Block-ciphers

Question 1

Practical block ciphers consist of several rounds.

a) What do we achieve by using rounds in block ciphers?
b) Each round of a block cipher uses a key that is obtained from the master key. What is the name of the process of obtaining these round keys?

Question 2

Practical block ciphers use confusion and diffusion to make cryptanalysis difficult. They also consist of several rounds.

a) Define confusion. How do we achieve it?
b) Define diffusion. How do we achieve it?
c) What do we achieve by using rounds in block ciphers?

Question 3

a) Many block ciphers contain non-linear Boolean tables, so-called S-boxes. What do we achieve with them?
b) Block ciphers also contain bit-permutations. What is their role?
c) Why are practical block ciphers composed of several rounds?
d) What is the key schedule of a block cipher? Is it a good idea to use only linear functions in the key schedule? Why?

Question 4

Explain the output feedback mode of operation of block ciphers.

Question 5

For a fixed key, the encipherment transformation of a block cipher is the following:

010

001

100

010

110

111

000

011

Can we decipher in such a cipher system? If so, determine the decipherment transformation.

Question 6

a) How do we achieve confusion in block ciphers?
b) Why must every block cipher be a permutation of 2ⁿ entries where n is the block length?
c) Explain the cipher block chaining mode of operation of block ciphers.

Question 7

Explain the counter mode of operation of block ciphers.

Question 8

a) Explain the difference between Feistel-type block ciphers and SubstitutionPermutation networks. (5 points)
b) Explain the counter mode of operation of block ciphers. (10 points)

Question 9

a) What is the perfect block cipher? Why is such a cipher impractical?
b) How many rounds are needed in a Feistel-type block cipher to ensure non-linear transformation of all the input bits? Why?
c) Explain the cipher block chaining.

Question 10

Find the linear complexity, the initial state and the feedback polynomial of the minimal LFSR that generates the sequence S=1100101 in GF(2), by means of the BerlekampMassey algorithm. Draw the LFSR after processing each bit of S. The Berlekamp-Massey algorithm is given below:

Answer 10

IMT4552+Cryptology2+09august2016.pdf

Question 11

a) Check whether the polynomial f (x) + x 3 + x 2 + 1 with coefficients in GF(2) is irreducible.
b) Check whether the polynomial f (x) — + x 3 + 1 with coefficients in GF(2) is primitive.

Answer 11

IMT4552+Cryptology2+09august2016.pdf

Question 12

Given the irreducible polynomial f (x) = 1 + x + x 2 + x 3 + x 5 , with coefficients in GF(2), the polynomials with coefficients in GF(2) a(x) = 1 and b (x) = x4 + 1, design the S-box F (x) = a(x)x d + b(x) such that d is a Gold’s function d = 2 k + 1, (n, k) — 1, 1 k m, n = 2m + 1, n = deg f (x). Set k=l. What is the non-linear order of each Boolean function realized by the obtained S-box?

Answer 12

IMT4552+Cryptology2+09august2016.pdf

Question 13

Compute for the following S-box:

Addr.01234567

Cont.52706413

a) The following elements of the linear approximation table: (0,2), (2,4).

The following elements of the difference distribution table: (1,7), (4,6)

Answer 13

IMT4552+Cryptology2+09august2016.pdf

Question 14

Find the linear complexity, the initial state and the feedback polynomial of the minimal LFSR that generates the sequence S—OI 1 101 in GF(2), by means of the BerlekampMassey algorithm. Draw the LFSR after processing each bit of S, The Berlekamp-Massey algorithm is given below

Answer 14

IMT4552+Cryptology2+07januar2016.pdf

Question 15

Check whether the polynomial f (x) = x 5 + x 3 + 1 with coefficients in GF(2) is primitive. Hint: try irreducibility first and then, iff(x) is irreducible, check the conditions of the Alanen-K-nuth-Herlestam theorem.

Answer 15

IMT4552+Cryptology2+07januar2016.pdf

Question 16

Given the ilTeducible polynomial f (x) = 1 + x 2 + x 3 +x 4 + x 5 with coefficients in GF(2), the polynomials with coefficients in GF(2) a(x) = 1 and b(x) = x3 + 1, design the S-box F (x) = a(x)x d + b(x) such that dis a Gold’s function d = 2 k + 1, (n, k) — 1, 1 k m, n = 2m + 1, n = deg f (x). Set k=2. What is the non-linear order of each Boolean function realized by the obtained S-box?

Answer 16

IMT4552+Cryptology2+07januar2016.pdf

Question 17

Compute for the following S-box:

Addr.O1234567

Cont.21034675

a) The following elements of the linear approximation table: (1 ,2), (3,3).
b) The following elements of the difference distribution table: (1,3), (253)

Answer 17

IMT4552+Cryptology2+07januar2016.pdf

Question 18

a) Compute the greatest common divisor of the polynomials f (x) = x 4 + x2 + x + 1 and g(x) = x 2 + 1 with coefficients in GF(2).
b) Check whether the polynomial f (x) = x4 + x 2 + x + 1 with coefficients in GF(2) is irt•educible.
c) What is the reciprocal polynomial of the polynomialf(x) = x 4 + x + 1?

Answer 18

IMT4552+Cryptology2+inkl+l_prcent_F8sningsforslag+14mars2016.pdf

Question 19

Given the irreducible polynomial with coefficients in GF(2), f (x) = 1 + x 2 + x 5 , the polynomials with coefficients in GF(2) a(x) = 1 and b(x) = x4 + x + 1, design the Sbox F (x) = a(x)x d + b(x) such that dis a Gold’s ftnction d = 2 k + 1, (n, k) 1 k m, n = 2m -k 1, n = deg f (x). Set k=l. What is the non-linear order of each Boolean function realized by the obtained S-box?

Answer 19

IMT4552+Cryptology2+inkl+l_prcent_F8sningsforslag+14mars2016.pdf

Question 20

Check whether the polynomial f (x) — x 5 + x 2 + 1 with coefficients in GF(2) is irreducible.

Answer 20

IMT4552+Cryptology2+16+mars+2015.pdf

Question 21

Given the irreducible polynomial with coefficients in GF(2), f (x) = 1 + x 3 + x 5 , the polynomials with coefficients in GF(2) a(x) = 1 and b(x) = x 2 + 1, design the S-box F (x) = a(x)x d + b(x) such that dis a Gold’s function d = 2 k + 1, (n, k) = 1, 1 k m, n = 2m + 1, n = deg f (x). Set k=2. What is the non-linear order of each Boolean function realized by the obtained S-box?

Answer 21

IMT4552+Cryptology2+inkl+l_prcent_F8sningsforslag+14mars2016.pdf

Question 22

Compute for the following S-box:

Addr.01234567

Cont.37o24615

a) The following elements of the linear approximation table: (1, 1), (4,3).
b) The following elements of the difference distribution table: (4,7), (2,3)

Answer 22

IMT4552+Cryptology2+16+mars+2015.pdf