Anonymous Asynchronous Ratchet Tree Protocol for Group Messaging

. 2021 Feb 4;21(4):1058. doi: 10.3390/s21041058

Algorithm 2 Update Group Tree

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function $U p d a t e$ ( $i, g p k_{j}, t y p e_{j}, n o d e_{j}$ )
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if $t y p e_{j} = 0$ , $p o s_{j} = i$ , otherwise $p o s_{j} \leftarrow p r g ({2, 4, 6, . . ., 2 n})$
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$n o d e_{j + 1} \leftarrow n o d e_{j}$ , $n o d e {[p o s_{j}]}_{j + 1} . s k \overset{$}{\leftarrow} Z_{q}^{*}$ , $n o d e {[p o s_{j}]}_{j + 1} . p k \leftarrow n o d e {[p o s_{j}]}_{j + 1} . s k \cdot P$
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return $p o s$ , $U p d a t e P a t h (g p k_{j}, n o d e_{j + 1}, p o s_{j})$
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end function
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function $U p d a t e P a t h$ ( $g p k_{j}, n o d e_{j}, p o s_{j}$ )
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$c u r \leftarrow n o d e {[p o s]}_{j + 1}, p a t h_{j} \leftarrow []$
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while current node $c u r$ is not the root do
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the $s k$ of $c u r$ ’s parent is $t (c u r . s k \cdot c u r . s i b l i n g . p k)$ , the $p k$ of $c u r$ ’s parent is its $s k \cdot P$
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$p a t h_{j} . p u s h (c u r . p k)$ , let $c u r$ move to the parent of $c u r$
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end while
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return $p a t h_{j}, c u r$
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end function
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function $U p d a t e G p k$ ( $p o s_{j}, g p k_{j}, p a t h_{j}, n o d e_{j}$ )
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$t m p \leftarrow n o d e [p o s_{j}]$
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while $p a t h_{j} \neq []$ do
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$t m p . p k \leftarrow p a t h_{j} . p o p ()$ , $t m p \leftarrow t m p . p$
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end while
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return $t m p$
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end function