Department of Software
The University of Babylon
College of Information Technology, University of Babylon, Iraq
Samaher_hussein@yahoo.com
10/24/2012

Stream Cipher System ki
Key Generator
Letter
Plain Text Binary
Sequence Generator
Pi
Feedback Shift
Register( Linear or non Linear Function)
Ci
Binary Sequence of cipher text
Key Generator:
is part of stream cipher system that is responsible on generating of a long random sequence of binary key that used in ciphering and deciphering process
Feedback Shift Register
used the Linear or Non-linear functions to mix the plain text with the key
1. Linear Feedback Shift Register (XOR)
2. Nonlinear Feedback Shift Register (And , Or)
10/24/2012 Dr. Samaher Hussein Ali
Notes of Lecture 6

Stream Cipher System
Max Length of Key= 2 𝑛
− 1
where
n number of state
Number of Correct Connection= 𝜙 ( 2 𝑛 𝑛
1 )
Logic of XOR
X1 X2 Output
0 0 0
1 0 1
0 1 1
1 1 0
Example:
Let the initial State of Sift Register is {0, 1, 0} and Feed Back coefficient 1011 find States, then cipher the massage
GOOD
C0=1
0
C1=0
+
1
C2=1
0
C3=1
S0 S1 S2
10/24/2012 Dr. Samaher Hussein Ali
Notes of Lecture 6

Stream Cipher System
Max Length of Key= 2
3
− 1
No
= 7
FB
1
2
3
4
5
6
7
1
1
0
0
1
0
1
1
0
0
1
S0 S1
0 1
1 0
1
1
1
0
0
0 1
Key = 0101110
0
1
1
1
0
S2
0
1
0
Output
0
1
0
1
1
1
0
10/24/2012 Dr. Samaher Hussein Ali
Notes of Lecture 6

Stream Cipher System
1
4
2
Initial State
5
7- States
6
3 7
Message = GOOD
G= 7= 0111
O= 15=1111
O= 15= 1111
D= 4 = 0100
PLAIN TEXT = 0111 1111 1111 0100
KEY = 0101 110 0 1011 10 01
10/24/2012 Dr. Samaher Hussein Ali
Notes of Lecture 6

Stream Cipher System
Example:
Let the initial State of Sift Register is {1,0, 1, 0} and Feed Back coefficient 10011 find States, then cipher the massage
Happy New Year
C0=1
1
S0
C1=0
0
S1
C2=0
+
1
S2
C3=1
0
S3
C4=1
Max Length of Key= 2 −
4
1 = 15
No FB S1 S2 Output
1
2
3
4
5
6
1
1
0
0
0
1
S0
1
1
0
0
1
1
0
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
1
1
S3
0
1 0
1
0
1
1
1
10/24/2012 Dr. Samaher Hussein Ali
Notes of Lecture 6

Stream Cipher System
12
13
14
15
9
10
11
No
7
8
FB
0
1
0
1
1
0
1
1
0
S0
1
0
1
0
1
0
0
1
1
S1
0
1
0
1
0
1
0
0
1
Key = 01011 11000 10011
Message = Happy New Year
H= 8= 1000
…
…
r= 18 = 1010
10/24/2012 Dr. Samaher Hussein Ali
S2
0
1
1
0
1
0
1
0
0
S3
0
0
1
1
0
0
0
1
0
Output
1
0
0
1
1
0
0
0
1
Notes of Lecture 6

Stream Cipher System ( Nonlinear Feedback Shift Register )
One general technique for destroying the linearity inherent in LFSRs is to use several LFSRs in parallel. The keystream is generated as a nonlinear function F of the outputs of the component LFSRs; this construction is illustrated in Figure 1. Such keystream generators are called nonlinear combination generators, and F is called the combining function. The remainder of this subsection demonstrates that the function F must satisfy several criteria in order to withstand certain particular cryptographic attacks.
Figure 1: A nonlinear combination generator. F is a nonlinear combining function.
( Geffe Generator ) The Geffe generator, as depicted in Figure 2, is defined by three maximum-length LFSRs whose lengths
L1 ,L2, and L3 are pairwise relatively prime, with nonlinear combining function
The keystream generated has period
10/24/2012 Dr. Samaher Hussein Ali
Notes of Lecture 6

Stream Cipher System ( Nonlinear Feedback Shift Register “NLFSR “ ) and linear complexity
Figure
2
: The Geffe generator.
10/24/2012 Dr. Samaher Hussein Ali
Notes of Lecture 6

Stream Cipher System ( Nonlinear Feedback Shift Register )
Logic of AND
X1 X2 Output
0 0 0
1 0 0
0 1 0
1 1 1
Logic of OR
X1 X2 Output
0 0 0
1 0 1
0 1 1
1 1 1
LFBSR1
X1
Nonlinear Function
X2
LFBSR2
10/24/2012 Dr. Samaher Hussein Ali
Notes of Lecture 6

Stream Cipher System ( Nonlinear Feedback Shift Register )
+
C3=1
1
S3
C2=0
0
S2
C1=1
1
S0
C0=1
X1
C4=1
1
S3
C3=1
1
S2
C2=0
+
1
S1
C1=0
0
S0
C0=1
X2
AND
O/P
10/24/2012 Dr. Samaher Hussein Ali
Notes of Lecture 6

3
4
1
2
5
6
7
10
11
8
9
Stream Cipher System ( Nonlinear Feedback Shift Register “NLFSR “ )
No
1
1
0
1
0
1
0
FB
1
0
1
1
1
S2
1
0
0
1
1
0
0
1
S1
0
1
0
1
1
1
0
0
S0
1
0
1
0/P FB
1
0
1
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
S3
1
1
0
0
1
1
0
1
1
0
0
0
S2
1
1
1
1
0
1
1
0
0
1
1
0
S1
1
1
1
0
1
0
1
1
0
0
1
1
S0
0
1
1
O/P
1
1
0
1
1
0
1
1
0
0
1
Output
0
0
0
0
1
0
1
1
0
0
0
10/24/2012 Dr. Samaher Hussein Ali
Notes of Lecture 6

Stream Cipher System ( Nonlinear Feedback Shift Register “NLFSR “ )
S1 No
12
13
14
15
FB S2 S0 0/P
0
1
1
1
FB
1
1
1
1
1
1
S3
0
0
1
1
S2
0
0
0
1
S1
0
0
0
0
S0
1
O/P
0
1
0
0
Output
0
1
0
0
Key = 00001 01001 00100
10/24/2012 Dr. Samaher Hussein Ali
Notes of Lecture 6