perm filename NBS.NOT[NBS,WD]3 blob sn#231148 filedate 1976-08-06 generic text, type C, neo UTF8
COMMENT āŠ—   VALID 00022 PAGES
C REC  PAGE   DESCRIPTION
C00001 00001
C00003 00002				The Initial Permutation
C00005 00003		These  are  the  selection functions S1...S8 of the NBS algorithm, which
C00010 00004		Each row of an S is a permutation of the numbers 0 through 15 and
C00012 00005					S5
C00014 00006		The process which decomposes a six bit number by taking  the  first  and
C00016 00007			Permuted Choice 1
C00018 00008		K1 through K16 are the 48 bit  subsets  of  the  64  bit  key
C00020 00009				    K5
C00022 00010				    K9
C00024 00011				    K13
C00026 00012		The following are the bits omitted in each of K1  through  K16,  by  the
C00029 00013		K1 through K16 are the 48 bit subsets of the 64 bit key employed in each
C00031 00014				    K5
C00033 00015				    K9
C00035 00016				    K13
C00037 00017		The following are the bits omitted in each of K1  through  K16,  by  the
C00039 00018		K1 through K16 are the 48 bit subsets of the 64 bit key employed in each
C00041 00019				    K5
C00043 00020				    K9
C00045 00021				    K13
C00047 00022					PC2
C00053 ENDMK
CāŠ—;
			The 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


	The initial permutation can easily  be  seen  to  have  been  formed  as
follows.   The  numbers  1  through  64 were written from top to bottom and from
right to left in a square array eight elements on a side.  The  even  rows  were
then  separated  out and placed above the odd.  The result is then read off from
left to right and from top to bottom.

	IP may be decomposed into cycles as follows:

(1 58 55 13 28 40)

(2 50 53 29 32 8)

(3 42 51 45 27 48)

(4 34 49 61 31 16)

(5 26 56)

(6 18 54 21 30 24)

(7 10 52 37 25 64)

(9 60 39)

(11 4435 41 59 47)

(12 36 33 57 63 15)

(14 20 38 17 62 23)

(19 46)

(22)


	These  are  the  selection functions S1...S8 of the NBS algorithm, which
map 6 bit quantities to four bit ones.   The  image  of  a  six  bit  number  is
obtained  by  taking  the  first  and  last bits as the row number in one of the
following tables, and the middle four bits as the column number.
	Note that each row is a permutation of the numbers 0...15.

                                       S1
         14   4  13   1   2  15  11   8   3  10   6  12   5   9   0   7
          0  15   7   4  14   2  13   1  10   6  12  11   9   5   3   8
          4   1  14   8  13   6   2  11  15  12   9   7   3  10   5   0
         15  12   8   2   4   9   1   7   5  11   3  14  10   0   6  13

                                       S2
         15   1   8  14   6  11   3   4   9   7   2  13  12   0   5  10
          3  13   4   7  15   2   8  14  12   0   1  10   6   9  11   5
          0  14   7  11  10   4  13   1   5   8  12   6   9   3   2  15
         13   8  10   1   3  15   4   2  11   6   7  12   0   5  14   9

                                       S3
         10   0   9  14   6   3  15   5   1  13  12   7  11   4   2   8
         13   7   0   9   3   4   6  10   2   8   5  14  12  11  15   1
         13   6   4   9   8  15   3   0  11   1   2  12   5  10  14   7
          1  10  13   0   6   9   8   7   4  15  14   3  11   5   2  12

                                       S4
          7  13  14   3   0   6   9  10   1   2   8   5  11  12   4  15
         13   8  11   5   6  15   0   3   4   7   2  12   1  10  14   9
         10   6   9   0  12  11   7  13  15   1   3  14   5   2   8   4
          3  15   0   6  10   1  13   8   9   4   5  11  12   7   2  14

