# LECTURE NOTES ON By Dr. Samaher Hussein Ali

Department of Software

The University of Babylon

### Dr. Samaher Hussein Ali

College of Information Technology, University of Babylon, Iraq

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