Algorithm 4 Verify

Input: $pp$, e, and $\mu$ Output: Accept or Reject   1:Verifier first checks: if $\left|\right|e_2\left|\right|>T$ then   2:   Rejects   3:else Continues   4:If $\left|\right|e_2{\left|\right|}_{\infty }\ge q/4$ then   5:   Rejects   6:else Continues   7:If $e_1=H_4(X+A{e}_2-a_{I{D}_i}{e}_{1}modq,U)$   8:   Accepts