                                       S5
          2  12   4   1   7  10  11   6   8   5   3  15  13   0  14   9
         14  11   2  12   4   7  13   1   5   0  15  10   3   9   8   6
          4   2   1  11  10  13   7   8  15   9  12   5   6   3   0  14
         11   8  12   7   1  14   2  13   6  15   0   9  10   4   5   3

                                       S6
         12   1  10  15   9   2   6   8   0  13   3   4  14   7   5  11
         10  15   4   2   7  12   9   5   6   1  13  14   0  11   3   8
          9  14  15   5   2   8  12   3   7   0   4  10   1  13  11   6
          4   3   2  12   9   5  15  10  11  14   1   7   6   0   8  13

                                       S7
          4  11   2  14  15   0   8  13   3  12   9   7   5  10   6   1
         13   0  11   7   4   9   1  10  14   3   5  12   2  15   8   6
          1   4  11  13  12   3   7  14  10  15   6   8   0   5   9   2
          6  11  13   8   1   4  10   7   9   5   0  15  14   2   3  12

                                       S8
         13   2   8   4   6  15  11   1  10   9   3  14   5   0  12   7
          1  15  13   8  10   3   7   4  12   5   6  11   0  14   9   2
          7  11   4   1   9  12  14   2   0   6  10  13  15   3   5   8
          2   1  14   7   4  10   8  13  15  12   9   0   3   5   6  11


	Each row of an S is a permutation of the numbers 0 through 15 and
may be written as a product of cycles.

			S1

Row 1:	(0 14) (1 4 2 13 9 10 6 11 12 5 15 7 8 3)

Row 2:	(0) (1 15 8 10 12 9 6 13 5 2 7) (3 4 14)

Row 3:	(0 4 13 10 9 12 3 8 15) (1) (2 14 5 6) (7 11)

Row 4:	(0 15 13) (1 12 10 3 2 8 5 9 11 14 6) (4) (7)


				S2

	(0 15 10 2 8 9 7 4 6 3 14 5 11 13) (1) (12)

	(0 3 7 14 11 10 1 13 9) (2 4 15 5) (6 8 12)

	(0) (1 14 2 7) (3 11 6 13) (4 10 12 9 8 5) (15)

	(0 13 5 15 9 6 4 3 18 11 12) (2 10 7) (14)


				S3

	(0 10 12 11 7 5 3 14 2 9 13 4 6 15 8 1)

	(0 13 11 14 15 1 7 10 5 4 3 9 8 2)

	(0 13 10 2 4 8 11 12 5 15 7) (1 6 3 9) (14)

	(0 1 10 14 2 13 5 9 15 12 11 3) (4 6 8) (7)


				S4

	(0 7 10 8 1 13 12 11 5 6 9 2 14 4) (3) (15)

	(0 13 10 2 11 12 1 8 4 6) (3 5 15 9 7) (14)

	(0 10 3) (1 6 7 13 2 9) (4 12 5 11 14 8 15)

	(0 3 6 13 7 8 9 4 10 5 1 15 14 2) (11) (12)


				S5

	(0 2 4 7 6 11 15 9 5 10 3 1 12 13) (8) (14)

	(0 14 8 5 7 1 11 10 15 6 13 9) (2) (3 12) (4)

	(0 4 10 12 6  7 8 15 14) (1 2) (3 11 5 13) (9)

	(0 11 9 15 3 7 13 4 1 8 6 2 12 19) (5 14)


			S6

	(0 12 14 5 2 10 3 15 11 4 9 13 7 8) (1) (6)

	(0 10 13 11 14 3 2 4 7 5 12) (1 15 8 6 9)

	(0 9) (1 14 11 10 4 2 15 6 12) (3 5 8 7) (13)

	(0 4 9 14 8 11 7 10 1 3 12 6 15 13) (2) (5)


			S7

	(0 4 15 1 11 7 13 10 9 12 5) (2) (3 14 6 8)

	(0 13 15 6 1) (2 11 12) (3 7 10 5 9) (4) (8 14)

