Secure Image Transmission over Wireless Channels

M Padmaja Assistant professor ECE department

VR Siddhartha Engineering College Vijayawada-520 007

Padmaja19_m@yahoo.co.in

Syed Shameem Assistant professor ECE department

Nimra Engineering College Hyderabad

shameemsyed@yahoo.com

Abstract

The advances in communication technology have seen strong interest in digital signal transmission. However, illegal data access has become more easy and prevalent in wireless and general communication networks. Data security has become a critical issue. In order to protect valuable data from undesirable readers, data encryption is essential. Furthermore, the wireless channels have fluctuating channel qualities and high bit error rates. For reliable communications, channel coding is often employed. As such in this paper, a scheme based on encryption and channel coding has been proposed for secure data transmission over wireless channels.

In the proposed scheme, the encryption and decryption algorithms based on Brahmagupta-Bhaskara equation are developed for data security. Turbo codes are used as channel coding for data communication over wireless channels with burst errors. The efficacy of the proposed scheme is demonstrated through implementation results for an image communication over wireless channels. 1. Introduction

Transmission of data in the form of images also has received wide attention in the last two decades. Therefore secure image data transmission is also a cause of concern. The complete transmission and reception process can be represented as shown in the fig1.1. Original image

Reconstructed image

Figure 1. Block diagram of the transmission and reception scheme

In the first step the image is applied to wavelet transform to get the image coefficients and these are compressed with JPEG2000 coding. The next part of transmission process is the encryption of the image. In this paper, encryption and decryption algorithms based on BB-equation are discussed. The next step in the transmission process is source coding the encrypted image. This is done in order to achieve compression so as to transmit the image using the shortest possible memory. Here error free compression technique is done, by using Huffman code.

The next step is dependent on the type of channel that is being used i.e. noisy or noiseless channel. If a noiseless channel is assumed then there is no need for the implementation of this

CHANNEL Inverse

wavelet transform

JPEG 2000 Decoding

Brahmagupta-Bhaskara Decryption

Source Decoding (Huffman Decoder)

Channel Decoding (Turbo decoder)

wavelet transform

Brahmagupta-Bhaskara Encryption

Source Coding (Huffman Encoder)

Channel Coding (Turbo encoder)

JPEG 2000 Coding

International Conference on Computational Intelligence and Multimedia Applications 2007

0-7695-3050-8/07 $25.00 © 2007 IEEEDOI 10.1109/ICCIMA.2007.38

44

International Conference on Computational Intelligence and Multimedia Applications 2007

0-7695-3050-8/07 $25.00 © 2007 IEEEDOI 10.1109/ICCIMA.2007.38

44

block. If noisy channel is assumed then using channel code so as to control the error that can occur along the channel carries out the robust transmission. Here, the efficiency of turbo codes under the noisy conditions is demonstrated.

The receiver of the system will be equipped with all the decoders, i.e. channel decoder (Turbo decoder), source decoder (Huffman decoder), and finally the decryption block meant for restoring the original image.

2. Cryptographic Applications of Brahmagupta–Bhãskara Equation

The Brahmagupta–Bhãskara (BB) equation is a quadratic Diophantine equation of the form:

NX2 + k = Y2 (2.1) Where k is an integer (positive or negative) and N is a positive integer such that √N is

irrational. ‹r›m – denote the least positive remainder of r modulo m ‹nx2+1›p = ‹y2›p (2.2)

(xi, yi) referred as root to eq (2) provided 0≤ xi , yi ≤ (p-1)

2.1. Process of Encryption With the use of p (primary key), a&b (secondary keys), we find Sq= (a* Qx+ b* Qy) mod (p) Dq= (a* Qx- b* Qy) mod (p)

for a given “n” the encrypted values are (Sq,Dq). 2.2. Process of Decryption

Step 1: find Qx = (2a)-1 (Sq+Dq) mod (p) Qy = (2b)-1 (Sq-Dq) mod (p)

Step 2: find n = (Qx)-1(Qy-1) mod (p) In the above steps we find the multiplicative inverse using Euclid’s algorithm. 3. Turbo-codes Error corrective coding is used to enhance the efficiency and accuracy of information transmitted. Turbo-codes, a new family of convolutional codes, built from a particular concatenation of two recursive systematic codes, linked together by non-uniform interleaving. Decoding calls on iterative processing in which each component decoder takes advantage of the work of the other at the previous step, with the aid of the original concept of extrinsic information. For sufficiently large interleaving sizes, the correcting performance of turbo-codes, investigated by simulation, appears to be close to the theoretical limit predicted by Shannon. Figure 2. Turbo- encoder Figure 3.turbo- decoder

RSC1

RSC2 I

xs

xp1

xp2

u

D1 D2 I

Inv(I)

Parity2

Parity1Le12 Le21

Systematic

4545

3.1. Implementation

• Rate 1/3 coding, Constraint length = 3, Frame length = 1000 • BCJR algorithm used • Number of iterations are flexible • Signal to noise ratio is flexible

3.2. Turbo code decoding of proposed algorithm

The log-likelihood ratio L(uk) of a binary random variable uk is defined as

))/0()/1(

log( )(1

1N

k

Nk

k yuPyuP

uL==

∆ . (3.1)

