Suppose we are using the RSA public scheme to generate dual signature in the SET protocol. Given p = 7, q = 17, n = 119, the public key of the gateway is 5, the public key of the buyer is 11. We use a simple way to calculate H(m), i.e., H(m) = m mod 64, and HH(mm1)||HH(mm2), i.e., HH(mm1)||HH(mm2) = (HH(mm1) + HH(mm2)) mod 64. Suppose message size is 6 bits, m1= 10, m2 = 15. The takes two inputs with 6 bits. (a) What is the private key for the gateway and buyer respectively? (6') (b) Suppose (mm2, HH(mm2)}PPPPGG can be represented by {mm2}PPPPGG and {HH(mm2)}PPPPGG. What is the message sent to the merchant? Calculate the message value for each item. (10') (c) Illustrate the process for the merchant to do the authentication, using the received data. (4')