Secure OFDM-PON System Based on Chaos and Fractional Fourier Transform

Techniques

Author: Lei Deng, Mengfan Cheng, Xiaolong Wang, Hao Li, Ming Tang, Senior Member, IEEE, Songnian Fu,

Ping Shum, Senior Member, IEEE, and Deming Liu

Link to the video : https://youtu.be/rCJFGwSTmWo

Overview

OFDM-PON

Physical layer

Cryptography

Chaos

Fractional fourier transform

Implementation

Results

Extension

Passive Optical Network● A fiber optic access network to serve multiple end points from a

single optical fiber with unpowered optical splitters where it can serve upto 128 customers per fiber.

● In comparison to the Active Optical Network, the PON has low building and maintenance costs owing to the lesser number of moving electrical parts.

● The network has it’s origin from the Optical Network Terminal or the server through the Optical line terminal (OLT), to the fiber feeder reaching at the Optical splitter in the remote end where the optical power is split and reaches the Optical Network Terminal (ONT).

● A star topology is realized between the end users, with the OLT placed at the center node.

Orthogonal Frequency Division Multiplexing

OFDM-PON

OFDM is a FDM scheme, which employs orthogonal sub-carrier frequencies.

For Downstream transmission, the data streams are modulated signals for WDM-OFDM.

A demux is used to separate the channels and deliver to each ONU.

Security- Physical layer

Fiber tapping is a method that extracts the signal from an optical fiber without breaking the connection.

To access the core carrying the traffic, the fibers within the cable must be accessed physically. Once done, several methods to extract data include:

Fiber bending

Optical splitting

Evanescent Coupling

V-Groove Cut

There is a need for encryption of the data.

Cryptography

Involves rendering a message unintelligible to any unauthorised party.

Encryption involves combining a cipher to a message with some additional information. To unlock the cryptogram a key is required.

Symmetrical and Asymmetrical cryptosystems:

Secret key

Public key

Cryptoanalysis deals with the art of code breaking by performing statistical analysis on the encrypted data stream, to search for patterns in the message or cipher.

Chaos based cryptography

Diffusion property : If a character of the plaintext or the ciphertext is changed, several characters of the other should change.

This property translates into a statistical structure involving long combinations of letters in the cryptogram. So, intercepting requires a large amount of material and analysis.

A chaotic system is sensitive to initial conditions and parameter values.

Chaotic systems : Logistic map

A logistic map can be defined as below

xn+1 = rxn(1-xn)

0<x<1

The iterative process of updating the next value can be seen from the visualisation.

The parameter ‘r’ is the growth rate which determines the fluctuation.

Period doubling and chaotic nature

An attractor can be of fixed type or oscillatory in nature.

As the parameter increases, period doubling occurs.

For particular parameter values, the system enters deterministic chaos, which is statistically similar to randomness.

Lorenz chaotic system

Defined by the following set of differential equations.

x’ = a(y − x)

y’ = cx − xz − y

z’ = xy − bz

2 equilibria.

Attractors in phase plane : Chen’s chaotic system

Defined by the following set of differential equations:

x’ = a(y − x)

y’ = (c − a)x + cy + xz

z’ = bz + xy

3 equilibria.

Enters chaotic region when

a = 35

b = 3

c = [20,28.4]

Sensitivity to initial conditions

Control systems are based on linear systems.

Nearby points (initial states) converge over time.

In dynamical systems, the phase space is warped, leading to close points diverging in time.

This property is referred to as the so called Butterfly effect.

The measure of the divergence property of a dynamical system is given by Lyapunov exponent. The values for a few of the dynamical systems are given below:

CHAOTIC SYSTEMS

LORENZ CHEN HENON ROSSLER LOGISTIC

LARGEST LYAPUNOV EXPONENT

2.066 2.168 1.26 2.004 0.693

Logistic map based security

Logistic map has been implemented to introduce chaotic scrambling.

● A one dimensional logistic map chaos model is chosen.

● When r falls into the domain 3.569945<r≤4, the sequence will fall into chaos.

Fractional fourier transform

The mathematical operation is as below:

The interpretation is a counterclockwise axis rotation of the representation of the signal corresponding to p*pi/2 in the time-frequency distribution.

The parameter p is the measure of the rotation and is unique.

3-D security enhanced strategy

Chen’s chaotic system is employed based on its high Lyapunov exponent value.

3-D chaotic sequences are generated which are used for :

Time synchronization

Subcarrier masking

FrFT order

The differential equations are solved by fourth order Runge-Kutta method with time step k = 0.001

Key extraction

The values for each frame is selected by solving for the following variables:

Dxi = mod (Extract (xi , 12, 13, 14) , 256)

Dyi = mod (Extract (yi , 12, 13, 14) , 256)

Dzi = mod (Extract (zi , 12, 13, 14) , 256)

Extract (α, m, n, p) returns an integer, which is constructed by the mth, nth, and pth digits in the decimal part of α.

Histogram

The distributions of Dx, Dy, Dz

are fairly uniform.

The sequences are statistically random.

Schematic and methodology of the proposed technique

Dx : Training sequence for

time synchronization.

Dy : Chaotic phase factors for

OFDM subcarriers.

Dz : Fractional order of FrFT.● Key Space 1050 ● With the fastest computing

speed 2.5 *1013/s, time taken to do a complete search is 1.27 * 1029 years!

Experimental Setup A PBRS of length 2^15 -

1

16-QAM

257 subcarriers

128 : Data

128 : Complex conjugate

1 : unfilled dc subcarrier

CP : 1/10

OFDM symbol size : 563

1 TS for every 9 data symbols.

Experimental Results : Transmission performance

Experimental Results : Security

Extension of the model

In the above model a 3-D chaotic system is used for encryption.

The model is further extended by employing a 4-D chaotic system.

References

[1] J. Kani, M. Teshima, K. Akimoto, N. Takachio, H. Suzuki, K. Iwatsuki, and M. Ishii, “A WDM-based optical access network for wide-area giga- bit access services,” IEEE Commun. Mag., vol. 41, no. 2, pp. S43–S48, Feb. 2003.

[2] J. Yu, M.-F. Huang, D. Qian, L. Chen, and G.-K. Chang, “Centralized lightwave WDM-PON employing 16-QAM intensity modulated OFDM downstream and OOK modulated upstream signals,” IEEE Photon. Tech- nol. Lett., vol. 20, no. 18, pp. 1545–1547, Sep. 2008.

[3] N. Cvijetic, “OFDM for next-generation optical access networks,” J. Lightw. Technol., vol. 30, no. 4, pp. 384–398, Feb. 2012.

[4] L. Zhang, X. Xin, B. Liu, and J. Yu, “Physical-enhanced secure strategy in an OFDM-PON,” Opt. Exp., vol. 20, no. 3, pp. 2255–2265, Jan. 2012.

[5] Nonlinear Dynamics and Chaos - Steven Strogatz

[6] Wikipedia