Due Saturday, June 15, 8:00 PM

Problem 1 (5 points)

Introduction:

A historical affine cipher is defined as follows:

1. Each letter of the message M, M_i, is encrypted separately to the corresponding letter of the ciphertext C_i

2. A letter M_i is first encoded to the corresponding number m_i according the following encoding/decoding table.

3. The ciphertext letter code, c_i, is obtained from the message letter code, m_i, using the following equation

c_i = k₁ * m_i + k₀  mod 26

where k₁ and k₀ are the elements of the cipher key K=(k₁, k₀),  0<= k₀, k₁ <=25, gcd (k₁, 26)=1..

4. The ciphertext letter C_i is obtained from the ciphertext letter code, c_i, using the same encoding/decoding table which was used in step 2.

Questions:

1. What is a total number of all possible keys in this cipher?

2. Decrypt the following message encrypted using the affine cipher with the key k₁=11, k₀=17. Ciphertext = “XFC”.

3. Break the affine cipher by computing the cipher key (k₁, k₀) based on the knowledge that the most frequent letter of the ciphertext is 'B', and the second most frequent letter of the ciphertext is 'U' (you must not use exhaustive key search).

Hint: An average frequency of letters in long English texts is given by the following frequency table.

Problem 2 (5 points)

Compute the bits number 32 and 33 at the output of the first round of the DES decryption, assuming that the ciphertext block is composed of all ones and the external key is composed of all ones.

Problem 3 (5 points)

X_a = 2001, K_a = 4567

X_b = CDEF, K_b = 6543

X_c = 8899, K_c = 23CB

X_d = 0002, K_d = 0000

Hint: Note that all values can be computed without using a calculator by applying the following formula:

ab mod (2¹⁶+1) º ab mod 2¹⁶ – ab div 2¹⁶ (mod 2¹⁶+1)

Problem 4 (5 points)

Given below are the internal keys used during the first full round of IDEA during encryption. What are the values of the corresponding internal keys used during decryption (these keys are computed based on the listed below internal keys and are used during the last round and the output transformation of the decryption):

K_a = 0008

K_b = ABBA

K_c = FEFE

K_d = 0000

K_e = 2345

K_f = 1111

Problem 5 (5 points)

Stallings, Problem 6.12