We consider the Diffie–Hellman key exchange scheme with certificates. We have a system with the three users Alice, Bob a

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We consider the Diffie–Hellman key exchange scheme withcertificates. We have a system with the three users Alice, Bob andCharley.The Diffie–Hellman algorithm uses p=61 and alpha=18. The threesecret keys are a=11, b=22 and c=33. The three IDs are ID(A)=1,ID(B)=2 and ID(C)=3. For signature generation, the Elgamalsignature scheme is used. We apply the system parameters p`=467,d`=127, alpha`=2 and ß. The CA uses the ephemeral keys k_E=213, 215and 217 for Alice’s, Bob’s and Charley’s signatures, respectively.(In practice, the CA should use a better pseudorandom generator toobtain the k_E values.)To obtain the certificates, the CA computesx_i=4×bi+ID(i) (where bi is the public key of person i) anduses this value as input for the signature algorithm. (Givenx_i,ID(i) is then ID(i)=x_i mod 4.)
Verify all three certificates: t_1=____ ; t_2=____; t_3=____