|
@@ -76,7 +76,7 @@ independent aggregation of the stakes, meaning the property of a leader winning
|
|
|
$1-\phi(\sum_{i}\sigma_i)=1-(1+(1-f)^{\sigma_i})=-(1-f)^{\sum_{i}\sigma_i}$,
|
|
$1-\phi(\sum_{i}\sigma_i)=1-(1+(1-f)^{\sigma_i})=-(1-f)^{\sum_{i}\sigma_i}$,
|
|
|
the joint "one minus probability" of all the stakes (each with probability $\phi(\sigma_i))$
|
|
the joint "one minus probability" of all the stakes (each with probability $\phi(\sigma_i))$
|
|
|
winning aggregated winning the leadership
|
|
winning aggregated winning the leadership
|
|
|
-$\prod_{i}^{n}(1-\phi(\sigma_i))=-(1-f)^{\sum_{\sigma_i}}$
|
|
|
|
|
|
|
+$\prod_{i}^{n}(1-\phi(\sigma_i))=-(1-f)^{\sum_i(\sigma_i)}$
|
|
|
thus:
|
|
thus:
|
|
|
$$ 1-\phi(\sum_{i}\sigma_i) =\prod_{i}^{n}(1-\phi(\sigma_i)) $$
|
|
$$ 1-\phi(\sum_{i}\sigma_i) =\prod_{i}^{n}(1-\phi(\sigma_i)) $$
|
|
|
|
|
|
|
@@ -104,7 +104,8 @@ note that $(\frac{1}{v_{max}})^{n-1} < 1, V>1$, thus competing with single coin
|
|
|
$$y<2^{\frac{l}{v}}\Sigma$$ for example for a group order or l=24 bits, and maximum value of $v_{max}=2^{10}$, then lead statement:
|
|
$$y<2^{\frac{l}{v}}\Sigma$$ for example for a group order or l=24 bits, and maximum value of $v_{max}=2^{10}$, then lead statement:
|
|
|
$$y<2^{14}\Sigma$$
|
|
$$y<2^{14}\Sigma$$
|
|
|
|
|
|
|
|
-
|
|
|
|
|
|
|
+### pairing leader selection independent aggregation function
|
|
|
|
|
+TODO
|
|
|
|
|
|
|
|
## Leaky non-resettable beacon
|
|
## Leaky non-resettable beacon
|
|
|
|
|
|
mohab