* Problem 5 (20 points) * Here is a variation of the ElGammal signature scheme SETUP FOR ALICE. Alice chooses: a large prime p with primitive root g . a function f : Zp Zp-1 * a Zp and b -g" mod p To sIGN A MESSaGE m, Alice: Chooses k E Z,_1 and computes: p, g publioc f public a private, b public ran (mod p)s(m -f(r)a) (mod p - 1) Sends (m,r,s) to Bob To veriF Y THE SIGNATURE, Bob checks that v1 = v2 , where: v1-b (mod p) v2=g" (mod p) (a) Show that if the protocol is followed, the verification succeeds. (b) Suppose Alice is lazy and chooses f(x) = 0 as her function Show that for any given message mi, Eve can find find values of k, r, and s so that (mi,r,s) passes the verification check, i.e., she can forge Alice's signature * Problem 5 (20 points) * Here is a variation of the ElGammal signature scheme SETUP FOR ALICE. Alice chooses: a large prime p with primitive root g . a function f : Zp Zp-1 * a Zp and b -g" mod p To sIGN A MESSaGE m, Alice: Chooses k E Z,_1 and computes: p, g publioc f public a private, b public ran (mod p)s(m -f(r)a) (mod p - 1) Sends (m,r,s) to Bob To veriF Y THE SIGNATURE, Bob checks that v1 = v2 , where: v1-b (mod p) v2=g" (mod p) (a) Show that if the protocol is followed, the verification succeeds. (b) Suppose Alice is lazy and chooses f(x) = 0 as her function Show that for any given message mi, Eve can find find values of k, r, and s so that (mi,r,s) passes the verification check, i.e., she can forge Alice's signature