1. Show that if someone discovers the value of k used in the ElGamal signature scheme, then a can also be determined. 2. Suppose that (m,r,s) is a message signed with the ElGamal signature scheme. Choose with gcd(h,p−1) = 1 and let √₁ = 7½ (mod p). Let 5₁ = s₁h¯¹¹ (mod p − 1). O.6. EXERCISES 253 (a) Find a message m₁ for which (m₁, T₁, s₁) is a valid signature. 11 (b) This method allows Eve to forge a signature on the message m₁. Why is it unlikely that this causes problems?