i am trying to figure out how Asmuth-Bloom secret sharing works and followed the example on wikipedia and replaced it with own numbers.
Namely, i used:
$m_0 = 13, m_1=45, m_2=46, m_3=47, m_4=49$
I've been able to construct the shares
$s_1 = (17, 45), s_2 = (2, 46), s_3 = (34, 47), s_4=(6,49)$
I then result in $x \equiv 692 \mod 46*47*48$ which is correct, since $S = 692 \equiv 3 \mod 13$ which is my secret.
However, i wonder where $m_0 = 13$ is coming from for the final secret reconstruction, it seems like it is not explained anywhere. The only thing i could find is this stating it would be "kept secret by the dealer unless stated otherwise".
Is $m_0$ just either a public parameter? Or do i need the dealer to store it "secretly" (which would require the dealer to reconstruct the secret)?