CS 463/563: Cryptography for Cyber Security
Fall 2021
Homework #9: Due: November 7, 2021
Points: 20
Q1. [Points 7] RSA Signature Scheme (page 265 in the textbook): Given the following table describing
the procedure for Alice to send a signed message with RSA signature to Bob, calculate the unknown
entities and verify that Bob has received the correct message sent by Alice.
Alice
Bob
Chooses p=17, q =47
Compute n=p*q=
Compute ?(n)=
Choose e=11
Compute d = e-1 mod ?(n)=
Compute
Public key (e,n) =
Private key (d,n) =
Send Public key (e,n) to Bob:
Receives Aliceàpublic key (e,n):
Message to send is m=6
Computes signatures s for m = md mod n =
Send (m,s) to Bob:
Receives (m,s):
Compute m: se mod n =
Verifies if m=m‘2. [Points 7] Elgamal Signature Scheme (page 270-272): Given the following table describing the
procedure for Alice to send a signed message with Elgamal signature to Bob, calculate the unknown
entities and verify that Bob has received the correct message sent by Alice.
Alice
Bob
Chooses p=17
Chooses a primitive element ?=7
Choose a random integer d=6
Compute ? = ?d mod p =
Public key is kpub = (p, ?, ?) =
Private key is kpr = d =
Send Public key kpub = (p, ?, ?) to Bob:
Receives Aliceàpublic key kpub = (p, ?, ?)=
Choose an ephemeral key KE = 7
Message to send is m=6
Computes signatures (s,r) for m
r= ?KE mod p =
Compute KE-1 mod (p-1) =
s= (m-d*r)* KE-1 mod (p-1) =
Send (m, (r,s)) to Bob:
Receives (m, (r,s)) =
Compute t = ?r * rs mod p =
Verifies if t = ?m mod p =
Q3 [Points 6] Compute CBC-MAC (pages 325-526 in textbook) for a message of 24 bits, ø9ABC(in
Hexa). Assume a block size of 8 bits with an IV=F5 (hexa) and key = D4 (hexa).
Assume the encryption (and decryption) to be as follows: If plaintext is LT||RT and the key is LK||RK,
where LC, RC, LT, and RT are each 4 bits, then ciphertext= LC||RC where LC=LK XOR RT;
and RC = RK XOR LT; Plaintext and ciphertext are each 8 bits. Similarly, to decrypt ciphertext, we
perform exactly the reverse operation where LT=RC XOR RK and RT = LC XOR LK.
(Hint: Divide the message into blocks of 8 bits each; XOR each block with the previous cipher output;
then encrypt this with the key. For the first block, XOR it with IV. Details in pages 325-326 Ch.12 of the
textbook)
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