IV054 Coding, Cryptography and Cryptographic Protocols
2012 - Exercises IV.
1. Decrypt the following ciphertexts:
(a) 3534315412244543 434145114215
(b) ZGYZHS XRKSVI
(c) DH DF DJ AJ AF CG BI DH BH CI DH DH BI BF DG AF BG AJ
(d) TICTACTOECIPHER
2. Let P = {A, B, C}, K = {k1, k2, k3}, C = {A, B, C, D}.
Let pP (x) = 1
3 where x ∈ P and pK(k1) = 1
2 , pK(k2) = 1
3 , pK(k3) = 1
6 . Let the encryption function
ek(x) be defined by the following table:
a b c
k1 B C D
k2 C D A
k3 D A B
Compute in detail pC(A) and pP (b|A).
3. Complete the Playfair square
P F
E X
B C D H
K O Q
V Z
provided you know that the message Using Playfair squares is pretty simple is encrypted as ZN RK
BY AY FP PE MN NW LE MO MK LI IV WP KM IF AR.
4. For the following cryptosystems, describe a chosen plaintext attack which enables the adversary to
determine the key using only one message. This message should be as short as possible.
(a) affine cryptosystem;
(b) Vigenere cryptosystem;
(c) monoalphabetic substitution cryptosystem;
(d) transposition cryptosystem with a block length not greater than the number of symbols of the
alphabet.
5. Decrypt the following ciphertexts:
(a) AACEIINNORSSTW
(b) UOWIGXIZWIGQOSGOF
(c) SSGOZIVBCOQRBB
Hint: (a),(b)
(d) YDQUI DBHJQ HJQIH DQISH JQUDQ IHQSH KFIRR IDHFK DGSHJ QGKSH
YGGQB YIHQA IEYVA JYMJI JWGIV XQYVU MIVSJ IDQAY HJIVK HJQDH
JQSQV SQKFA JIHYH YSHKX QIJWG IVXQY VU
6. Consider the Affine Hill cryptosystem with the following encryption and decryption functions:
ek(w) ≡ k1 · w + k2 (mod p) and dk(c) ≡ k−1
1 · (c − k2) (mod p),
where w, c and k2 are column vectors of dimension n and k1 is an n-by-n matrix.
(a) Let p = 7, k1 =
1 3
2 2
and k2 =
5
4
.
(i) Encrypt the message w =
2
1
.
(ii) What is the matrix k−1
1 used for decryption?
(iii) Decrypt the message c =
3
5
.
(b) Let p = 11. Find k1 and k2 if you obtain the following plaintext-ciphertext pairs:
w1 =
5
4
, c1 =
1
8
; w2 =
8
10
, c2 =
8
5
; w3 =
7
1
, c3 =
8
7
7. (Bonus) Decrypt the following ciphertext:
2 1, 24 8, 21 16, 154 1, 154 3, 142 3, 144 7, 5 9, 84 4, 52 1, 16 1, 38 12, 25 1, 104 2, 67 3, 108 6, 22
7, 22 6, 59 1, 116 4, 37 10, 126 8, 11 1, 57 9, 78 5, 58 6, 107 3, 136 4, 143 3, 109 10, 56 2, 24 8, 24 2,
104 23, 144 10, 154 5, 147 8, 96 6, 70 12, 70 7, 151 3, 151 4.
Hint: 154.