	(0 1 4 12) (2 11 8 10 6 7 14 9 15) (3 13 5)

	(0 6 10) (1 11 15 12 14 3 8 9 5 4) (2 13) (7)


			S8

	(0 13) (1 2 8 10 3 4 6 11 14 12 5 15 7) (9)

	(0 1 15 2 13 14 9 5 3 8 12) (4 10 6 7) (11)

	(0 7 2 4 9 6 14 5 12 15 8) (1 11 13 3) (10)

	(0 2 14 6 8 15 11) (1) (3 7 13 5 10 9 12) (4)

	The process which decomposes a six bit number by taking  the  first  and
last  bits to represent a row and the middle bits to represent a column, results
in elements being chosen from the any of the S tables in the following order.


     0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15

0    1   3   5   7   9  11  13  15  17  19  21  23  25  27  29  31  

1    2   4   6   8  10  12  14  16  18  20  22  24  26  28  30  32

2   33  35  37  39  41  43  45  47  49  51  53  55  57  59  61  63

3   34  36  38  40  42  44  46  48  50  52  54  56  58  60  62  64


				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


	Written as a product of cycles, P becomes:

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


		Permuted Choice 1

	The structure of permuted choice 1 is  more  clearly  visible
when  it  is presented in 8 columns rather than 7.  The division into
two parts is maintained.  Each half has four and  one  half  rows  of
length eight.

	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

	As the bits 8, 16, 24, 32, 40, 48, 56, and 64 are  not  used,
things  bocome  even clearer if the bits are renumbered from 1 to 56.
The above array then becomes:

	50	43	36	29	22	15	8	1
	51	44	37	30	23	16	9	2
	52	45	38	31	24	17	10	3
	53	46	39	32

	56	49	42	35	28	21	14	7
	55	48	41	34	27	20	13	6
	54	47	40	33	26	19	12	5
	25	18	11	4

	The  permutation  is  now clear.  Turn the lower group upside
down and slide the short row to the right, to get:

	50	43	36	29	22	15	8	1
	51	44	37	30	23	16	9	2
	52	45	38	31	24	17	10	3
	53	46	39	32

					25	18	11	4
	54	47	40	33	26	19	12	5
	55	48	41	34	27	20	13	6
	56	49	42	35	28	21	14	7

The  two parts can now be assembled into a rectangle written from top
to bottom and right to left.


	K1 through K16 are the 48 bit  subsets  of  the  64  bit  key
employed  in  each  of  the  16  rounds  of  the NBS cipher. They are
organized in eight rows of six columns, read across then down.


			    K1

	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


			    K2

	 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


			    K3

	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


			    K4

	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


			    K5

	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


			    K6

	 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


			    K7

	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


			    K8

	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


			    K9

	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


			    K10

	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


			    K11

	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


			    K12

	 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


			    K13

	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


			    K14

	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


			    K15

	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


			    K16

	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


	The following are the bits omitted in each of K1  through  K16,  by  the
reduction from 56 to 48 bits.

		(THIS PAGE IS IN ERROR)

