Download COMPUTER AND DATA SECURITY

Lecture 6
STREAM CIPHER SYSTEM
By:
NOOR DHIA AL- SHAKARCHY
2012-2013
STREAM CIPHER SYSTEMS
Statistical Tests:
X2 =
1-frequency test:
0 < x2 < 3.84
n = length of sequence.
n0= number of 0's in sequence.
n1= number of 1's in sequence.
X2 =
x2 ≤ 5.99
2- serial test:
n = length of sequence.
n0= number of 0's in sequence.
n1= number of 1's in sequence.
nij = numbers of ij in sequence.
STREAM CIPHER SYSTEMS
Example:Test the sequence : 0101011101100011111001101001000
1- frequency test:
n = 31
X2 =
=
31
n0= 15
(-1)2
(15 - 16 )2
=
31
0<
x2
1
31
< 3.84
n1= 16
pass
n00 = 6
4
n01= 8 X2 =
2- serial test:
n10= 8
n11 = 8
=
n-1
4
30
(n002+n012+n102+n112) -
(62+82+82+82) -
= 30 – 4 -31.032 +1 = 0.368 ≤ 5.99
pass
2
31
2
n
(n02+n12)
(152+162)
+1
+1
STREAM CIPHER SYSTEMS
Statistical Tests:
3- poker test:
X2 =
2m
∑im=0
-F
(mi))
F
F=
(xi)2
n
m
m
m!
i
(m-i) !i !
F = the number of segment in sequence.
m = the length oF the segment.
Xi = the number of segments contain i of 1's.
m-i = the number of segments contain i of 0's, (default with xi).
STREAM CIPHER SYSTEMS
Example poker test:
m= 5
01010
11101
11110
01101
00100
0
ignore
31
F=
10001
= 6
5
X0 = 0
5
X1 = 1
0
5
X2 = 2
1
5
X3 = 1
X4 = 2
2
5
X5 = 0
3
5
4
5
=
25
=
=
6
32
6
= 5.33
=
5*4!
=
5!
=
5*4*3!
=
5!
5*4*3!
=
5!
5*4!
=
5!
= 10
2!3 !
(5-4) ! 4 !
=
= 10
3!2 !
(5-3) ! 3 !
=
= 5
4!1 !
(5-2) ! 2 !
= 5
1!4 !
5!
=
(5-5) ! 5!
)5i) 1
0
+
1
2+4+1+8 5
10
5!
= 1
(5-0) ! 0 !
(5-1) ! 1 !
(xi)2
∑i5=0
5!
=
(5-0) ! 0 !
5
X2 =
5!
= 1
(0) ! 5 !
-6
+
-6
4
+
10
= 1.99
1
10
+
4
5
+
0
1
pass