The decision will be made based on the sign of L(u), i.e.,

[ ])(~kk uLsignu = . (3.2)

))(/),0()(/),1(log()L(u

11

11k NN

k

NNk

yPyuPyPyuP

===

])(/),0,'(

)(/),1,'(log[

1'

11

1'

11

N

s

Nkk

N

s

Nkk

yPyussP

yPyussP

∑∑

==

===

−

−

. (3.3)

Next, the received symbol can be broken into three parts. The first part only contains the past observation before time k, second part contains the present observation at time k and third part is the future observation after time k, i.e.,

{ }N

kkkN yyyy 1

111 ,, +

−= . (3.4)

By substituting (3.4) into (3.3), (3.3) becomes

])(/),,,0,'(

)(/),,,1,'(log[)(

111

11

111

11

N

u

Nkk

kkk

N

u

Nkk

kkk

k yPyyyussP

yPyyyussPuL

∑∑

−

+

+−

−

+−

−

==

=== (3.5)

where ∑+u

) ( is the summation over all the possible transition branch pair (sk-1, sk) at time k given

input uk=1, and ∑−u

) ( is the summation over all the possible transition branch pair (sk-1, sk) at time

k given input uk=0. From Bayes’s rule, the LAPP ratio for MAP decoder can be written as

==

+

==

=

==

=)0()1(

log)0/()1/(

log)/0()/1(

log)(1

1

1

1

k

k

kN

kN

Nk

Nk

k uPuP

uyPuyP

yuPyuP

uL (3.6)

4646

4. Results The performance analysis of the turbo channel coding technique on image transmission through wireless channels is described (See figs1-5). Secondly, the performance of the BB equation in encryption and decryption algorithms has been demonstrated. (See fig.6)

Figure 4. Original image Figure 5. Image received Figure.6 Image received

Without turbo-codes with turbo-code at 2db

Figure 7. Image received Figure 8. Reconstructed image Figure.9 Encrypted image with turbo-code at 4db at 6db(with 5 iterations) using BB-equation

Table 1. Performance comparison

Without Turbo coding: Eb/N0 = 2db With Turbo coding Eb/N0 = 2db

Noise: Impulse noise Number of frames transmitted is 10000 Number of frames in error is 9327 Bit error rate is 4.751000e-001

Frame size = 3, rate 1/2. Number of frames transmitted is 9000 Number of frames in error is 174 Bit error rate is 4.0222e-002

From the above one we can find the efficiency of secure image transmission using turbo codes, when compared to no error control coding. The number of frame errors, for the same signal to noise ratio, have reduced drastically in the case of use of turbo codes. From this one can say that, if turbo codes are used then the encrypted images can be transmitted securely over the noisy channel even if the signal to noise ratio is less. The performance evaluation of the turbo codes is demonstrated in terms of number of iterations is as follows.

4747

1 1.5 2 2.5 3 3.5 410

-5

10-4

10-3

10-2

10-1

SNRBER

iteration1

iteration2

iteration3

iteration4

iteration5

iteration6

Figure 10. Effects of the number of iterations on BER.

Figure11. Image reconstructed Figure 12. Image reconstructed at 4db with 2 iterations at 4db with 6 iterations

As the number of iterations is increased the number of bit errors is reduced. This is clearly

observed in Fig.11 and 12. 5. Conclusions

The advantage of Brahmagupta-Bhaskara equation is for a given p (odd prime i.e. primary key), the derived roots are many. There is no unique Encrypted block for a given Clear text block thus lending the cryptanalysis very difficult. For a given p, the encryption process is one to many while the decrypting process, is many to one. The simulation results show that Turbo code is a powerful error correcting coding technique under SNR environments. It has achieved near Shannon capacity. 6. References [1] Rama Murthy and M. N. S. Swamy, “Cryptographic Applications of Brahmagupta– Bhãskara Equation”, IEEE transactions on circuits and systems-1: Regular papers, vol. 53, No. 7, July 2006 [2] Charilaos Christopoulos, A.Skodras and T.Ebrahimi, “The JPEG Still Image Coding System: An Overview”, Published in IEEE transactions on Consumer Electronics, vol. 46, No.4, pp.1103-1127, November 2000. [3] W.B.Pennebaker and J.L. Mitchell, “JPEG: Still Image Data Compression Standard”, Van Nostrand Reinhold, 1993. [4] R.C.Gonzalez, Richard E.Woods, Digital image processing, Second edition, Pearson Education, 2002. [5] Wavelet Applications by M. Raghuveer Rao and S Bapartikar. [6] M.W.Marcellin, M.J.Gormisch, A.Bilgin and M.pBoliek: “An Overview of JPEG- 2000”, Proc. of IEEE Data Compression Conference (DCC’2000), pp.523-541, 2000. [7] C. Berrou, A. Glavieux, and P. Thitimajshima, “Near Shannon limit error-correcting coding and decoding: Turbo-codes,” in ICC’93, Geneva, Switzerland, May 93, pp. 1064-1070.

4848