K1:	1   3   8   16  22  23  24  27  28  32  40  48  56  59  62  64  

K2:	2   5   7   8   9   11  16  24  30  31  32  35  40  48  56  64  

K3:	8   16  18  21  23  24  25  27  32  40  46  47  48  51  56  64  

K4:	2   8   16  24  32  34  37  39  40  41  43  48  56  62  63  64  

K5:	8   12  15  16  18  24  32  40  48  50  53  55  56  57  59  64  

K6:	1   4   6   8   10  16  24  28  31  32  34  40  44  48  56  64  

K7:	8   13  16  17  20  22  24  26  32  40  47  48  50  56  60  64  

K8:	1   5   8   11  16  24  29  32  33  38  40  42  48  56  63  64  

K9:	4   8   9   13  16  19  24  32  37  40  41  46  48  50  56  64  

K10:	1   8   16  20  24  25  29  32  35  40  48  53  56  57  62  64  

K11:	5   6   8   15  16  17  24  32  40  41  44  45  48  51  56  64  

K12:	2   8   16  21  22  24  31  32  33  40  48  56  57  60  61  64  

K13:	8   11  14  16  18  24  32  37  38  40  44  47  48  49  56  64  

K14:	8   16  24  27  30  32  34  36  40  48  53  54  56  60  63  64  

K15:	6   7   8   11  12  16  24  32  40  43  46  48  50  52  56  64  

K16:	8   14  15  16  19  20  24  32  40  48  51  54  56  58  60  64  


	K1 through K16 are the 48 bit subsets of the 64 bit key employed in each
of the 16 rounds of the NBS cipher, renumbered from 1 to 56 by omitting the bits
8, 16, 24, 32, 40, 48, 56, and 64, which are never used. They are  organized  in
eight rows of six columns, read across then down.


			    K1

	 9	45	30	53	43	15
	29	50	 2	 8	17	37
	 3	31	23	22	39	51
	52	 1	32	24	16	36
	20	25	35	48	33	 4
	42	27	 5	47	21	26
	54	19	34	56	14	18
	40	13	12	55	49	28


			    K2

	 2	38	23	46	36	 8
	22	43	52	 1	10	30
	53	24	16	15	32	44
	45	51	50	17	 9	29
	13	18	28	41	26	56
	35	20	25	40	14	19
	47	12	27	49	 7	11
	33	 6	 5	48	42	21


			    K3

	45	24	 9	32	22	51
	 8	29	38	44	53	16
	39	10	 2	 1	43	30
	31	37	36	 3	52	15
	54	 4	14	27	12	42
	21	 6	11	26	55	 5
	33	25	13	35	48	56
	19	47	18	34	28	 7


			    K4

	31	10	52	43	 8	37
	51	15	24	30	39	 2
	50	53	45	44	29	16
	17	23	22	46	38	 1
	40	49	55	13	25	28
	 7	47	56	12	41	18
	19	11	54	21	34	42
	 5	33	 4	20	14	48


			    K5

	17	53	38	29	51	23
	37	 1	10	16	50	45
	36	39	31	30	15	 2
	 3	 9	 8	32	24	44
	26	35	41	54	11	14
	48	33	42	25	27	 4
	 5	56	40	 7	20	28
	18	19	49	 6	55	34


			    K6

	 3	39	24	15	37	 9
	23	44	53	 2	36	31
	22	50	17	16	 1	45
	46	52	51	43	10	30
	12	21	27	40	56	55
	34	19	28	11	13	49
	18	42	26	48	 6	14
	 4	 5	35	47	41	20


			    K7

	46	50	10	 1	23	52
	 9	30	39	45	22	17
	 8	36	 3	 2	44	31
	32	38	37	29	53	16
	25	 7	13	26	42	41
	20	 5	14	56	54	35
	 4	28	12	34	47	55
	49	18	21	33	27	 6


			    K8

	32	36	53	44	 9	38
	52	16	50	31	 8	 3
	51	22	46	45	30	17
	43	24	23	15	39	 2
	11	48	54	12	28	27
	 6	18	55	42	40	21
	49	14	25	20	33	41
	35	 4	 7	19	13	47


			    K9

	50	29	46	37	 2	31
	45	 9	43	24	 1	53
	44	15	39	38	23	10
	36	17	16	 8	32	52
	 4	41	47	 5	21	20
	54	11	48	35	33	14
	42	 7	18	13	26	34
	28	56	55	12	 6	40


			    K10

	36	15	32	23	45	17
	31	52	29	10	44	39
	30	 1	50	24	 9	53
	22	 3	 2	51	43	38
	49	27	33	18	 7	 6
	40	56	34	21	19	55
	28	48	 4	54	12	20
	14	42	41	25	47	26


