CHAOS BASED ENCRYPTION

NEIL PARMAR

DEPARTMENT OF COMPUTER SCIENCE

ENCRYPTION

• Medical systems

• In this paper, Electroencephalograms (EEGs) – brain waves and can be used to detect epilepsy and other diseases– Mood Swings– Cognitive functions of the patients– 16-Channel EEG Visual User Environment Scheme

• Goal: To create a robust and real-time chaos-based image encryption functionality.

Figure 1. 16- Channel EEG Vue Signals

Chaos Based Encryption System for Encrypting Electroencephalogram Signals

1. Purposea) Encrypt the medical EEG 16-channel EEG Vue Signals.

b) Generate robust and real-time encryption

c) Electroencephalograms Visual User Environment Signals are encrypted

2. Unique Approacha) Microsoft Visual development kit and C# Programming language

b) Three Level Approach

3. Overviewa) C# based Level I, II, III chaos-based encryption algorithm.

b) Level I uses bifurcation parameters, chaotic map and initial value to achieve high-speed, real-time encryption.

c) Threshold parameters were added in Level II to enhance level of robustness.

d) In Level III, moreover to all the above parameters, a bit stream address index assignment strategy is incorporated in order to achieve the most robust level encryption.

AlgorithmLEVEL I

STEP 1: Enter the starting point x, and bifurcation parameter r

STEP 2: Generate a chaotic sequence of (Length of the clinical EEG Vue signal bit stream (EEGS)) length LF

cn+1 = CMT (cn); c0 = x; n = {1,2,…..LF} (1)

i.e., cn+1 = rcn(1-cn)

STEP 3: The A Chaos-based encryption bit streams (CBEBS) are generated as follows

CBEBS = {yn} n = {1,2,…..LF}

yn = {1 cn >= 0.5}yn = {0 cn< 0.5}

STEP 4: Deliver Electroencephalograms Visual User Environment Signal Bit Stream of Length LF

EEGS = {eeg1, eeg2, eeg3,……eegLF}

STEP 5: Generate encrypted Generated encrypted clinical Electroencephalogram Visual User Environment Signal Bit Streams (GEEG)

GEEG = EEGS CBEBS+

Limitation of Level I

The starting point and the chaotic map can be easily tracked.

LEVEL II

STEP 1: Enter the starting point x, bifurcation parameter r, CMT, bit stream length LF, number of discarded initial chaotic index points nF(10<=nF<=1000000), and level of security dF(0.01<=dF<=0.99).

STEP 2: (a) c0 = x

(b) Generate nF chaotic points

cn+1 = CMT(cn)

then discard them.

STEP 3: (a) cnF + 1 = CMTF(cnF)

(b) If cn>dF then discard this point and go to step 3 (a);

otherwise perform step 3(c).

(c) Generate a chaotic sequence of length LF.

cn; n = {1,2,3,…..LF}

STEP 4: The A Chaos based encryption bit streams (CBEBS) is generated as follows:

CBEBS = {yn} n = {1,2,…..LF}

yn = {1 cn >= 0.5}

yn = {0 cn< 0.5}

STEP 5: Deliver Electroencephalograms Visual User Environment Signal Bit Stream of Length LF

EEGS = {eeg1, eeg2, eeg3,……eegLF}

STEP 5: Generate encrypted Generated encrypted clinical Electroencephalogram Visual User Environment Signal Bit Streams (GEEG)

GEEG = EEGS CBEBS+

Scope for Level III

In Order to enhance the security, the paper introduces the Level III security.

LEVEL III

C#- based Level III encryption algorithm, which is described as follows:

A chaotic logistic map was employed in the chaotic maps CMTF and CMT.

CMT is the chaotic map of GCCS, the chaotic candidate point generator process.

CMTF is the chaotic map of FCIA, the chaotic address index assignment process

STEP 1: Enter the starting points x, and x2, length LF, number of discarded initial chaotic index points nF, and the level of security dF.

STEP 2: Generate nF chaotic points

cn+1 = CMT(cn)

and then discard them.

