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Digital Image ScramblingUsing Cellular Automata

Ajith K.P.-B100189EC Arun Tony-B100171EC

Aswin E Augustine-B100305EC Basil Babu-B100523EC

Vaisakh R.P. -B100087EC

National Institute of Technology

November 12th 2013

Major Project Image Encryption 1/24


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Introduction

Need for Scrambling



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Introduction

Need for Scrambling

security reasons



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Introduction

Need for Scrambling

security reasons

Areas of Application



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Introduction

Need for Scrambling

security reasons

Areas of Application confidential remote video conferencing



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Introduction

Need for Scrambling

security reasons

Areas of Application confidential remote video conferencing security communication



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Introduction

Need for Scrambling

security reasons

Areas of Application confidential remote video conferencing security communication military applications



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Introduction

Image Scrambling methods

Advanced Encryption Standard



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Introduction



Magic Cube



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Introduction



Magic Cube Arnolds Cat Map



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Introduction




Twice Internal Division



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Introduction




Twice Internal Division

Cellular Automaton


C ll l A


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Cellular Automata

Introduced by Ulam and von Neumann in 1940


C ll l A


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Cellular Automata


Consist of rectangular grid of identical cells


C ll l A t t


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Cellular Automata



Each cell takes finite number of states


C ll l A t t


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Cellular Automata




At each step cells update synchronously by applying

rules(transition functions)


C ll l A t t


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Cellular Automata




At each step cells update synchronously by applying

rules(transition functions)

These rules are based on the states of the respective cells

and their neighbours


C ll l A t t


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Cellular Automata

Related Automata

variation in cells


Cell lar A tomata


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Cellular Automata

Related Automata

variation in cells

hexagonal cells


Cellular Automata


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Cellular Automata

Related Automata

variation in cells

hexagonal cells

irregular cells


Cellular Automata


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Cellular Automata

Related Automata

variation in cells

hexagonal cells

irregular cells probabilistic rules instead of deterministic


Cellular Automata


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Cellular Automata

Related Automata

variation in cells

hexagonal cells


.001% probability that each cell will transition to oppositecolour


Cellular Automata


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Cellular Automata

Related Automata

variation in cells

hexagonal cells


.001% probability that each cell will transition to oppositecolour

continuous automata


Cellular Automata


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Cellular Automata

Cellular Automata Neighbourhood

1D CA


Cellular Automata


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Cellular Automata


1D CA

Each cell and its immediate left and right neighbours


Cellular Automata


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Cellular Automata


1D CA


2D CA


Cellular Automata


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Cellular Automata


1D CA


2D CA Von Neumann Neighbourhood


Cellular Automata


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Cellular Automata


1D CA


2D CA Von Neumann Neighbourhood Moore Neighbourhood

Conways Game of Life uses the Moore Neighbourhood


Von Neumann Neghbourhood


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Von Neumann Neghbourhood

defined by

NH(x0, y0, r) = [(x, y) : x x0 + y y0 r]

number of cells in each neighbourhood

n= 2r(r + 1) + 1

if r=1 , then n= 5


Von Neumann Neighbourhood


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Von Neumann Neighbourhood


Moore Neighbourhood


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Moore Neighbourhood

defined by

NH(x0, y0, r) = [(x, y) : x x0 r,y y0 r]

number of cells in each neighbourhood

n= (2r + 1)2

if r=1 , then n= 9


Moore Neighbourhood


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Moore Neighbourhood


Boundary Conditions


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Boundary Conditions

To determine neighbours of cells at the edges

periodic

1D - rows turned into circles 2D - rectangular grids turned into toroids

static

extreme cells are connected to permanent zero state cells


Conways Game of Life


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Conway s Game of Life

consists of [M X N] matrix of cells with two states alive or

dead

uses Moore neighbourhood

at every generation each cell compute its new state using

transition rules

every cell are updated simultaneously(synchronous)


Conways Game of Life


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Co ay s Ga e o e

The Transition Rules

Birth - A dead cell becomes alive if exactly three

neighbours were alive

Death by Overcrowding - An alive cell dies if more than

three of its neighbours were alive

Death by Exposure - An alive cell dies if one or none of its


Survival - An alive cell remains alive if two or three of its



Procedure


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Encoding

Image file is read in as a matrix

An initial random configuration is set up for game of life

algorithm

Read the positions of the alive cells

Take the grey value of first pixel and put it in the position ofthe first alive cell

Take the next value and continue likewise

Continue like this for the required generations

If an alive cell has already appeared before, then discard it After the last generation, fill the scrambled image with the

remaining pixel



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Figure:Image Scrambling Using First Generation


Procedure


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Decoding

In decoding we know the initial configuration and the number of

generations and we can execute the inverse of the scramblingalgorithm to obtain the original image.


Analysis


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y

Grey Difference,

GD(i, j) =1

4

i,j

[P(i, j) P(i, j)]2

Average Neighbourhood Grey Differernce,

E[GD(i, j)] =

M1i=2

N1j=2 GD(i, j)

(M 2)X(N 2)

Grey Value Degree,

GDD =E(GD(i, j)) E(GD(i, j))

E(GD(i, j)) + E(GD(i, j))

Better scrambling correspondes to an absolute value near one


Observations


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Figure: original image of a rino Figure: scrambled image of the

rino


Observations


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Figure:original image of a boat Figure: scrambled image of the

boat


Observations


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Figure:original image of lena Figure: scrambled image of lena


Observations


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Figure:original image ofletterP

Figure:scrambled image of theletterP


Observations


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no. of generations lena boat rino letter P

1 0.9979 0.7128 0.9847 1.0000

5 0.9983 0.4618 0.9938 1.0000

20 0.9989 0.6801 0.9991 1.0000100 0.9984 0.8446 0.9987 1.0000

Table: GDD



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Figure:resolution of 50 X 50

Figure:GDD value vs no. of generations


Conclusion


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Attacker cannot break the encrypted image even if the

algorithm is open

We can provide high security by using double scrambling Due to diffusion process rate of encryption and decryption

increases


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