Algorithm 12:Recipient verification of a signed message.

Input: $M_{sent},(r,s),P{U}_s$

Output: $Verifiedciphertexts$

1  $Recipient:check(r,s)areintegers\in 1,2,3,...,p-1)$;

2  $Recipient:calculatee=HASH\left(M_{sent}\right)$;

3  $Recipient:calculatez=leftmostpbitsofe$;

4  $Recipient:calculate{u}_1=e{s}^{-1}modp$;

5  $Recipient:calculate{u}_2=r{s}^{-1}modp$;

6  $Recipient:calculate(x_1,y_1)=u_1\ast G+u_2\ast P{U}_s$;

7  $Verified\leftarrow r\equiv x_{1}modp$