			    K11

	22	 1	43	 9	31	 3
	17	38	15	53	30	50
	16	44	36	10	52	39
	 8	46	45	37	29	24
	35	13	19	 4	48	47
	26	42	20	 7	 5	41
	14	34	49	40	25	 6
	55	28	27	11	33	12


			    K12

	 8	44	29	52	17	46
	 3	24	 1	39	16	36
	 2	30	22	53	38	50
	51	32	31	23	15	10
	21	54	 5	49	34	33
	12	28	 6	48	18	27
	55	20	35	26	11	47
	41	14	13	56	19	25


			    K13

	51	30	15	38	 3	32
	46	10	44	50	 2	22
	45	16	 8	39	24	36
	37	43	17	 9	 1	53
	 7	40	18	35	20	19
	25	14	47	34	 4	13
	41	 6	21	12	56	33
	27	55	54	42	 5	11


			    K14

	37	16	 1	24	46	43
	32	53	30	36	45	 8
	31	 2	51	50	10	22
	23	29	 3	52	44	39
	48	26	 4	21	 6	 5
	11	55	33	20	49	54
	27	47	 7	25	42	19
	13	41	40	28	18	56


			    K15

	23	 2	44	10	32	29
	43	39	16	22	31	51
	17	45	37	36	53	 8
	 9	15	46	38	30	50
	34	12	49	 7	47	18
	56	41	19	 6	35	40
	13	33	48	11	28	 5
	54	27	26	14	 4	42


			    K16

	16	52	37	 3	50	22
	36	32	 9	15	24	44
	10	38	30	29	46	 1
	 2	 8	39	31	23	43
	27	 5	42	55	40	11
	49	34	12	54	28	33
	 6	26	41	 4	21	25
	47	20	19	 7	56	35


	The following are the bits omitted in each of K1  through  K16,  by  the
reduction from 56 to 48 bits.

		(THIS PAGE IS IN ERROR)

K1:	 1	 3	20	21	24	25	52	55	

K2:	 2	 5	 7	 8	10	27	28	31	

K3:	16	19	21	22	24	41	42	45	

K4:	 2	30	33	35	36	38	55	56	

K5:	11	14	16	44	47	49	50	52	

K6:	 1	 4	 6	 9	25	28	30	39	

K7:	12	15	18	20	23	42	44	53	

K8:	 1	 5	10	26	29	34	37	56	

K9:	 4	 8	12	17	33	36	41	44	

K10:	 1	18	22	26	31	47	50	55	

K11:	 5	 6	14	15	36	39	40	45	

K12:	 2	19	20	28	29	50	53	54	

K13:	10	13	16	33	34	39	42	43	

K14:	24	27	30	32	47	48	53	56	

K15:	 6	 7	10	11	38	41	44	46	

K16:	13	14	17	18	45	48	51	53	

	K1 through K16 are the 48 bit subsets of the 64 bit key employed in each
of the 16 rounds of the NBS cipher, renumbered from 0 to 55 by omitting the bits
8, 16, 24, 32, 40, 48, 56, and 64, which are never used.  PC1  has been omitted.
They are organized in eight rows of six columns, read across then down.


			    K1

	14	17	11	24	 1	 5
	 3	 0	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	28	34	53
	46	42	50	36	29	32


			    K2

	15	18	12	25	 2	 6
	 4	 1	16	 7	22	11
	24	20	13	 5	27	 9
	17	 8	 0	21	14	 3
	42	53	32	38	48	28
	31	41	52	46	34	49
	45	50	40	29	35	54
	47	43	51	37	30	33


			    K3

	17	20	14	27	 4	 8
	 6	 3	18	 9	24	13
	26	22	15	 7	 1	11
	19	10	 2	23	16	 5
	44	55	34	40	50	30
	33	43	54	48	36	51
	47	52	42	31	37	28
	49	45	53	39	32	35


			    K4

	19	22	16	 1	 6	10
	 8	 5	20	11	26	15
	 0	24	17	 9	 3	13
	21	12	 4	25	18	 7
	46	29	36	42	52	32
	35	45	28	50	38	53
	49	54	44	33	39	30
	51	47	55	41	34	37


