Algorithm 1. Processing of SUBMSG Message

/*Upon a cluster node vx receiving a SUBMSG message from the CH node vIDi*/ flg = false; // flg records whether the accusation in the SUBMSG message is true. if (rcd = 0)  if (the z nodes to be substituted did not send their kjP to vIDi) flg = true; else if (rcd = 1)  if (the z nodes to be substituted did not provide their σj or provided incorrect σj) flg = true; if (flg = false)  Perform Algorithm 3 to substitute vIDi; else {  for (each node vIDm to be substituted) {   TVIDm = TVIDm − 0.2;   if (TVIDm < TTv && NAIDm < Nc/2) {    Broadcast an ALARM message for vIDm;    vx, and each cluster node that hears the ALARM message, executes Algorithm 2;   }  }//end for  if (the number of trusted non-participating cluster nodes < z) {   Fail_flag = true; // Report generation fails.   Cancel the timer TRG;  }  else {   Select the z trusted non-participating cluster nodes, whose IDs are closer to hv than the others, to participate in report generation;   if (vx is a new participating node) {    Pick kx in [1, q − 1] and send kxP to vIDi;    Compute σx after receiving X(R);    Send σx to vIDi;   }   else if (vx is a participating node that has not been substituted) {    Recompute σx after receiving X(R);    Send σx to vIDi;   }  } }