This problem provides a numerical example of encryption using a one-round version of DES. We start with the same bit pattern for the key K and the plaintext, namely:

Binary notation: 0000 0001 0010 0011 0100 0101 0110 01111000 1001 1010 1011 1100 1101 1110 1111

Hexadecimal notation: 0 1 2 3 4 5 6 7 8 9 A B C D E F

a. Derive K1 , the first-round sub key.

b. Derive, L0R0

c. Expand R0 to get, E[R0] where E[.] is the expansion function of Table 3.2.

d. Calculate A = E[R0] ⊕ K1 .

e. Group the 48-bit result of (d) into sets of 6 bits and evaluate the corresponding

S-box sub stitutions.

f. Concatenate the results of (e) to get a 32-bit result, .

g. Apply the permutation to get P(B) .

h. Calculate R1 = P(B) ⊕ L0 .

i. Write down the cipher rtext.

Table 3.2.

(a) Initial Permutation (IP)
58	50	42	34	26	18	10	2
60	52	44	36	28	20	12	4
62	54	46	38	30	22	14	6
64	56	48	40	32	24	16	8
57	49	41	33	25	17	9	1
59	51	43	35	27	19	11	3
61	53	45	37	29	21	13	5
63	55	47	39	31	23	15	7

 

(b) Inverse Initial Permutation (IP–1)
40	8	48	16	56	24	64	32
39	7	47	15	55	23	63	31
38	6	46	14	54	22	62	30
37	5	45	13	53	21	61	29
36	4	44	12	52	20	60	28
35	3	43	11	51	19	59	27
34	2	42	10	50	18	58	26
33	1	41	9	49	17	57	25

 

(d) Permutation Function (P)

16	7	20	21	29	12	28	17
1	15	23	26	5	18	31	10
2	8	24	14	32	27	3	9
19	13	30	6	22	11	4	25