			    K5

	21	24	18	 3	 8	12
	10	 7	22	13	 0	17
	 2	26	19	11	 5	15
	23	14	 6	27	20	 9
	48	31	38	44	54	34
	37	47	30	52	40	55
	51	28	46	35	41	32
	53	49	29	43	36	39


			    K6

	23	26	20	 5	10	14
	12	 9	24	15	 2	19
	 4	 0	21	13	 7	17
	25	16	 8	 1	22	11
	50	33	40	46	28	36
	39	49	32	54	42	29
	53	30	48	37	43	34
	55	51	31	45	38	41


			    K7

	25	 0	22	 7	12	16
	14	11	26	17	 4	21
	 6	 2	23	15	 9	19
	27	18	10	 3	24	13
	52	35	42	48	30	38
	41	51	34	28	44	31
	55	32	50	39	45	36
	29	53	33	47	40	43


			    K8

	27	 2	24	 9	14	18
	16	13	 0	19	 6	23
	 8	 4	25	17	11	21
	 1	20	12	 5	26	15
	54	37	44	50	32	40
	43	53	36	30	46	33
	29	34	52	41	47	38
	31	55	35	49	42	45


			    K9

	 0	 3	25	10	15	19
	17	14	 1	20	 7	24
	 9	 5	26	18	12	22
	 2	21	13	 6	27	16
	55	38	45	51	33	41
	44	54	37	31	47	34
	30	35	53	42	48	39
	32	28	36	50	43	46


			    K10

	 2	 5	27	12	17	21
	19	16	 3	22	 9	26
	11	 7	 0	20	14	24
	 4	23	15	 8	 1	18
	29	40	47	53	35	43
	46	28	39	33	49	36
	32	37	55	44	50	41
	34	30	38	52	45	48


			    K11

	 4	 7	 1	14	19	23
	21	18	 5	24	11	 0
	13	 9	 2	22	16	26
	 6	25	17	10	 3	20
	31	42	49	55	37	45
	48	30	41	35	51	38
	34	39	29	46	52	43
	36	32	40	54	47	50


			    K12

	 6	 9	 3	16	21	25
	23	20	 7	26	13	 2
	15	11	 4	24	18	 0
	 8	27	19	12	 5	22
	33	44	51	29	39	47
	50	32	43	37	53	40
	36	41	31	48	54	45
	38	34	42	28	49	52


			    K13

	 8	11	 5	18	23	27
	25	22	 9	 0	15	 4
	17	13	 6	26	20	 2
	10	 1	21	14	 7	24
	35	46	53	31	41	49
	52	34	45	39	55	42
	38	43	33	50	28	47
	40	36	44	30	51	54


			    K14

	10	13	 7	20	25	 1
	27	24	11	 2	17	 6
	19	15	 8	 0	22	 4
	12	 3	23	16	 9	26
	37	48	55	33	43	51
	54	36	47	41	29	44
	40	45	35	52	30	49
	42	38	46	32	53	28


			    K15

	12	15	 9	22	27	 3
	 1	26	13	 4	19	 8
	21	17	10	 2	24	 6
	14	 5	25	18	11	 0
	39	50	29	35	45	53
	28	38	49	43	31	46
	42	47	37	54	32	51
	44	40	48	34	55	30


			    K16

	13	16	10	23	 0	 4
	 2	27	14	 5	20	 9
	22	18	11	 3	25	 7
	15	 6	26	19	12	 1
	40	51	30	36	46	54
	29	39	50	44	32	47
	43	48	38	55	33	52
	45	41	49	35	28	31


				PC2


	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


	Notice that the first 24 elements are selected entirely from the  inputs
between  1 an 28 while the latter 24 are take entirely from those between 29 and
56.

	The elements omitted are: 9, 18, 22, 25, 35, 38, 43, and 54.  These  are
taken equally from the two halves.