Structural Properties of Cryptographic Sequences - Computational Intelligence in Security for Information Systems - page 185

⎛ ⎞ ⎛ ⎞

11011010
00101000
00111111
10110101
00011001
11111001
01010011
01010001

01000101
01111111
00110110
11001111
01110110
00011101
00000011
10110001

⎝ ⎠ ⎝ ⎠

,P − 1 = P = .

Since matrix A is constructed as a companion matrix of a primitive polyno-
mial, its period is guaranteed to be 2 8 − 1 or 255 iterations [6].

Generator Seeding. The initial state of the generator, X 0
j

,with j =0 , 1 ,..., 7,
is a function of the whole message block M (with words M 1 to M 128 )andthe
hash working variables h 0 ,h 1 ,...,h 31 .
For j =0to7:

g 1 = h j + h j +8
g 2 = M j + M j +8 + M j +16 + M j +24
g 3 = M j +32 + M j +40 + M j +48 + M j +56
g 4 = h j +16 + h j +24
g 5 = M j +64 + M j +72 + M j +80 + M j +88
g 6 = M j +96 + M j +104 + M j +112 + M j +120
X j = FR 1 ( g 1 + g 2 + g 3 )+ FR 2 ( g 4 + g 5 + g 6 )

Iteration and Extraction. The generator is iterated R/ 2 times using the
following expression and, on each iteration of the generator, 4 message expansion
words ( W t ) are extracted using a nonlinear output function. K i is constant i as
defined in the original specification of Tangle (see [2])
For k =1to R/ 2:

X 0 = X k− 1

0

⊕ X k− 1
3

⊕ X k− 1
6

⊕ X k− 1
7

X 1 = X k− 1 ⊕ X k− 1

1

⊕ X k− 1
3

⊕ X k− 1
6 0

X 2 = X k− 1 ⊕ X k− 1

1

⊕ X k− 1
3

⊕ X k− 1
4

⊕ X k− 1
5 0

X 3 = X k− 1

4

⊕ X k− 1
5

⊕ X k− 1
6

⊕ X k− 1
7

X 4 = X k− 1 ⊕ X k− 1

2

⊕ X k− 1
7

0

X 5 = X k− 1 ⊕ X k− 1

5

⊕ X k− 1
6

⊕ X k− 1
7 2

X 6 = X k− 1

2

⊕ X k− 1
3

⊕ X k− 1
4

⊕ X k− 1
6

⊕ X k− 1
7

X 7 = X k− 1 ⊕ X k− 1

4

⊕ X k− 1
6 0