Algorithm 2 Symmetric DC-Nets with Shamir’s Secret Sharing executed by user $u_k$.

Input: Users $u_i$ for $i=1,...,n$ with $i\ne k$, message $m_k$. Output: Message $m_{k,out}$, the message share transmitted for this user.  1: Split $m_k$ into n parts $m_{k,i}$ for $i=1,...,n$ with $i\ne k$ using a Secret-Sharing scheme.  2: Establish shared random secrets $s_{k,i}$ for each user $u_i$, with $i\ne k$ like the original DC-Net.  3: Calculate $M_{k,i}=m_{k,i}+{\sum }_{j=1,j\ne k}^n{s}_{k,j}$ for $i=1,...,n$.  4: Send $M_{k,i}$ for $u_i,\forall i\in \{1,...,n\}\setminus \left\{k\right\}$.  5: Receive $M_{i,k}$ from $u_i,\forall i\in \{1,...,n\}\setminus \left\{k\right\}$.  6: Calculate $m_{k,out}={\sum }_{j=1}^n{M}_{i,k}$.  7: Send $m_{k,out}$ to all participants in the network.  8: Reconstruct $m_{out}$ after receiving $k-1$ other shares.