# 7CCSMCIS Cryptography and Information Security

## Coursework 3

MSc Computing and Security

What is a meet-in-the-middle attack?

In 2DES (2 keys, running run encryption twice), a meet-in-the-middle attack is where an attacker can run the ciphertext through the encrypt function for all $2^{56}$ possible $K_1$ . They can store this in a table, sorted. The attacker can then run the cipher-text through the decrypt function for all $2^{56}$ possible $K_2$

How many keys are used in triple-DES and why?

There are 2 keys used in 3DES. This is to maintain compatibility with standard DES.

Why is the middle portion of triple-DES a decryption rather than an encryption?

a

• Consider a block cipher that applies bit permutations (transpositions) to bit vectors length 4. i.e. the permutation cipher with alphabet $\mathcal{A} = \left \lbrace 0, 1 \right \rbrace$ and block length 4.
• Consider the key $K$ that transforms a bit vector of length 4 by shifiting it by one bit to the left i.e. $K$ permutes the bit order 1,2,3,4 to 2,3,4,1. The for example $E(K, 1000) = 0001$ .
• Consider $IV = 1010$ .

Use the ECB mode of operation to encrypt the plaintext $P = 101100010100101$ .

P = 101100010100101


Becomes:

P = 1011 0001 0100 101
P = 1011 0001 0100 1010

E(K, 1011) = 0111
E(K, 0001) = 0010
E(K, 0100) = 1000
E(K, 1010) = 0101

C = 0111 0010 1000 0101


We pad the last block by appending a 0 (or 1 if we like).

Use the CBC mode of operation to encrypt the plaintext $P = 101100010100101$ with $IV = 1010$ , and then decrypt it.

P = 101100010100101


Becomes:

P = 1011 0001 0100 101
P = 1011 0001 0100 1010

1. $C_1 = E(K, IV \oplus P_1) = E(K, 1010 \oplus 1011) = E(K, 0001) = 0010$
2. $C_2 = E(K, C_1 \oplus P_2) = E(K, 0010 \oplus 0001) = E(K, 0011) = 0110$
3. $C_3 = E(K, C_2 \oplus P_3) = E(K, 0110 \oplus 0100) = E(K, 0010) = 0100$
4. $C_4 = E(K, C_3 \oplus P_4) = E(K, 0100 \oplus 1010) = E(K, 1110) = 1101$
C = 0010 0110 0100 1101


Decryption:

C = 0010 0110 0100 1101

1. $P_1 = D(K, C_1) \oplus IV = D(K, 0010) \oplus 1010 = 0001 \oplus 1010 = 1011$
2. $P_2 = D(K, C_2) \oplus C_1 = D(K, 0110) \oplus 0010 = 0011 \oplus 0010 = 0001$
3. $P_3 = D(K, C_3) \oplus C_2 = D(K, 0100) \oplus 0110 = 0010 \oplus 0110 = 0100$
4. $P_4 = D(K, C_4) \oplus C_3 = D(K, 1101) \oplus 0100 = 1110 \oplus 0100 = 1010$
P = 1011 0001 0100 1010

• Consider a block cipher that applies bit permutations (transpositions) to bit vectors of length 3, i.e., $S = 3$ .
• Consider the key $K$ that transforms a bit vector of length 4 by shifting it one bit to the left, i.e. $K$ permutes the bit order 1,2,3,4 to 2,3,4,1.
• Consider $IV = 1010$ .

Use CFB mode of operation to encrypt the plaintext $P = 101100010100101$ .

S = 3, therefore split plaintext into 3s.

P = 101 100 010 100 101
IV = 1010

1. $C_1 = P_1 \oplus MSB_s(E(K, IV)) = 101 \oplus MSB_3(0101) = 101 \oplus 010 = 111$
2. $C_2 = P_2 \oplus MSB_s(E(K, C_1)) = 100 \oplus MSB_3(E(K, 0111)) = 100 \oplus MSB_3(1110) = 100 \oplus 111 = 011$
3. $C_3 = P_3 \oplus MSB_s(E(K, C_2)) = 010 \oplus MSB_3(E(K, 0011)) = 010 \oplus MSB_3(0110) = 010 \oplus 011 = 001$
4. $C_4 = P_4 \oplus MSB_s(E(K, C_3)) = 100 \oplus MSB_3(E(K, 0001)) = 100 \oplus MSB_3(0010) = 100 \oplus 001 = 101$
5. $C_5 = P_5 \oplus MSB_s(E(K, C_4)) = 101 \oplus MSB_3(E(K, 0101)) = 101 \oplus MSB_3(1010) = 101 \oplus 101 = 000$

Gives:

C = 111 011 001 101 000


Use OFB mode of operation to encrypt the plaintext $P = 101100010100101$ (with block length 4).

P = 1011 0001 0100 101
IV = 1010

1. $C_1 = P_1 \oplus E(K, IV) = 1011 \oplus E(K, 1010) = 1011 \oplus 0101 = 1110$ .
2. $C_2 = P_2 \oplus E(K, IV) = 0001 \oplus E(K, 0101) = 0001 \oplus 1010 = 1011$ .
3. $C_3 = P_3 \oplus E(K, IV) = 0100 \oplus E(K, 1010) = 0100 \oplus 0101 = 0001$ .
4. $C_4 = P_4 \oplus E(K, IV) = 101 \oplus E(K, 0101) = 101 \oplus 1010 = 000$ .

Gives:

C = 1110 1011 0001 000