}\quad j=b_a\\0 & \mathrm{else}\end{cases}$ and publish $\alpha_{aj}=b_{aj}+r_{aj}y$ and $\beta_{aj}=r_{aj}g$ for each j. + \item $\forall j:$ Prove that $(\alpha_{aj}, \beta_{aj})$ decrypts to either $0$ or $g$. + \item Prove that $ ECDL_y\left(\left(\sum_{j=1}^k\alpha_{aj}\right) - g\right) = ECDL_g\left(\sum_{j=1}^k\beta_{aj}\right)$ \end{enumerate} \subsubsection{Round 2: Compute outcome} +The message has $nk$ parts, each consisting of $5$ Points. Therefore the message +is $5nk*32 = 160nk$ bytes large. + \begin{enumerate} \item Compute and publish for each $i$ and $j$: \\[2.0ex] $\gamma_{ij}^{\times a} = m_{ij}^{+a}\displaystyle\left(\left(\sum_{h=1}^n\sum_{d=j+1}^k\alpha_{hd}\right)+\left(\sum_{d=1}^{j-1}\alpha_{id}\right)+\left(\sum_{h=1}^{i-1}\alpha_{hj}\right)\right)$ and \\[2.0ex] |