Course # 60475
Assignment # 3
Name : Hasan M Chowdhury
ID # 101938596
Calculation of question #
Name: hasanchowdhury
Ascii and the total: 104 + 97 + 115 + 97 + 110 + 99 + 104 + 111 + 119 + 100 + 104 +
117 + 114 + 121 = 1512
1512 mod 23 = 17
17+1=18
Question # 18
9.18 The problem illustrates a simple application of the chosen ciphertext attack. Bob
intercepts a ciphertext C intended for Alice and encrypted with Alice's public key e.
Bob want to obtain the original message M = Cd mod n. Bob chooses a random value r
less than n and computes
Z = re mod n
X = ZC mod n
t = r1 mod n
Next, Bob gets Alice to authenticate (sign) X with her private key (as in Figure 9.3),
thereby decrypting X. Alice returns Y = Xd mod n. Show how Bob can use the
information now available to him to determine M.
Solution:
Z = re mod n
X = ZC mod n
t = r1 mod n
Y = Xd mod n
Therefore, r = Zd mod n
So the computation is as follows:
tY mod n
= r-1 . Xd mod n
= r-1 . Zd . Cd mod n
= r-1 . r . Cd mod n
= Cd mod n
=M