Q10.7 in the textbook (modified): Consider the Elgamal signature scheme with Bobs private key K_pr=d=67 and the corresponding public key K_pub =(p,alpha,beta)=(97,23,15). 1. Calculate the Elgamal signature (r,s) and the corresponding verification for a message from Bob to Alice with the following messages x and ephemeral keys k_E: a. x=17.0 and k_E=31.0: r= mod 97; s= mod 96; and for the verification: t= mod 97; alpha^x= mod 97. Is the signature verified? Yes (Y) or No (N) b. x=17 and k_E=49: r= mod 97; s= mod 96; and for the verification: t= mod 97; alpha^x= mod 97. Is the signature verified? Yes (Y) or No (N) 2. You receive two alleged messages x1,x2 with their corresponding signatures (ri,si) from Bob. Did the message (x1,r1,s1)=(22,37,33) originate from Bob? Yes (Y) or No (N)? , repeat for (x2,r2,s2)=(82,13,65) .

Problem 10.10 in the textbook (modified): Consider the Elgamal signature scheme with Bob's private key K_pr=d=67 and the corresponding public key K_pub = (p,alpha, beta )=(97,23,15). 1. Calculate the Elgamal signature (r,s) and the corresponding verification for a message from Bob to Alice with the following messages x and ephemeral keys k : a. x=17.0 and k_E=31.0:r=mod97;s=mod96; and for the verification: t=mod97; alpha x=mod97. Is the signature verified? Yes (Y) or No (N) b. x=17 and k_E=49:r=mod97;s=mod96; and for the verification: t=mod97; alpha x=mod97. Is the signature verified? Yes (Y) or No (N) 2. You receive two alleged messages x1,x2 with their corresponding signatures (ri,si) from Bob. Did the message (x1,r1,s1)=(22,37,33) originate from Bob? Yes (Y) or No (N)? repeat for (x2,r2,s2)=(82,13,65)