Is the following scheme private? By private i mean an untrusted aggregator (UA) cannot reveal anything other then an aggregate function output on plaintext data
Each party holds a secret key $k_i$ and data $d_i$. It sends to the aggregator $d_i H(r)^{k_i}$. $H$ is a hash function that maps elements to a group $N$ in which $H(r)^S \equiv 1 mod {N}$ Lets say a trusted dealer(TD) for two parties sends to the untrusted aggregator $H(r)^{S-k_1}$ and $H(r)^{S-k_2}$ and UA wants to learn the multiplication of the data of those parties. Then UA computes
$$d_1 H(r)^{k_1}d_2 H(r)^{k_2}H(r)^{S-k_1}H(r)^{S-k_2} =d_1d_2H(r)^{2S}=d_1d_2H(r)^{S^2}=d_1d_2$$