Cryptography Reference
In-Depth Information
b
5
=(2
,
12
,
6
,
3
,
2
,
12
,
6
,
8
,
9
,
11
,
2
,
5)
,
b
6
=(2
,
6
,
4
,
1
,
2
,
10
,
8
,
0
,
1
,
8
,
0
,
12)
,
b
7
=(6
,
9
,
11
,
2
,
0
,
10
,
0
,
6
,
4
,
1
,
11
,
9)
,
b
8
=(5
,
10
,
2
,
4
,
6
,
8
,
10
,
2
,
4
,
12
,
2
,
4)
,
b
9
=(10
,
3
,
10
,
11
,
4
,
6
,
4
,
7
,
3
,
3
,
5
,
1)
,
b
10
=(8
,
2
,
1
,
10
,
1
,
12
,
5
,
10
,
11
,
11
,
8
,
2)
,
b
11
=(1
,
7
,
6
,
10
,
8
,
12
,
10
,
5
,
7
,
9
,
0
,
8)
,
b
12
=(3
,
3
,
5
,
1
,
1
,
8
,
11
,
0
,
3
,
10
,
12
,
6)
,
c
5
=11
, c
6
=1
, c
7
=1
, c
8
=4
, c
9
=1
, c
10
=12
, c
11
=11
, c
12
=4
.
The above HS scheme corresponds to Rainbow(
K
;4
,
4
,
4) by Proposition 3. The
central map
G
=(
g
5
,g
6
,g
7
,g
8
,g
9
,g
10
,g
11
,g
12
):
K
12
K
8
of the corresponding
→
Rainbow is described as
g
k
(
x
)=
x
T
A
k
x
+
b
k
x
+
c
k
.
K
12
,c
k
∈
where
A
k
∈
M
(12
,K
)
,b
k
∈
K
are defined by
⎛
⎝
⎞
⎠
⎛
⎝
⎞
⎠
19001 0 50
02000 2 03
12200010 8
01100105 0
0
0
00198 0 10
000201002
0
0 0 11108 0 12
0 00250120
0
A
5
=
,A
6
=
,
0
0
⎛
⎞
⎛
⎞
110008 010
040001002
001120501
00298010
⎝
⎠
⎝
⎠
0
0
0011012080
0004011010
0
00000108
00001050
0
A
7
=
,A
8
=
,
0
0
⎛
⎝
⎞
⎠
⎛
⎝
⎞
⎠
54051212511112210
010801211232939
0054821212113112
0 0 0 10 11 10 12 11 10 4 2 9
000012605123411
00000118031125
00000012692123
000000011118311
0
1104061218111811
0 2 0 5 12 12 5 11 11 2 2 10
001231871811122
0001151111210211
00008114081219
00000305123411
000000521951
000000010411110
0
A
9
=
,A
10
=
,
⎛
⎞
⎛
⎞
2000 2 0 7211 3 11 2
0900 0 9 2110 4 2 9
002061120211113
000911120911 4 10 4
0000 4 0 00 9 2 12 3
0000 0 5 0011 8 3 11
0000 0 0 40 1 10 9 2
0000 0 0 0510 2 11 8
0
11 0 2 10 12 5 6 12 5 2 1 11
0 4 10 4 8 2 12 12 11 3 11 2
002061218111811
0 0 0 9 12 12 5 11 11 2 2 10
0000110311124812
00000411692123
0000002081219
00000009123411
0
⎝
⎠
⎝
⎠
A
11
=
,A
12
=
,
