Suppose there is a set $P=\{p_1, p_2, ..,p_l\}$ of stock buyers who can make commitments to a share $s_i$ in a set $S=\{s_1,s_2,...,s_m\}$ of shares for an amount $a_i$ in a set $A=\{a_1,a_2,...,a_n\}$. They can make commitments only till a certain time period, say $T$. But people in this group are nasty and will try to break the scheme. They may send wrong commitments, may commit to shares not in S or may not open their commitments later.
The commitments are provided to a person $\mathcal{B}$.
Intent of $\mathcal{B}$ is to find, after time $T$, the total amounts commited to each individual share $s_i$ in $S$ without knowing which person in $P$ commited to which share in $S$. $\mathcal{B}$ wants to ignore (and may be report) any incorrect commitment or the ones which are not opened even after expiry of time $T$.
I thought Pederson commitments can be used here since they have homomorphic additive property. But, I have few queries.
How can we do homomorphic addition for individual shares in $S$?
When we homomorphically add two commitments, we assume they are correct and will be opened later. But, in this case, people in $P$ may not do any of them. How to tackle this part?
Or, should I look for some other commitment scheme?
