Cryptography: Theory and Practice:The Data Encryption Standard

Cryptography: Theory and Practice
by Douglas Stinson
CRC Press, CRC Press LLC
ISBN: 0849385210   Pub Date: 03/17/95  

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Finally, we need to describe the computation of the key schedule from the key K. Actually, K is a bitstring of length 64, of which 56 bits comprise the key and 8 bits are parity-check bits (for error-detection). The bits in positions 8, 16, . . . , 64 are defined so that each byte contains an odd number of 1’s. Hence, a single error can be detected within each group of 8 bits. The parity-check bits are ignored in the computation of the key schedule.

1.  Given a 64-bit key K, discard the parity-check bits and permute the remaining bits of K according to a (fixed) permutation PC-1. We will write PC-1 (K) = C₀D₀, where C₀ comprises the first 28 bits of PC-1(K) and D₀ the last 28 bits.

2.  For i ranging from 1 to 16, compute

and K_i = PC-2(C_iD_i). LS_i represents a cyclic shift (to the left) of either one or two positions, depending on the value of i: shift one position if i = 1, 2, 9 or 16, and shift two positions otherwise. PC-2 is another fixed permutation.

The key schedule computation is depicted in Figure 3.3.

The permutations PC-1 and PC-2 used in the key schedule computation are as follows:

PC-1
57	49	41	33	25	17	9
1	58	50	42	34	26	18
10	2	59	51	43	35	27
19	11	3	60	52	44	36
63	55	47	39	31	23	15
7	62	54	46	38	30	22
14	6	61	53	45	37	29
21	13	5	28	20	12	4

Figure 3.3  Computation of DES key schedule

PC-2
14	17	11	24	1	5
3	28	15	6	21	10
23	19	12	4	26	8
16	7	27	20	13	2
41	52	31	37	47	55
30	40	51	45	33	48
44	49	39	56	34	53
46	42	50	36	29	32

We now display the resulting key schedule. As mentioned above, each round uses a 48-bit key comprised of 48 of the bits in K. The entries in the tables below refer to the bits in K that are used in the various rounds.

Round 1
10	51	34	60	49	17	33	57	2	9	19	42
3	35	26	25	44	58	59	1	36	27	18	41
22	28	39	54	37	4	47	30	5	53	23	29
61	21	38	63	15	20	45	14	13	62	55	31

Round 2
2	43	26	52	41	9	25	49	59	1	11	34
60	27	18	17	36	50	51	58	57	19	10	33
14	20	31	46	29	63	39	22	28	45	15	21
53	13	30	55	7	12	37	6	5	54	47	23

Round 3
51	27	10	36	25	58	9	33	43	50	60	18
44	11	2	1	49	34	35	42	41	3	59	17
61	4	15	30	13	47	23	6	12	29	62	5
37	28	14	39	54	63	21	53	20	38	31	7

Round 4
35	11	59	49	9	42	58	17	27	34	44	2
57	60	51	50	33	18	19	26	25	52	43	1
45	55	62	14	28	31	7	53	63	13	46	20
21	12	61	23	38	47	5	37	4	22	15	54

Round 5
19	60	43	33	58	26	42	1	11	18	57	51
41	44	35	34	17	2	3	10	9	36	27	50
29	39	46	61	12	15	54	37	47	28	30	4
5	63	45	7	22	31	20	21	55	6	62	38

Round 6
3	44	27	17	42	10	26	50	60	2	41	35
25	57	19	18	1	51	52	59	58	49	11	34
13	23	30	45	63	62	38	21	31	12	14	55
20	47	29	54	6	15	4	5	39	53	46	22

Round 7
52	57	11	1	26	59	10	34	44	51	25	19
9	41	3	2	50	35	36	43	42	33	60	18
28	7	14	29	47	46	22	5	15	63	61	39
4	31	13	38	53	62	55	20	23	37	30	6

Round 8
36	41	60	50	10	43	59	18	57	35	9	3
58	25	52	51	34	19	49	27	26	17	44	2
12	54	61	13	31	30	6	20	62	47	45	23
55	15	28	22	37	46	39	4	7	21	14	53

Round 9
57	33	52	42	2	35	51	10	49	27	1	60
50	17	44	43	26	11	41	19	18	9	36	59
4	46	53	5	23	22	61	12	54	39	37	15
47	7	20	14	29	38	31	63	62	13	6	45

Round 10
41	17	36	26	51	19	35	59	33	11	50	44
34	1	57	27	10	60	25	3	2	58	49	43
55	30	37	20	7	6	45	63	38	23	21	62
31	54	4	61	13	22	15	47	46	28	53	29

Round 11
25	1	49	10	35	3	19	43	17	60	34	57
18	50	41	11	59	44	9	52	51	42	33	27
39	14	21	4	54	53	29	47	22	7	5	46
15	38	55	45	28	6	62	31	30	12	37	13

Round 12
9	50	33	59	19	52	3	27	1	44	18	41
2	34	25	60	43	57	58	36	35	26	17	11
23	61	5	55	38	37	13	31	6	54	20	30
62	22	39	29	12	53	46	15	14	63	21	28

Round 13
58	34	17	43	3	36	52	11	50	57	2	25
51	18	9	44	27	41	42	49	19	10	1	60
7	45	20	39	22	21	28	15	53	38	4	14
46	6	23	13	63	37	30	62	61	47	5	12

Round 14
42	18	1	27	52	49	36	60	34	41	51	9
35	2	58	57	11	25	26	33	3	59	50	44
54	29	4	23	6	5	12	62	37	22	55	61
30	53	7	28	47	21	14	46	45	31	20	63

Round 15
26	2	50	11	36	33	49	44	18	25	35	58
19	51	42	41	60	9	10	17	52	43	34	57
38	13	55	7	53	20	63	46	21	6	39	45
14	37	54	12	31	5	61	30	29	15	4	47

Round 16
18	59	42	3	57	25	41	36	10	17	27	50
11	43	34	33	52	1	2	9	44	35	26	49
30	5	47	62	45	12	55	38	13	61	31	37
6	29	46	4	23	28	53	22	21	7	63	39

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