Representative Ring Signature Algorithm Based on Smart Contract

. 2022 Sep 8;22(18):6805. doi: 10.3390/s22186805

Algorithm 1 Ring Signature
Input: $p k [n - 1], t$ Output: $\partial$
1	$η = v / n$
2	$p k_{s}, s k_{s} \leftarrow K e y G e n ();$
3	$p k [n] \leftarrow a p p e n d (p k [n - 1], p k_{s});$
4	$I \leftarrow G e n K e y I m a g e (p k_{s});$
5	$⊳ t h e i n i t i a t o r s t a r t s s i g n i n g$
6	$u \leftarrow r a n d . I n t ()$ ;
7	$L_{s} = u * G$
8	$R_{s} = u * H_{0} (p k_{s})$ ;
9	$c [s + 1] = H_{1} (m, L_{s}, R_{s});$
10	$⊳ t h e p a r t i c i p a n t s s t a r t s i g n i n g$
11	$f o r i = 1; i < n; i + + d o$
12	$i n d e x = (s + i) m o d n$ ;
13	$s [i] = r a n d . I n t ()$ ;
14	$s [i n d e x] = s [i]$ ;
15	$L_{i} = s_{i} * G + c_{i} * p k_{i}$ ;
16	$R_{i} = s_{i} * H_{0} (p k_{i}) + c_{i} * I$ ;
17	$c [i + 1] = H_{1} (m, L_{i}, R_{i})$ ;
18	$i f i = = n - 1 t h e n$
19	$c [s] = c [i]$
20	else
21	$c [(i n d e x + 1) m o d n] = c [i];$
22	end if
23	end for
24	$s [s] = u - c [s] * s k_{s}$ ;
25	$\partial = (m, I, η, c [0], s [0], \dots, s [n - 1])$ ;
26	$R e t u r n \partial$ ;