STEP 3: (a) cn+1 = CMT(Cn)

(b) The initial value of index j is 1, and j=j+1

mj = 1

cn+1

Step 4: [compare mj and the previous mk, 1<=k<=j-1 ]

If mj ϵ {mk, 1<=k<=j-1}, then discard this point and go to step 3;

otherwise proceed to the next step.

Step 5: If j>= LF, terminate the procedure, output mj, 1<=j<=LF, and perform the next step;

Otherwise, go to step 3.

Step 6: [ FCIA: generate the chaotic index address assignment ]

(a) 1<=j<=LF, mj ϵ N

FCIA: M = {m1, m2, m3,…. mLF}

(b) mC* = maximum index address = max1<=j<=LF mj

Step 7: Input x2, the starting point for CMTG.

yn+1 = CMTG(yn), y0 = x2;

Step 8: If yn>dF then discard this point and go to step 7; otherwise, perform the next step.

STEP 9: Generate a chaotic sequence with a finite length mc* by performing the

following iterative algorithm:

Y = {y0, y1, y2,…. Ymc*}

STEP 10: Generate a chaotic sequence of length LF.

Zn = {z0, z1, z2,…. zLF} = {ym0, ym1, ym2,…. YmLF};

STEP 11: The A Chaos based encryption bit streams (CBEBS) of W is generated as follows:

CBEBSW = {wn} n = {1,2,…..LF}

wn = {1 zn >= 0.5}

wn = {0 zn< 0.5}

STEP 12: Deliver Electroencephalograms Visual User Environment Signal Bit Stream of Length LF

EEGS = {eeg1, eeg2, eeg3,……eegLF}

STEP 13: Generate encrypted Generated encrypted clinical Electroencephalogram Visual User Environment Signal Bit Streams (GEEG)

GEEG = EEGS CBEBSW+

Limitations of the Paper

• Microsoft-based operating system.

• Speed, is it necessary for encryption?

Thank YouAny Questions?

References[1]. Chin-Feng Lin, Shun-Han Shih, and Jin-De Zhu, Chaos Based Encryption System for Encrypting Electroencephalogram Signals, J Med Syst, 2014.

[2]. Shih-Liang Chen, Ting Ting Hwang, Wen-Wei Lin, “Randomness Encryption Using Digitalized Modified Logistic Map,” IEEE Transactions on Circuits and Systems, Vol.57, No.12, December 2010. [Online]. Available: http://ieeexplore.ieee.org.ezproxy.proxy.library.oregonstate.edu/stamp/stamp.jsp?tp=&arnumber=5659895. [Accessed: Nov. 26,2014].

[3]. Jiahui Liu, Hongli Zhang, Dahua Song, M.K. Buza, Bo Yang, and Cong Guo, “A new property of logistic map with scalable precision,” IEEE Computer Society , 2012. [Online]. Available: http://ieeexplore.ieee.org.ezproxy.proxy.library.oregonstate.edu/stamp/stamp.jsp?tp=&arnumber=6383273. [Accessed: Nov. 27, 2014].

[4]. Chin-Feng Lin, Shun-Han Shih, Jin-De Zhu, and Sang-Hung Lee, “Implementation of An Offline Chaos-Based EEG Encryption Software,” Proc. IEEE 14th Int. Conf. Adv. Commun. Tech, 430-433, 2012. [Online] Available: http://ieeexplore.ieee.org.ezproxy.proxy.library.oregonstate.edu/stamp/stamp.jsp?tp=&arnumber=6174702. [Accessed: Nov.28, 2014].

[5]. Lin, C.F., Shih., Zhu, J.D., et al., “C3 based EEG encryption system using chaos algorithm,” Proc. 1st Int. Conf. Compl. Syst. Chaos (COSC’13). 59-62, 2013. [Online] Available:

http://www.wseas.us/e-library/conferences/2013/Morioka/CINC/CINC-08.pdf. [Accessed: Nov. 28, 2014].

[6]. T.Gopalakrishnan, S. Ramakrishnan, and M. BalaKumar, “Image Encryption using Chaos and Parity based Pixel Modification,” International Journal of Computer Applications, 2014